bias_variance_linear_regression.ipynb

{
 "cells": [
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Thorough analysis of bias and variance in the linear regression**\n",
    "\n",
    "I had trouble to clearly understand the connection between the definitions of the [variance](https://en.wikipedia.org/wiki/Variance) and the [bias of an estimator](https://en.wikipedia.org/wiki/Bias_of_an_estimator) in my probability courses and the explanation in the machine learning courses I then followed. In the first case, the mathematical definitions seem thorough without any room for ambiguity, conversely to the second case where estimator bias and variance were regularly explained with visual explanations, like the well known illustration from [Understanding the Bias-Variance Tradeoff Scott Fortmann-Roe's article](http://scott.fortmann-roe.com/docs/BiasVariance.html), or with general rules like the following extracts: \"[Both bias and variance are connected to the model’s complexity. Low complexity means high bias and low variance. Increased complexity means low bias and high variance](https://medium.com/swlh/how-bias-and-variance-affect-a-machine-learning-model-6d258d9221db)\" or \"[The bias-variance tradeoff is a tradeoff between a complicated and simple model, in which an intermediate complexity is likely best](https://towardsdatascience.com/bias-variance-and-regularization-in-linear-regression-lasso-ridge-and-elastic-net-8bf81991d0c5)\". The \"[Bias and variance in linear models](https://towardsdatascience.com/bias-and-variance-in-linear-models-e772546e0c30)\" illustrates the bias and variance changes when adding regularization. At first glance I was satisfied with these two explanations, from my probability and my machine learning courses. But then, I started being annoyed with this second non-mathematical definition. So I decided to thoroughly study the linear regression to better understand the connection between the two definitions.\n",
    "\n",
    "In this notebook, I have analyzed the change of the bias and variance when adding explanatory variables (also named features) for a linear regression model. From the machine learning general explanations, I expect the bias to reduce and the variance to increase. However, what do improving or worsening the bias and the variance mean when the estimators are not a single scalar? Can we compare the bias and the covariance of two vector estimators? In this notebook, the analysis of the bias and variance of a vector estimator and of a single estimator are studied for the linear regression model when increasing the number of explanatory variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 1;\n",
       "                var nbb_unformatted_code = \"%load_ext nb_black\\nimport numpy as np\\nfrom scipy import stats\\nimport pandas as pd\\nimport matplotlib.pyplot as plt\";\n",
       "                var nbb_formatted_code = \"%load_ext nb_black\\nimport numpy as np\\nfrom scipy import stats\\nimport pandas as pd\\nimport matplotlib.pyplot as plt\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%load_ext nb_black\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Data\n",
    "To illustrate my results, I built a dataset with some independent variables $X$ and a dependent variable, a.k.a. a target, depending linearly on the independent variables by means of a set of coefficients $\\beta$. I have deliberately chosen some coefficients with a 0 value to consider the case when a useless explanatory variable is added to the linear regression model. The measured target is then the product of the independent variables and the coefficients plus some noise $\\epsilon \\sim \\mathcal{N}(0,\\sigma^{2}I)$:\n",
    "$$Y=X\\beta+\\epsilon$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 2;\n",
       "                var nbb_unformatted_code = \"np.random.seed(4)  # from reproducibility purpose\\nm = 100\\nsigma_noise = 10\\nbeta = np.array([1, 0, 0, 2, -1, 5, 0, 0])\";\n",
       "                var nbb_formatted_code = \"np.random.seed(4)  # from reproducibility purpose\\nm = 100\\nsigma_noise = 10\\nbeta = np.array([1, 0, 0, 2, -1, 5, 0, 0])\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(4)  # from reproducibility purpose\n",
    "m = 100\n",
    "sigma_noise = 10\n",
    "beta = np.array([1, 0, 0, 2, -1, 5, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Independent variables\n",
    "Some arbitrary independent variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 3;\n",
       "                var nbb_unformatted_code = \"X = np.concatenate(\\n    (\\n        np.ones((m, 1)),\\n        np.random.gamma(1, scale=1.0, size=(m, 1)),\\n        np.random.normal(1, scale=1.0, size=(m, 1)),\\n        np.random.gamma(1, scale=1.0, size=(m, 1)),\\n        np.random.normal(1, scale=1.0, size=(m, 1)),\\n        np.random.normal(0, scale=1.0, size=(m, 1)),\\n        np.random.normal(0, scale=1.0, size=(m, 1)),\\n        np.random.normal(0, scale=1.0, size=(m, 1)),\\n    ),\\n    axis=1,\\n)\";\n",
       "                var nbb_formatted_code = \"X = np.concatenate(\\n    (\\n        np.ones((m, 1)),\\n        np.random.gamma(1, scale=1.0, size=(m, 1)),\\n        np.random.normal(1, scale=1.0, size=(m, 1)),\\n        np.random.gamma(1, scale=1.0, size=(m, 1)),\\n        np.random.normal(1, scale=1.0, size=(m, 1)),\\n        np.random.normal(0, scale=1.0, size=(m, 1)),\\n        np.random.normal(0, scale=1.0, size=(m, 1)),\\n        np.random.normal(0, scale=1.0, size=(m, 1)),\\n    ),\\n    axis=1,\\n)\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.concatenate(\n",
    "    (\n",
    "        np.ones((m, 1)),\n",
    "        np.random.gamma(1, scale=1.0, size=(m, 1)),\n",
    "        np.random.normal(1, scale=1.0, size=(m, 1)),\n",
    "        np.random.gamma(1, scale=1.0, size=(m, 1)),\n",
    "        np.random.normal(1, scale=1.0, size=(m, 1)),\n",
    "        np.random.normal(0, scale=1.0, size=(m, 1)),\n",
    "        np.random.normal(0, scale=1.0, size=(m, 1)),\n",
    "        np.random.normal(0, scale=1.0, size=(m, 1)),\n",
    "    ),\n",
    "    axis=1,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dependent variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 4;\n",
       "                var nbb_unformatted_code = \"X_beta = np.matmul(X, beta)\";\n",
       "                var nbb_formatted_code = \"X_beta = np.matmul(X, beta)\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_beta = np.matmul(X, beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 5;\n",
       "                var nbb_unformatted_code = \"def get_beta_hat(X0, y, alpha):\\n    \\\"\\\"\\\"\\n    Get beta statistic.\\n    When alpha=0, this is equivalent to the ordinary least squares parameter estimation.\\n    When alpha>0, this is equivalent to the paremeter estimation with L2 regularized least squares.\\n    \\\"\\\"\\\"\\n    X0t_X0 = np.matmul(X0.T, X0)\\n    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\\n    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\\n    beta_hat = np.matmul(np.matmul(X0t_X0_alphaI_1, X0.T), y)\\n    return beta_hat\\n\\n\\ndef get_y_hat(X0, beta_hat):\\n    \\\"\\\"\\\"\\n    Get target statistic.\\n    \\\"\\\"\\\"\\n    return np.matmul(X0, beta_hat)\\n\\n\\ndef get_cov_mat(X0, alpha, sigma_noise):\\n    \\\"\\\"\\\"\\n    Get covariance matrix of target statistic.\\n    \\\"\\\"\\\"\\n    X0t_X0 = np.matmul(X0.T, X0)\\n    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\\n    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\\n    XO_X0t_X0_alphaI_1_XOt = np.matmul(X0, np.matmul(X0t_X0_alphaI_1, X0.T))\\n    cov_mat = sigma_noise ** 2 * np.matmul(\\n        XO_X0t_X0_alphaI_1_XOt, XO_X0t_X0_alphaI_1_XOt\\n    )\\n    return cov_mat\\n\\n\\ndef get_biases(X0, X_beta, alpha):\\n    \\\"\\\"\\\"\\n    Get vector of biases of target statistic.\\n    \\\"\\\"\\\"\\n    X0t_X0 = np.matmul(X0.T, X0)\\n    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\\n    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\\n    XO_X0t_X0_alphaI_1_XOt = np.matmul(X0, np.matmul(X0t_X0_alphaI_1, X0.T))\\n    return np.matmul(\\n        XO_X0t_X0_alphaI_1_XOt - np.eye(XO_X0t_X0_alphaI_1_XOt.shape[0]), X_beta\\n    )\\n\\n\\ndef get_expected_mse_var_term(X0, alpha, p0):\\n    \\\"\\\"\\\"\\n    Get mse var term.\\n    \\\"\\\"\\\"\\n    if alpha == 0:\\n        return p0\\n    else:\\n        d, P = np.linalg.eig(np.matmul(X0.T, X0))\\n        D_1 = np.diag(1 / d)\\n        D_aI_1 = np.diag(1 / (d + alpha))\\n        Pt_X0t = np.matmul(P.T, X0.T)\\n        Pt_X0t_2 = Pt_X0t ** 2\\n        return np.dot(\\n            d / ((d + alpha) ** 2), np.matmul((Pt_X0t_2), np.ones(Pt_X0t_2.shape[1]))\\n        )\\n\\n\\ndef get_common_results(X, x_cols, X_beta, alpha, sigma_noise):\\n    \\\"\\\"\\\"\\n    Get common results, the fixed values or the expectations of random variables.\\n    \\\"\\\"\\\"\\n    p0 = len(x_cols)\\n    X0 = X[:, x_cols]\\n    biases = get_biases(X0, X_beta, alpha)\\n    cov_mat = get_cov_mat(X0, alpha, sigma_noise)\\n    return p0, X0, biases, cov_mat\";\n",
       "                var nbb_formatted_code = \"def get_beta_hat(X0, y, alpha):\\n    \\\"\\\"\\\"\\n    Get beta statistic.\\n    When alpha=0, this is equivalent to the ordinary least squares parameter estimation.\\n    When alpha>0, this is equivalent to the paremeter estimation with L2 regularized least squares.\\n    \\\"\\\"\\\"\\n    X0t_X0 = np.matmul(X0.T, X0)\\n    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\\n    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\\n    beta_hat = np.matmul(np.matmul(X0t_X0_alphaI_1, X0.T), y)\\n    return beta_hat\\n\\n\\ndef get_y_hat(X0, beta_hat):\\n    \\\"\\\"\\\"\\n    Get target statistic.\\n    \\\"\\\"\\\"\\n    return np.matmul(X0, beta_hat)\\n\\n\\ndef get_cov_mat(X0, alpha, sigma_noise):\\n    \\\"\\\"\\\"\\n    Get covariance matrix of target statistic.\\n    \\\"\\\"\\\"\\n    X0t_X0 = np.matmul(X0.T, X0)\\n    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\\n    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\\n    XO_X0t_X0_alphaI_1_XOt = np.matmul(X0, np.matmul(X0t_X0_alphaI_1, X0.T))\\n    cov_mat = sigma_noise ** 2 * np.matmul(\\n        XO_X0t_X0_alphaI_1_XOt, XO_X0t_X0_alphaI_1_XOt\\n    )\\n    return cov_mat\\n\\n\\ndef get_biases(X0, X_beta, alpha):\\n    \\\"\\\"\\\"\\n    Get vector of biases of target statistic.\\n    \\\"\\\"\\\"\\n    X0t_X0 = np.matmul(X0.T, X0)\\n    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\\n    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\\n    XO_X0t_X0_alphaI_1_XOt = np.matmul(X0, np.matmul(X0t_X0_alphaI_1, X0.T))\\n    return np.matmul(\\n        XO_X0t_X0_alphaI_1_XOt - np.eye(XO_X0t_X0_alphaI_1_XOt.shape[0]), X_beta\\n    )\\n\\n\\ndef get_expected_mse_var_term(X0, alpha, p0):\\n    \\\"\\\"\\\"\\n    Get mse var term.\\n    \\\"\\\"\\\"\\n    if alpha == 0:\\n        return p0\\n    else:\\n        d, P = np.linalg.eig(np.matmul(X0.T, X0))\\n        D_1 = np.diag(1 / d)\\n        D_aI_1 = np.diag(1 / (d + alpha))\\n        Pt_X0t = np.matmul(P.T, X0.T)\\n        Pt_X0t_2 = Pt_X0t ** 2\\n        return np.dot(\\n            d / ((d + alpha) ** 2), np.matmul((Pt_X0t_2), np.ones(Pt_X0t_2.shape[1]))\\n        )\\n\\n\\ndef get_common_results(X, x_cols, X_beta, alpha, sigma_noise):\\n    \\\"\\\"\\\"\\n    Get common results, the fixed values or the expectations of random variables.\\n    \\\"\\\"\\\"\\n    p0 = len(x_cols)\\n    X0 = X[:, x_cols]\\n    biases = get_biases(X0, X_beta, alpha)\\n    cov_mat = get_cov_mat(X0, alpha, sigma_noise)\\n    return p0, X0, biases, cov_mat\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_beta_hat(X0, y, alpha):\n",
    "    \"\"\"\n",
    "    Get beta statistic.\n",
    "    When alpha=0, this is equivalent to the ordinary least squares parameter estimation.\n",
    "    When alpha>0, this is equivalent to the paremeter estimation with L2 regularized least squares.\n",
    "    \"\"\"\n",
    "    X0t_X0 = np.matmul(X0.T, X0)\n",
    "    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\n",
    "    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\n",
    "    beta_hat = np.matmul(np.matmul(X0t_X0_alphaI_1, X0.T), y)\n",
    "    return beta_hat\n",
    "\n",
    "\n",
    "def get_y_hat(X0, beta_hat):\n",
    "    \"\"\"\n",
    "    Get target statistic.\n",
    "    \"\"\"\n",
    "    return np.matmul(X0, beta_hat)\n",
    "\n",
    "\n",
    "def get_cov_mat(X0, alpha, sigma_noise):\n",
    "    \"\"\"\n",
    "    Get covariance matrix of target statistic.\n",
    "    \"\"\"\n",
    "    X0t_X0 = np.matmul(X0.T, X0)\n",
    "    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\n",
    "    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\n",
    "    XO_X0t_X0_alphaI_1_XOt = np.matmul(X0, np.matmul(X0t_X0_alphaI_1, X0.T))\n",
    "    cov_mat = sigma_noise ** 2 * np.matmul(\n",
    "        XO_X0t_X0_alphaI_1_XOt, XO_X0t_X0_alphaI_1_XOt\n",
    "    )\n",
    "    return cov_mat\n",
    "\n",
    "\n",
    "def get_biases(X0, X_beta, alpha):\n",
    "    \"\"\"\n",
    "    Get vector of biases of target statistic.\n",
    "    \"\"\"\n",
    "    X0t_X0 = np.matmul(X0.T, X0)\n",
    "    X0t_X0_alphaI = X0t_X0 + alpha * np.eye(X0t_X0.shape[0])\n",
    "    X0t_X0_alphaI_1 = np.linalg.inv(X0t_X0_alphaI)\n",
    "    XO_X0t_X0_alphaI_1_XOt = np.matmul(X0, np.matmul(X0t_X0_alphaI_1, X0.T))\n",
    "    return np.matmul(\n",
    "        XO_X0t_X0_alphaI_1_XOt - np.eye(XO_X0t_X0_alphaI_1_XOt.shape[0]), X_beta\n",
    "    )\n",
    "\n",
    "\n",
    "def get_expected_mse_var_term(X0, alpha, p0):\n",
    "    \"\"\"\n",
    "    Get mse var term.\n",
    "    \"\"\"\n",
    "    if alpha == 0:\n",
    "        return p0\n",
    "    else:\n",
    "        d, P = np.linalg.eig(np.matmul(X0.T, X0))\n",
    "        D_1 = np.diag(1 / d)\n",
    "        D_aI_1 = np.diag(1 / (d + alpha))\n",
    "        Pt_X0t = np.matmul(P.T, X0.T)\n",
    "        Pt_X0t_2 = Pt_X0t ** 2\n",
    "        return np.dot(\n",
    "            d / ((d + alpha) ** 2), np.matmul((Pt_X0t_2), np.ones(Pt_X0t_2.shape[1]))\n",
    "        )\n",
    "\n",
    "\n",
    "def get_common_results(X, x_cols, X_beta, alpha, sigma_noise):\n",
    "    \"\"\"\n",
    "    Get common results, the fixed values or the expectations of random variables.\n",
    "    \"\"\"\n",
    "    p0 = len(x_cols)\n",
    "    X0 = X[:, x_cols]\n",
    "    biases = get_biases(X0, X_beta, alpha)\n",
    "    cov_mat = get_cov_mat(X0, alpha, sigma_noise)\n",
    "    return p0, X0, biases, cov_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 6;\n",
       "                var nbb_unformatted_code = \"def make_experimentation(n, sigma_noise, m, X_beta, X0, alpha):\\n    \\\"\\\"\\\"\\n    Perform n experimentations and return n target and MSE statistics.\\n    \\\"\\\"\\\"\\n    y_hat_list = []\\n    mse_list = []\\n    for i in range(n):\\n        error = np.random.normal(scale=sigma_noise, size=m)\\n        y = X_beta + error\\n        beta_hat = get_beta_hat(X0, y, alpha)\\n        y_hat = get_y_hat(X0, beta_hat)\\n        y_hat_list.append(y_hat)\\n        mse = np.sum((y_hat - X_beta) ** 2)\\n        mse_list.append(mse)\\n    return y_hat_list, mse_list\";\n",
       "                var nbb_formatted_code = \"def make_experimentation(n, sigma_noise, m, X_beta, X0, alpha):\\n    \\\"\\\"\\\"\\n    Perform n experimentations and return n target and MSE statistics.\\n    \\\"\\\"\\\"\\n    y_hat_list = []\\n    mse_list = []\\n    for i in range(n):\\n        error = np.random.normal(scale=sigma_noise, size=m)\\n        y = X_beta + error\\n        beta_hat = get_beta_hat(X0, y, alpha)\\n        y_hat = get_y_hat(X0, beta_hat)\\n        y_hat_list.append(y_hat)\\n        mse = np.sum((y_hat - X_beta) ** 2)\\n        mse_list.append(mse)\\n    return y_hat_list, mse_list\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def make_experimentation(n, sigma_noise, m, X_beta, X0, alpha):\n",
    "    \"\"\"\n",
    "    Perform n experimentations and return n target and MSE statistics.\n",
    "    \"\"\"\n",
    "    y_hat_list = []\n",
    "    mse_list = []\n",
    "    for i in range(n):\n",
    "        error = np.random.normal(scale=sigma_noise, size=m)\n",
    "        y = X_beta + error\n",
    "        beta_hat = get_beta_hat(X0, y, alpha)\n",
    "        y_hat = get_y_hat(X0, beta_hat)\n",
    "        y_hat_list.append(y_hat)\n",
    "        mse = np.sum((y_hat - X_beta) ** 2)\n",
    "        mse_list.append(mse)\n",
    "    return y_hat_list, mse_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Bias and variance analysis for vector estimators\n",
    "In this first section, let's look at the change of the bias and the variance of a vector estimator when adding new explanatory variables. This is a tool to compare vector estimators, this is the [mean squared error of an estimator](https://en.wikipedia.org/wiki/Mean_squared_error#Estimator). When the estimator is a scalar the definition is clear. However, when the estimator is multidimensional, I have found the two following definitions: $E[(\\hat{\\theta}-\\theta)(\\hat{\\theta}-\\theta)^{T})]$[[1]](https://cermics.enpc.fr/~delmas/Enseig/ensta_cours.pdf) which is a matrix and $E[\\lVert(\\hat{\\theta}-\\theta)\\rVert^{2}]$[[2]](http://theanalysisofdata.com/notes/estimators1.pdf)[[3]](https://lerasle.perso.math.cnrs.fr/docs/PC4Corrige.html) which is a scalar. Since I wasn't able so far to get rid of one the two definitions, I considered them both, first the matrix definition and secondly the scalar definition. When considering the MSE matrix, the comparison of two estimators can be performed by analyzing the sign of the difference of the two MSE matrices. If the resulting matrix is positive then the second vector estimator is better. If it is negative, then the first vector estimator is better. If the resulting is neither positive nor negative, nothing can be concluded."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}\n",
    "MSE&=E[(\\hat{Y} - X\\beta)(\\hat{Y} - X\\beta)^{T}]\\\\\n",
    "&=E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}] + (E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}\\\\\n",
    "&= MSE_{var} + MSE_{bias} \\\\\n",
    "\\\\\n",
    "MSE_{var}&=E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}] \\\\\n",
    "MSE_{bias}&=(E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSE matrix\n",
    "In the linear regression case, the MSE matrix is:  \n",
    "$$\\begin{align}\n",
    "MSE&=E[(\\hat{Y} - X\\beta)(\\hat{Y} - X\\beta)^{T}]\\\\\n",
    "&=E[(\\hat{Y} - E[\\hat{Y}] + E[\\hat{Y}] - X\\beta)(\\hat{Y} - E[\\hat{Y}] + E[\\hat{Y}] - X\\beta)^{T}]\\\\\n",
    "&=E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}] + E[(E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}] + E[(\\hat{Y} - E[\\hat{Y}])(E[\\hat{Y}] - X\\beta)^{T}] + E[(E[\\hat{Y}] - X\\beta)(\\hat{Y} - E[\\hat{Y}])^{T}]\\\\\n",
    "&=E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}] + E[(E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}] + (E[\\hat{Y}] - E[\\hat{Y}])(E[\\hat{Y}] - X\\beta)^{T} + (E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - E[\\hat{Y}])^{T}\\\\\n",
    "&=E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}] + E[(E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}]\\\\\n",
    "&=\\underbrace{E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}]}_\\text{MSE_{var}} + \\underbrace{(E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}}_\\text{MSE_{bias}}\n",
    "\\end{align}$$\n",
    "\n",
    "Considering the following notation:\n",
    "$$\\begin{align}\n",
    "MSE_{var}&=E[(\\hat{Y} - E[\\hat{Y}])(\\hat{Y} - E[\\hat{Y}])^{T}] \\\\\n",
    "MSE_{bias}&=(E[\\hat{Y}] - X\\beta)(E[\\hat{Y}] - X\\beta)^{T}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequentist approach\n",
    "In the frequentist approach, the parameter estimation depends on the considered independent variables. Let's assume, only a subset $X_0$ (with $p_{0}$ columns) of $X$ has been selected. The estimated parameters are then:\n",
    "$$\\hat{\\beta_{0}}=(X_{0}^{T}X_{0})^{-1}X_{0}^{T}Y$$\n",
    "\n",
    "And consequently, the estimated predictions are:\n",
    "$$\\hat{Y_{0}}=X_{0}\\hat{\\beta_{0}}=X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}Y$$\n",
    "\n",
    "The expected value of $\\hat{Y_{0}}$ is then:\n",
    "$$E[\\hat{Y_{0}}]=X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}X\\beta$$\n",
    "\n",
    "___\n",
    "* **$MSE_{var}$**\n",
    "\n",
    "Let's derive the variance term of the MSE:\n",
    "$$\\begin{align}\n",
    "\\hat{Y_{0}} - E[\\hat{Y_{0}}] &= X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}Y - E[\\hat{Y_{0}}]\\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\\epsilon\n",
    "\\end{align}$$\n",
    "\n",
    "Hence:\n",
    "$$\\begin{align}\n",
    "MSE_{var}(X_{0}) &= E[(X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\\epsilon)(X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\\epsilon)^{T}] \\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T} E[\\epsilon \\epsilon^{T}] X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T} \\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T} \\sigma^{2} I X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T} \\\\\n",
    "&= \\sigma^{2} X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\n",
    "\\end{align}$$\n",
    "\n",
    "Let's compare $MSE_{var}(X_{0})$ and $MSE_{var}(X_{1})$, with $X_{1}$ including $X_{0}$ (for instance $X_{1}=\\begin{pmatrix} X_{0} & x_{p_{0}+1} \\end{pmatrix}$). We can show that $MSE_{var}(X_{1}) - MSE_{var}(X_{0})$ is positive. Let's note $E_{i} = \\{X_{i}u | u \\in \\mathbb{R}^{p_{i}}\\}$. $X_{i}(X_{i}^{T}X_{i})^{-1}X_{i}^{T}$ is a projector, so $u^{T}X_{i}(X_{i}^{T}X_{i})^{-1}X_{i}^{T}u = ||u_{E_{i}}||^{2}$.\n",
    "$$\\begin{align}\n",
    "\\forall u \\in \\mathbb{R}^{n} \\quad u^{T} \\sigma^{2} (X_{1}(X_{1}^{T}X_{1})^{-1}X_{1}^{T} - X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}) u &= \\sigma^{2} (||u_{E_{1}}||^{2} - ||u_{E_{0}}||^{2}) \\\\\n",
    "&= \\sigma^{2}  ( (||u||^{2} - ||u_{E_{1}^{\\bot}}||^{2}) - (||u||^{2} - ||u_{E_{0}^{\\bot}}||^{2})) \\\\\n",
    "&= \\sigma^{2}  ( ||u_{E_{0}^{\\bot}}||^{2} - ||u_{E_{1}^{\\bot}}||^{2} ) \\\\\n",
    "&= \\sigma^{2}  ( \\min\\limits_{v\\in\\mathbb{R}^{p_{0}}}(||u - X_{0}v||^{2} - \\min\\limits_{v\\in\\mathbb{R}^{p_{1}}}(||u - X_{1}v||^{2} )\n",
    "\\end{align}$$\n",
    "\n",
    "Since $X_{1}$ contains $X_{0}$, then the result of the second minimization problem is lower than (or equal to) the first one. The MSE matrix resulting from the two estimator MSE matrix difference is then positive. The matrix $\\sigma^{2} X_{1}(X_{1}^{T}X_{1})^{-1}X_{1}^{T}$ is then greater than the matrix $\\sigma^{2} X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}$.\n",
    "\n",
    "**The variance term of the MSE matrix then increase when adding new independent variable, whether this is a useful one variable ($\\beta_{i} \\neq 0$) or not ($\\beta_{i} = 0$).**\n",
    "\n",
    "___\n",
    "* **$MSE_{bias}$**\n",
    "\n",
    "Let derive the bias term of the MSE:\n",
    "$$E[\\hat{Y_{0}}] - X\\beta = (X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}-I)X\\beta$$\n",
    "\n",
    "Hence:\n",
    "$$\\begin{align}\n",
    "MSE_{bias} &= (X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}-I)X\\beta ((X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}-I)X\\beta)^{T} \\\\\n",
    "&= (X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}-I)X\\beta \\beta^{T}X^{T} (X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}-I)\n",
    "\\end{align}$$\n",
    "\n",
    "**Unfortunately, nothing can be concluded for this term.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 7;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha = 0  # since we are in a frequentist approach without regularization\\n\\n# initialization\\nmse_mat_bias_list = []\\nmse_mat_var_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    _, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    mse_mat_bias_list.append(\\n        np.matmul(\\n            np.reshape(biases, (len(biases), 1)), np.reshape(biases, (1, len(biases)))\\n        )\\n    )\\n    mse_mat_var_list.append(get_cov_mat(X0, alpha, sigma_noise))\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha = 0  # since we are in a frequentist approach without regularization\\n\\n# initialization\\nmse_mat_bias_list = []\\nmse_mat_var_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    _, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    mse_mat_bias_list.append(\\n        np.matmul(\\n            np.reshape(biases, (len(biases), 1)), np.reshape(biases, (1, len(biases)))\\n        )\\n    )\\n    mse_mat_var_list.append(get_cov_mat(X0, alpha, sigma_noise))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha = 0  # since we are in a frequentist approach without regularization\n",
    "\n",
    "# initialization\n",
    "mse_mat_bias_list = []\n",
    "mse_mat_var_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    _, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\n",
    "    mse_mat_bias_list.append(\n",
    "        np.matmul(\n",
    "            np.reshape(biases, (len(biases), 1)), np.reshape(biases, (1, len(biases)))\n",
    "        )\n",
    "    )\n",
    "    mse_mat_var_list.append(get_cov_mat(X0, alpha, sigma_noise))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $MSE_{var}$ increases when adding explanatory variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-1.15094384258883e-14+0j) (99.9999999999997+0j)\n",
      "(-1.7658427167671792e-14+0j) (100.00000000000004+0j)\n",
      "(-2.9363277131202554e-14+0j) (99.99999999999997+0j)\n",
      "(-3.281628950474632e-13+0j) (100.00000000000006+0j)\n",
      "(-8.352266027704196e-14+0j) (99.99999999999987+0j)\n",
      "(-2.3187862086841947e-13+0j) (100.00000000000011+0j)\n",
      "(-4.1487064488299177e-14-5.1414772292082595e-15j) (100.00000000000017+0j)\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 8;\n",
       "                var nbb_unformatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_var_list[ii + 1] - mse_mat_var_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_formatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_var_list[ii + 1] - mse_mat_var_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ii in range(0, X.shape[1] - 1):\n",
    "    eigvals = np.linalg.eigvals(mse_mat_var_list[ii + 1] - mse_mat_var_list[ii])\n",
    "    print(np.min(eigvals), np.max(eigvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $MSE_{bias}$ does not increase of decrease when adding explanatory variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-94.44303714738214+0j) (90.6643423058386+0j)\n",
      "(-133.3040850229547+0j) (125.87485202627272+0j)\n",
      "(-727.2280381028207+0j) (538.1279597151861+0j)\n",
      "(-570.2210474561782+0j) (440.68785767074365+0j)\n",
      "(-1939.9621997920299+0j) (3.053566645191639e-14+0j)\n",
      "(-5.537875687571283e-28+0j) (8.140146006108649e-28+0j)\n",
      "(-9.362310256271155e-28+0j) (5.434455097821107e-28+0j)\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 9;\n",
       "                var nbb_unformatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_bias_list[ii + 1] - mse_mat_bias_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_formatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_bias_list[ii + 1] - mse_mat_bias_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ii in range(0, X.shape[1] - 1):\n",
    "    eigvals = np.linalg.eigvals(mse_mat_bias_list[ii + 1] - mse_mat_bias_list[ii])\n",
    "    print(np.min(eigvals), np.max(eigvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian approach\n",
    "In the bayesian approach, the results are the following:\n",
    "$$\\hat{\\beta_{0}}=(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}Y$$\n",
    "$$\\hat{Y_{0}}=X_{0}\\hat{\\beta_{0}}=X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}Y$$\n",
    "The expected value of $\\hat{Y_{0}}$ is then:\n",
    "$$E[\\hat{Y_{0}}]=X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}X\\beta$$\n",
    "\n",
    "___\n",
    "* **$MSE_{var}$**\n",
    "\n",
    "Let's compare the variance term in the bayesian approach vs in the frequentist approach.\n",
    "$$\\begin{align}\n",
    "\\hat{Y_{0}} - E[\\hat{Y_{0}}] &= X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}Y - E[\\hat{Y_{0}}]\\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}\\epsilon\n",
    "\\end{align}$$\n",
    "\n",
    "Hence:\n",
    "$$\\begin{align}\n",
    "MSE_{var}(X_{0}) &= E[(X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}\\epsilon)(X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}\\epsilon)^{T}] \\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T} E[\\epsilon \\epsilon^{T}] X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T} \\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T} \\sigma^{2} I X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T} \\\\\n",
    "&= \\sigma^{2}X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T} X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}\n",
    "\\end{align}$$\n",
    "\n",
    "**Unfortunately, nothing can be concluded for this term.**\n",
    "\n",
    "___\n",
    "* **$MSE_{bias}$**\n",
    "\n",
    "Let derive the bias term of the MSE:\n",
    "$$E[\\hat{Y_{0}}] - X\\beta = (X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}-I)X\\beta$$\n",
    "\n",
    "Hence:\n",
    "$$\\begin{align}\n",
    "MSE_{bias} &= (X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}-I)X\\beta ((X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}-I)X\\beta)^{T} \\\\\n",
    "&= (X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}-I)X\\beta \\beta^{T}X^{T} (X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}-I)\n",
    "\\end{align}$$\n",
    "\n",
    "**Unfortunately, nothing can be concluded for this term.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 10;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha = 40  # since we are in a frequentist approach without regularization\\n\\n# initialization\\nmse_mat_bias_list = []\\nmse_mat_var_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    _, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    mse_mat_bias_list.append(\\n        np.matmul(\\n            np.reshape(biases, (len(biases), 1)), np.reshape(biases, (1, len(biases)))\\n        )\\n    )\\n    mse_mat_var_list.append(get_cov_mat(X0, alpha, sigma_noise))\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha = 40  # since we are in a frequentist approach without regularization\\n\\n# initialization\\nmse_mat_bias_list = []\\nmse_mat_var_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    _, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    mse_mat_bias_list.append(\\n        np.matmul(\\n            np.reshape(biases, (len(biases), 1)), np.reshape(biases, (1, len(biases)))\\n        )\\n    )\\n    mse_mat_var_list.append(get_cov_mat(X0, alpha, sigma_noise))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha = 40  # since we are in a frequentist approach without regularization\n",
    "\n",
    "# initialization\n",
    "mse_mat_bias_list = []\n",
    "mse_mat_var_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    _, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\n",
    "    mse_mat_bias_list.append(\n",
    "        np.matmul(\n",
    "            np.reshape(biases, (len(biases), 1)), np.reshape(biases, (1, len(biases)))\n",
    "        )\n",
    "    )\n",
    "    mse_mat_var_list.append(get_cov_mat(X0, alpha, sigma_noise))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $MSE_{var}$ does not increase of decrease when adding explanatory variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-3.267029962486426+0j) (46.748650742125186+0j)\n",
      "(-2.292877523253305+0j) (47.53946785501041+0j)\n",
      "(-1.2495557385860738+0j) (41.22918650958304+0j)\n",
      "(-1.0279344778987423+0j) (49.028793803920976+0j)\n",
      "(-0.037390864780485526+0j) (43.78267737127335+0j)\n",
      "(-0.2797828810320388+0j) (48.14628628697182+0j)\n",
      "(-0.3320741414618705+0j) (45.417980988033534+0j)\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 11;\n",
       "                var nbb_unformatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_var_list[ii + 1] - mse_mat_var_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_formatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_var_list[ii + 1] - mse_mat_var_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ii in range(0, X.shape[1] - 1):\n",
    "    eigvals = np.linalg.eigvals(mse_mat_var_list[ii + 1] - mse_mat_var_list[ii])\n",
    "    print(np.min(eigvals), np.max(eigvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $MSE_{bias}$ does not increase of decrease when adding explanatory variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-107.07955970917595+0j) (113.38069863891053+0j)\n",
      "(-79.57954124689562+0j) (84.02201418468508+0j)\n",
      "(-594.4019294824184+0j) (386.4089629314528+0j)\n",
      "(-291.24919186893703+0j) (207.58430762086232+0j)\n",
      "(-1767.8758822188888+0j) (25.971031084769667+0j)\n",
      "(-41.89459345878093+0j) (41.84231402122852+0j)\n",
      "(-25.616209563136383+0j) (25.440386019080304+0j)\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 12;\n",
       "                var nbb_unformatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_bias_list[ii + 1] - mse_mat_bias_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_formatted_code = \"for ii in range(0, X.shape[1] - 1):\\n    eigvals = np.linalg.eigvals(mse_mat_bias_list[ii + 1] - mse_mat_bias_list[ii])\\n    print(np.min(eigvals), np.max(eigvals))\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for ii in range(0, X.shape[1] - 1):\n",
    "    eigvals = np.linalg.eigvals(mse_mat_bias_list[ii + 1] - mse_mat_bias_list[ii])\n",
    "    print(np.min(eigvals), np.max(eigvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSE scalar\n",
    "In this part, I have considered the scalar definition of the MSE. The MSE value breaks down to two terms linked to the variance and bias.\n",
    "$$\\begin{align}\n",
    "MSE&=E[||\\hat{Y} - X\\beta||^{2}]\\\\\n",
    "&=E[||\\hat{Y} - E[\\hat{Y}] + E[\\hat{Y}] - X\\beta||^{2}]\\\\\n",
    "&=E[||\\hat{Y} - E[\\hat{Y}]||^{2}] + E[||E[\\hat{Y}] - X\\beta||^{2}] + 2E[(\\hat{Y} - E[\\hat{Y}])^{T}(E[\\hat{Y}] - X\\beta)]\\\\\n",
    "&=\\underbrace{E[||\\hat{Y} - E[\\hat{Y}]||^{2}]}_\\text{MSE_{var}} + \\underbrace{||E[\\hat{Y}] - X\\beta||^{2}}_\\text{MSE_{bias}}\n",
    "\\end{align}$$\n",
    "\n",
    "Considering the following notation:\n",
    "$$\\begin{align}\n",
    "MSE_{var}=E[||\\hat{Y} - E[\\hat{Y}]||^{2}]\\\\\n",
    "MSE_{bias}=||E[\\hat{Y}] - X\\beta||^{2}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequentist approach\n",
    "In the frequentist approach, the parameter estimation depends on the considered independent variables. Let's assume, only a subset $X_0$ (with $p_{0}$ columns) of $X$ has been selected. The estimated parameter is then:\n",
    "$$\\hat{\\beta_{0}}=(X_{0}^{T}X_{0})^{-1}X_{0}^{T}Y$$\n",
    "And consequently, the estimated prediction is:\n",
    "$$\\hat{Y_{0}}=X_{0}\\hat{\\beta_{0}}=X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}Y$$\n",
    "\n",
    "The expected value of $\\hat{Y_{0}}$ is then:\n",
    "$$E[\\hat{Y_{0}}]=X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}X\\beta$$\n",
    "\n",
    "___\n",
    "* **$MSE_{var}$**\n",
    "\n",
    "Let derive the variance term of the MSE:\n",
    "$$\\begin{align}\n",
    "\\hat{Y_{0}} - E[\\hat{Y_{0}}] &= X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}Y - E[\\hat{Y_{0}}]\\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\\epsilon\n",
    "\\end{align}$$\n",
    "Since $X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}$ is a projector of rank $p_{0}$ (since all variables are assumed to be linearly independent), by means of Cochran theorem, we have the following result:\n",
    "$$\\frac{||\\hat{Y_{0}} - E[\\hat{Y_{0}}]||^{2}}{\\sigma^{2}}\\sim\\chi^{2}(p_{0})$$\n",
    "Then:\n",
    "$$\\boxed{E[||\\hat{Y_{0}} - E[\\hat{Y_{0}}]||^{2}]=\\sigma^{2}p_{0}}$$\n",
    "**$MSE_{var}$ increases when $p_{0}$ increases, whether a new useful independent variable is added or not.**\n",
    "\n",
    "___\n",
    "* **$MSE_{bias}$**\n",
    "\n",
    "Let derive the bias term of the MSE:\n",
    "$$E[\\hat{Y_{0}}] - X\\beta = (X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}-I)X\\beta$$\n",
    "\n",
    "$I-X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}$ is as also a projector of rank $m-p_{0}$. Then:\n",
    "$$\\boxed{||E[\\hat{Y_{0}}] - X\\beta||^{2}=\\min\\limits_{u\\in\\mathbb{R}^{p_{0}}}(||X\\beta-X_{0}u||^{2})}$$\n",
    "**$MSE_{bias}$ decreases when a new variable is added in $X_{0}$, whether this new variable is useful or not.** This may be suprising, at least it was for me at the beginning, that when adding a new useless variable this term decreases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 13;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha = 0  # since we are in a frequentist approach without regularization\\nn_exp = 10\\n\\n# initialization\\nmse_mean_observed_list = []\\nmse_expected_list = []\\nmse_bias_list = []\\nmse_mean_observed_var_list = []\\nmse_expected_var_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    p0_list.append(p0)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_mean_observed_list.append(np.mean(mse_list))\\n    mse_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * p0)\\n    mse_bias_list.append(np.sum(biases ** 2))\\n    mse_mean_observed_var_list.append(np.mean(mse_list) - np.sum(biases ** 2))\\n    mse_expected_var_list.append(sigma_noise ** 2 * p0)\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha = 0  # since we are in a frequentist approach without regularization\\nn_exp = 10\\n\\n# initialization\\nmse_mean_observed_list = []\\nmse_expected_list = []\\nmse_bias_list = []\\nmse_mean_observed_var_list = []\\nmse_expected_var_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    p0_list.append(p0)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_mean_observed_list.append(np.mean(mse_list))\\n    mse_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * p0)\\n    mse_bias_list.append(np.sum(biases ** 2))\\n    mse_mean_observed_var_list.append(np.mean(mse_list) - np.sum(biases ** 2))\\n    mse_expected_var_list.append(sigma_noise ** 2 * p0)\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha = 0  # since we are in a frequentist approach without regularization\n",
    "n_exp = 10\n",
    "\n",
    "# initialization\n",
    "mse_mean_observed_list = []\n",
    "mse_expected_list = []\n",
    "mse_bias_list = []\n",
    "mse_mean_observed_var_list = []\n",
    "mse_expected_var_list = []\n",
    "p0_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\n",
    "    p0_list.append(p0)\n",
    "\n",
    "    y_hat_list, mse_list = make_experimentation(\n",
    "        n_exp, sigma_noise, m, X_beta, X0, alpha\n",
    "    )\n",
    "\n",
    "    mse_mean_observed_list.append(np.mean(mse_list))\n",
    "    mse_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * p0)\n",
    "    mse_bias_list.append(np.sum(biases ** 2))\n",
    "    mse_mean_observed_var_list.append(np.mean(mse_list) - np.sum(biases ** 2))\n",
    "    mse_expected_var_list.append(sigma_noise ** 2 * p0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0lrpj/+JsDb0/FqU4XaHIKtO/R7v76cHAiz+Xc6LYQp059Qxq58C98U4ALD5Sjb+LRrCbgUBXDSdjC+0FUmZKSstb9PdQpVlhMoBB00jNNbM1s4asMgtZZYr8CoUGzB3liqNR45sDVaTmmgl00wh2NRDoaiDITaOj15UHcfJ/7OLkHl1Y3fvj5eVF586dm7lFLU9r2IKqMdn7/hw8eJDCwsJ6x4YPH970c9TO0DTNHfgKeFQpVaRp2tvAy+jz1l4G/gHc1dD3UUq9C7wL+mKCpphcK5N4L+xS7o9SitNl1eSWVNI1SJ+s+fLCPWw4mMuR3FIqaywA9OzgzQM36skVx5bvxcGgEenvRmSAG5F+bvi4OdrqvOJ/krJ8qCqFmgr9UV0BRhO0S9DPH1gOxZn1z3sEQ6/b9PPLX4TCE1BTCdXl+jWhvWH0y/r5d4ZA0Sn9dTUVoMxkBQ4l6IEf9PNb/h94tgf/LuAdDsaWtSg76TflimozJ0+X0zlQ/yV4wukoOamZHM0tZWO6NV2AuyNb/6jnIvr70r2cOl1OhL++ECPcT/+383I9/5w4+T92cXKPLuy3iwlk0vzZZDHBhdn7/jg7O9OzZ89Lvr5RfxNommZCD9I+VUp9DaCUyqpz/r/AQmvxFBBW5+Xtrce4wHFxlSivMuPiqP9F8t2OU6zZl8Ph3FKO5pZSWF5NiJczG/9vGFSXUV1RSqgbDA71ItILIjt2pVOgO2TtgfxDPB1aATXlekCUXgMdZupvsnM+nPhFP34mmHJwhsnv6ed//D84uMJ63vp6z3bw0Bb9/Be3w9F19RseFAcz1+vPV/8F0rfXP99hYG2glr4dCk/p72lyBgcXPdA7I3KoHsCdOW90JCfHQhBAVRkseqL2WqMj+HaEfr+DPjPAXAMZO8G/Mzh7Nfjfwx6cTUZbkAZw24AIbhsQAehB3PH8Mk6XVtnOny6rZsvR03y3M50zHflxoV788PBgAGYv348G1iDOlUj/2kSYQgjRVjXmqk8NeA9IU0rNrnM8xDp/DWASkGp9/j3wmaZps9EXE3QBNgMa0EXTtEj0AG0qULsPhmhx9qTt5udtO9l1NIN3NhzhCKHkl9WwZ3IRpq3v8mvWUH4p70KkIYcJhkwiR99Gx9AAWP0KrP8nL52p6Ew4PiIbHJxg/Qew+d36b2ZwgP7WQO3EL7DnWz0QcnAGkwu4+tVe6xWq9445uOj1OTiDe2Dt+QEPQfwU6+ud9Ne71NmYd8r/QKk6gZhz/UDsjh8ufGPG/PmsQ7lr1uhPHF3hqaOQexBy91sfB8DRGqwUHIP/N0J/7h4E/l3Br7MeJIb2Bot1pwNDyxi+cDYZbT2kZ/xlUhygB3En8ss4mldG3bUJq/ZmsTu9CPWbIe0znUWT3/4Zg6bh6mTEzdEBV0cjg7v4c31CKEopPvz5KG6ODrg5Odiuae/jQjtvF5RSlFaZcTUZZUGEaHN27NhBeno648aNu6zXJSUl8frrr9OnT5+zjh8+fJhjx47ZdiiYOHEiK1asoKSkBIvFwqOPPsqqVavQNA1nZ2e++OILIiMjiYiIwMPDwzaUOHToUObMmWOfD9pKNWaP2iDgNmCXpmk7rMeeBaZpmpaAPvR5FLgfQCm1W9O0L9AXCdQADyqlzACapj0ELEVPz/G+Ump3I7ZbXERpZQ37soo5nFPKoZwSDueUcDinlP9dU0Pw6sf5KSeOv9ZMw0cz0NF0miFd3YgMDaJaS8Hk7M2LnQ4wy3S8NmAa2F7vJXIapQdWZwKtMwGRZg0+Bj4CvW6vfZ3J+vWM8bP1x/kM+v2FP1i35Auf92p/aTfoSrn4QFii/vgt90CY+nltAJe7H3Z/A51G6IHasZ/h08ng20kfOvXvqj86jdC3umlBnE1GugR50OU3gdzCh4dYh1PLbOlF8k8etp33cXOkpKKG06VVnDxdTlllDQEe+r9/ZY2FP/1w9vqiB4d34skxURSUVdPzZX3RuYvJiJuTEVdHB2YmdWJa3w7kllTy/LepuDo62M65ORoZHhVIbKgXRRXVbDmSj5uTgx4kWgNBHzcTTg4tIzgW4nx27NjB1q1bLztQuxBvb282bNjA4MGDKSgoICMjw3Zu/vz5pKenk5KSgsFg4OTJk/W2ilq9ejX+/v52a0tr15irPtej94b91o8XeM2fgbO6Hax51s77OmF/NWYLJ0+Xczi3xBaQzRgUSdcgD5bvzuTRL/StQRww08HTQKf2wVQ6O0FANLf0TmJaZFd2HDhFUtLUOrV2hoQbzvlNAUDEIP1xPt5h1B8Fb0OcPCBqHFDnB61S2Lqf3AMh8R49iMvYCWnfg7LAPav0QC1tod4beSaA8++iPzxDQWs5PUz6cKoHnQP1IG7NmuO2c/+9/ZzzbAFwcjCw44VRlFaZKausoaSyhrIqMyFe+t6Cjg4GnhsXTWmVfrzUej7QGuiVV5k5lFNCaaWZsqoaSqvMVNVYCPBwIjbUi6O5pdz90dlJtP89NYHrE0LZcjSf+/+3DVdHoy2Qc3dy4InR3UgI82Z/VjFfbTtZPxB0MjK4sz9+7k4UllWTU1JhDRD11/92RbJoHT755BPmzJlDVVUV/fr14z//+Q/bt2/n7rvvZvPmzZjNZvr27cv8+fPJzc3lhRdewMPDg4MHDzJ8+HD+85//YDAYWLZsGS+++CKVlZV06tSJDz74AHd3d7Zs2cLvf/97SktLcXJyYvny5bzwwguUl5ezfv16nnnmGcaPH8/DDz9Mamoq1dXVPPXUU0ydOpXy8nJmzJjBzp07iYqKory8/LyfY+rUqcybN4/Bgwfz9ddfc8MNN7B7t96HkpGRQUhICAaD/j3cvn0j/5HbyrWs2cqiyRWWVXPIGozFhnoSFezJzhMF3PTORqrMFtt1vm6OjO7mQ9efn2Tg/i381+RJJy2dsOBATMOegBjrL9Gu87DNoDogUwkblabVBlkB3eoPrdZUQv5h8LFuWWWphspiSJkPlbV7k/LEPn1BxN4fIXNXbW+cXye9x/IqoWka3q6OeLue+7ybkwP3Du143teH+bqy7LFh9Y5V1/n+7xzozvcPDdIDwEqzLeBLCPMGwMfVkWvjQvTjdc6fWVV/NLeUjzYepaLaUu89vpo5ED93J5btyeTJBfX3KXQ0Gvjh4cF0C/bg+53pvLf+CG6OepDn7mTE1cmBJ0c3bJPqtm7K3I1nHRsfH8JtAyIorzJz5webzzo/uXd7buoTRn5pFTM/2Vbv3Pz7B1zw/dLS0pg/fz4bNmzAZDLxwAMP8Omnn3L77bdz3XXX8cc//pHy8nKmT59ObGwsa9asYfPmzezZs4fw8HCSk5P5+uuvSUpK4pVXXmHFihW4ubnx17/+ldmzZ/P0008zZcoU5s+fT2JiIkVFRbi6uvLSSy+xdetW3nzzTQCeffZZRowYwfvvv09BQQF9+vRhwoQJzJ07F1dXV9LS0khJSaFXr17n/SwjR47k3nvvxWw2M2/ePN59911efllfOHXzzTczePBg1q1bx8iRI5k+fXq9yfPDhw+3DX3ecccdPPbYYxe8b22dBGptwJneMaNBI8zXldOlVdz/v20czi0ht6R2svcTo7oSFexJB19X7hoUTkdjNp1Kf6Wjew0+o5/Ue2827CWwUw9Gdb5GH1bzOH9eLtGMHJwgsM4WJTGT9IdSUJKl97zlHdTnu4G+iGLT2+gzEgA0PVh7cAsYDPrQqsWsB3LuQS2qF66x1O3RcnV0IL6993mv7RzozssTY897fnRMMHtfHovZoiir06vXzlsPhvt39OONaT313rw6vXr+7vpqZicHA14uJsoqazhdVm69robHrul63vcULc/KlSvZtm2bbS/O8vJyAgP1ebIvvPACiYmJODs715uz1bdvXzp21P/ImDZtGuvXr8fZ2Zk9e/YwaJA+AlFVVcWAAQPYt28fISEhtvo9Pc+d/HrZsmV8//33vP66nne+srKS48ePs3btWh555BFA39PyzKbo52I0Ghk8eDDz5s2jvLyciIgI27n27duzb98+Vq1axapVqxg5ciRffvklI0fqK8Bl6PPySKDWilTVWHB0MOib4S7fz4GsEg7llHAsr4wqs4Vb+nXgL5Pi8HQxoWkwIiqQTgHudAxwp1OAG2G+rrDne3x2fcnTh3+CykLQDNB1rP4Gmgb3rWnWzygaSNP04NojGCKH1B5PfhVGvgB5h2rnwVUW6UEawJpX4cha/bmTp76QIXxgbS9e4UlwC6g/Z1CcxWjQ8HA2nbXXapivq/7/7zzGxOg7a5xLVqkFs0VhlEUSl+1CPWAujsYLnvd1c7xoD9pvKaW44447ePXVV886l5eXR0lJCdXV1VRUVNjmdGm/+aNI0zSUUowaNYrPP/+83rldu3Zdcju++uorunXTe2SvNP3E1KlTmTRpErNmzTrrnJOTE2PHjmXs2LG2Dd/PBGri8kigdpXacDCXPelFHM4t4VB2KYdzS4hv7837dyaiaRqLUjLQNOgY4M7I6CA6BrjRw9ojYDRo+g+Y6nI4tkH/BdztBTAa9PKp7RBzPXS+BiKHgYt3s35W0URMLhAcqz9+a9JcyNlXu5Ahdz+U5tSe/+g6OH1Ez/92Zg5cxJCLL9AQDfLT/hyeWldOWFQeAztJD0VLN3LkSK6//noee+wxAgMDyc/Pp7i4mPDwcO6//35efvlljhw5wlNPPWUbpty8eTNHjhwhPDyc+fPnc99999G/f38efPBBDh48SOfOnSktLeXUqVN069aNjIwMtmzZQmJiIsXFxbi4uODh4UFxcbGtHWPGjOGNN97gjTfeQNM0du7cyeDBgxk6dCifffYZI0aMIDU1lZSUlPN9FACGDBnCM888w7Rp0+od3759O8HBwbRr1w6LxUJKSsoFe+fEhUmg1kIVVVRzKLukzsrKUjQN3p7eG4B/rzjA5qP5+Lia6BTgzoioQHqH16aSWPH4sHOnISjK0FcLHlyhB2U1FWB0gh63QGAUXDMLkl9rE0Nb4jJ4ttMfnYaf+/yI5yB7L+Qd0IO5Iz9BeYEeqFks8K84/fV1FzKEJOgpU8QV6xvhi6MRFqZkSKB2FejevTuvvPIKo0ePxmKxYDKZeOutt/jpp58wmUzccsstmM1mBg4cyKpVqzAYDCQmJvLQQw/ZFhNMmjQJg8HAhx9+yLRp06isrATglVdeoWvXrsyfP5+HH36Y8vJyXFxcWLFiBcOHD+e1114jISGBZ555hueff55HH32U+Ph4LBYLYWFhLFmyhJkzZzJjxgyio6OJjo6md+/eF/w8mqbxhz/84azj2dnZ3Hvvvba29e3bl4ceqt1MqO4ctfj4eD7++GN73eJWqUm2kGpqffr0UVu3nr1Cy94amhG87srKQ9mlnCooZ9Z1MQA88vmvfL8zHdA3Dw/3cyWmnRdzpukTMo/nleHh7FAvI/85lRfovzQDovQJ54fXwMfXW1M3jNR7zcIH6nm87Ewypl9cq71HFgtUl+qrVavKYOmz+py43P36HDmAYU/B8Geh/DR8+2BtAHcmR5yrb+u9P3Z087+WcLDYyOZnR+IgK0XP8tudCaKjoy/8ghZkzZo1vP766yxcuPDiFzeA7ExwYfa+P+f6PtQ0rfm2kBJQWF5tyzV2bXwIziYjc386xOvL9lFtrg2UfVxNPDG6Kx7OJu4YGM51PdrR0Tp37LdL9Tv4nSewslggYwccXAmHVsKJzaDMMOQPMPJ5PZP+o7vAu0MjfmLR5hkMepAG+h8BE/5Ve66iUE/seya/W2ke5B+CA8v01alnXP8fIFRPN7Lypdokxme+9rlb7wXOOwT7l9buBnEmGXFYP3D11QPBkpw6ufesrzfWnyd2teoX4sDmzEp+PpTH0K4Bzd0cIYSdSaBmJ2d6xwI8nHBzcuDng7n8a+UBDueUkltSabsuKsSDmHZexLTz4q7BkXTyd6dToBsd/d3r9Y71Dve99DcvztL3kAztpQdlH1+vTwRv1xMGP6b3mrW3BuoOjhKkiebl7AXt6wyp+HeGB3/Rt8kqOFY7Dy6sr74lV02Vvg9rTYV1D1XrFmBR4/VALTMFlj5z9vvcvRxc+8LeRfDdg2ef/90GfT7e9v/BmtfODvRufA88gmDfEtj3Y/2twUzO+vZeJhc9rUn+4TqvtSZiDorVA9aqUv39HJwbZeeIOH89Z9uilAwJ1FqZpKQk6VEWEqhdqVMF5SzYX8XnJ7ZyOKfUtrLyvTv6MDI6CINBw2JRjIwKpGOAm21lZQfryq7BXfwZ3OUK55TUVOnbJR1aqc81y9ylD20++IveSzDtc/DvBu7yQ1tcRYwOekoQv051FiGc0ndquG/1+V8XNUHffqvaugfsma/+1hxjEYP1oKu6vHYP2OoK8AjRz3uF6vuw1n1tdUVtUJV/GPYvqT1ntqa06XO3HqjtnAcb3zy7XS+c1r8ufQ62faA/N5isW5N56z3bAKte0Rf01O0xdA+EcX/Xz++crwewDk61waCrvzUBMjgaNf7fHX2IDj53KgYhxNVNArUrVFpZw+Ij1YT7l9DR350R0YF08nenezv9h2X/jn4smDnQfm9YcLy2J+z7hyFlnr7PZVh/Pa1CpzrLniMG2+99hWjpjA769lvny8/rE6E/zqfTCP1xPgMe0B9nWCx6sHcmIfCg30OPaXV6/KzB4JnUJt2vB9/I+kFg3cU6Jlc9OKup0IdpayqgKL32fOoCfVi4Lv+ueqCmFI6V+fTv2LK2CRNC2I8Ealeoc4A7c0e5cs2IpMZ5g6pSOLpe7zE7uFKfw/Pwdr23IfFu6H6dnv7AWf6KFqJJGQz1F9+4B+qP8+k0/PyrZQGGPK4/zufWL/Vh4RrrsG91ub49GMBX95BwaCOMnsSX206SU1LJA0mdL+/zCCFaNAnUrpDBoOFgzwSTSoG5Wp9DdngNfHqTPsRictV7yPrdD87e+rVhfe33vkKIls/oAEaP2gUaZ0QMxjV1AWTsYPMRA4tTM7lrUCTOJtkoXojWQtZyN6eyfEj9Sk9NMDsatvw//XhQnB6Y3f6dPvfm1i/1spsMbwgh6uh+PRbNAVK+ZHyPdpRU1vDT/pyLv04IcdWQQK05WMzw3hj4eydYcBfsXainEgiw7tvn5gejX4GOSbIljxDi/Fx9yfftDalfMTDSGx9XEwtTMpq7VeICkpKSOHr0KB9++KFt66UPP/ywXkLYugYOtONc5/M4duxYvdWlZ9qYn5/PI488wuTJk3nrrbcavR3i3GTos7EVpetzzA6uAEsNTP1UX00W1F0PxDpfo6fVaIRl+0KI1i8raBj+e/6G6fh6kmND+G7HKcqrzLg4ys+U1uDnn39utvf29fVlzpw5pKamMnfu3GZrR1sngVpj2fYh/DIXsvfoZY8Q6Jqsz0XTNBj/z2ZtnhCidcjz6wNTPoXwgVxHCQezi8kuriDcz625m9ai/emH3exJL7Jrnd3befLihJgreu2JEydISkri1KlTTJ8+nRdffBEAd3d3SkpKKCkp4frrr+f06dNUV1fzyiuvcP3111NaWsrNN9/MyZMnMZvNPP/880yZMoVt27bx+OOPU1JSgr+/Px9++CEhISHMmTOHd955BwcHB7p37868efMu2K6UlBTefPNN5syZc0WfSzScBGoNpZSeGf3gCji0Cm6Yq6cKqC4HtwAY9TJ0HgmB3WX/TCGE3VmMThA9BoABnZz4slPjD5UJ+9u8eTOpqam4urqSmJjItddeS58+tTsKOTs788033+Dp6Ulubi79+/fnuuuuY8mSJbRr145FixYBUFhYSHV1NQ8//DDfffcdAQEBzJ8/n+eee47333+f1157jSNHjuDk5ERBQcEF25Sens4111zDtddeyz//+U+eeeYciaVFo5NA7UrlH6bL/rdhx8N6jjMA305QcEIP1PrP1B9CCNHYqsrg5zn6DiSdr6GgrApnk1FWf17AlfZ8NZZRo0bh56cvGLvhhhtYv359vUBNKcWzzz7L2rVrMRgMnDp1iqysLOLi4njiiSd46qmnGD9+PEOGDCE1NZXU1FRGjRoFgNlsJiRET/AcHx/PrbfeysSJE5k4ceIF29SuXTuys7Mb5wOLSyaB2pUy1xCUtUbvLRv0ez3hrG9kc7dKCNEWOTjB1g8gI4X9Hv24ds46Xr+pB9cnhDZ3y8Ql0n4z4vLb8qeffkpOTg7btm3DZDIRERFBRUUFXbt2Zfv27fz444/88Y9/ZOTIkUyaNImYmBg2btx41vssWrSItWvX8sMPP/DnP/+ZXbt2NernEg0nqz6vlH8XNgz6BKZ9Bon3SJAmhGg+BiPETYYDy+jsXoWfmxM/7JTVn1eT5cuXk5+fT3l5Od9++y2DBg2qd76wsJDAwEBMJhOrV6/m2LFjgD486erqyvTp03nyySfZvn073bp1IycnxxaoVVdXs3v3biwWCydOnGD48OH89a9/pbCwkJKSkib/rOLySI/aFbrxnY1k59fgsWsdBgNoaBg0QNO/aoBB09A0/S+jM+Uz1545fqXXollf85vXGjR9KtyZc5r1nO1aQ+3xS7mWM22pcy113vOc7bZeu/9kNXnbTmI0aBgMGkZNw2jQr6l/TLMdq3fedqzOc+t9OXPceIG6DNrZf5UK0WrF3QQb38SQ9j3j4vrxyaZjFJZX4+Viau6WiUvQt29fbrzxRk6ePMn06dPrDXsC3HrrrUyYMIG4uDj69OlDVFQUALt27eLJJ5/EYDBgMpl4++23cXR0ZMGCBTzyyCMUFhZSU1PDo48+SteuXZk+fTqFhYUopXjkkUfw9vbm5MmTzfGRxSWSQO0KtfdxwVJehJ+3C0opLEqhAIvS5xIoBQqFxWL9qsBsUVSb61+L0s/VXlv7ekudepW13rrXgn5N7bWA9b1s19raUv/aM+9T99pGkbqzkSq+NAaNcwR6dQM66h2zPbcdqz3vcJ7g0VbPud7nHPWcCSgdjBqcrqFPZQ3uTvJfUTRQSA99D9BdXzJ+5ETe33CE5XuymNy7fXO3TFzEnXfeyZ133nnOc2d6vPz9/c85lBkREcGYMWPOOp6QkMDatWvPOr5+/fqGNVY0OfntcIX+PbUna9asISmpz8UvvkqcL6iD2kDQFtTVCfjOXKvqlC0Kfv55I3379cNs0QNOs4U6zxVmpbBY6j7nHMf0r2deV2OuU1eda8+uk3qvP3ed1D9/po6z6qTe66tqLJdUT73zvzlWY1HUmC1YFPx313L6d/LjmuhARkYHEep9vt3FhbgATYOe0+HEZnq2cyPU24WFKekSqAlxlZNATdicGfoEMNLwIcMAV4PkcrqAGrOF975bTZ5zO1bsyeKF73bzwne7iQ7x5JroQK6JDiIu1Ms2BC3ERQ36PaBPkfj75HjaSdDf4tx55514e3uTkJBAREREczcHAC8vr3o9emfaKFoGCdSEaCYORgPdfI0kJUXz7LhoDuWUsDItixVp2by1+iBvrDpIgIcTI6P0oG1QZ3/JNi8uTcEJBnYOa+5WiHM4ExAlJCQ0azvq8vb2PitQEy2HBGpCtBCdAtzpFODOfUM7cbq0ijX7s1mRls3ClAzmbTmBk4OBIV38GRkdxMioQAI9nZu7yaIlSv0aFsyA321gbVEQO04U8MjILs3dKiHEFZJATYgWyMfNkUk92zOpZ3uqaixsPpLPirQs60NPQNmjvRcjo4O4JjqI6BAPWeEqdJFDQTPCri/4xXILb685xC39OuDv7tTcLRNCXAHJoyZEC+foYGBwF39mXRfDuv8bzpJHh/DkmG4YDBr/XLGfcXPWMei1VTz/bSo/7c+hssbc3E0WzcnNX0/EvesrxscGY1GwODWzuVslhLhCEqgJcRXRNI2oYE8eHN6Zbx4YxOZnr+FvN8YTG+rFgm0nueP9zfR6aTkzP9nGgm0nySupbO4mi+YQdzMUnSSqahedAtxYuDO9uVskWpGjR48SGxvb3M04S1JSElu3bj3r+KxZs/jwww8Bve1JSUl2e88777yTNWvWALBmzRrb/L5PPvmEmTNnMnbsWPLz8xv0HjL0KcRVLMDDiZsTw7g5MYyKajMbD+WxPC2LlWlZLE7NxKBBrw4+jIwOYlT3QDoFuMsQaVsQNQ5Mbmi7vmR8/EPMWXWArKIKgmReY6tkNpsxGq/uhUY1NTU4OFw9IYmezur8CUinT5/O9OnTue222ygrK8PX1/eK30t61IRoJZxNRoZHBfKXSXFsemYkPzw0mIdHdKGixsxfl+zlmtlrSXp9DS/9sIefD+VSbbY0d5NFY3F0g6mfwsgXmdAjhHBfV06eLm/uVglg4sSJ9O7dm5iYGN59910A3nnnHZ588knbNR9++CEPPfQQoPfM9O3bl4SEBO6//37MZn1qg7u7O0888QQ9evRg48aNvPTSSyQmJhIbG8t9991nCyK2bNlCfHw8CQkJPPnkk7aeMLPZzJNPPkliYiIDBgxg7ty552zv7NmziY2NJTY2ln/961+24zU1Ndx6661ER0czefJkysrKAHj66afp3r078fHx/OEPfwAgJyeHG2+8kcTERBITE9mwYQOg93TddtttDBo0iNtuu43+/fuze/du23uc6SErLS3lrrvuom/fvvTs2ZPvvvsOgPLycqZOnUp0dDSTJk2ivPzyvseffvpp3nrrLVt51qxZvP7665SUlDBy5Eh69epFXFwcixYtAvTeuG7dunH77bcTGxvLiRMnzlu3xWLhueee49Zbb6V9+wbmMjwTFbamR+/evVVTWL16dZO8z9VK7s/FNdU9Si8oU//beFTd8f4vqstzP6rwpxaquBeXqIc/266+/fWkKiirapJ2XC75Hrq4S7lHFoul8RvSQtW9P3v27Kl/8v1xSm3/RH9eU6WXd8zTy5WlennXAr1cXqCXd3+nl0ty9fLeH/VyUeYltScvL08ppVRZWZmKiYlRubm5Kjs7W3Xq1Ml2TXJyslq3bp3as2ePGj9+vKqq0v9/zpw5U3300UdKKaUANX/+/LPqVUqp6dOnq++//14ppVRMTIz6+eeflVJKPfXUUyomJkYppdTcuXPVyy+/rJRSKicnR/Xu3VsdPny4Xlu3bt2qYmNjVUlJiSouLlbdu3dX27dvV0eOHFGAWr9+vVJKqRkzZqi///3vKjc3V3Xt2tX2/Xb69GmllFLTpk1T69atU0opdezYMRUVFaWUUurFF19UvXr1UmVlZUoppWbPnq1eeOEFpZRS6enpqmvXrkoppZ555hn1v//9z1Znly5dVElJifrHP/6hZsyYoZRSaufOncpoNKotW7acdc9ffPFF9cEHHyillDpy5IgaNmyYUkqp7du3q6FDh9qui46OVsePH1fV1dWqsLDQdm8iIyOVxWJRR44cUZqmqY0bN9pec8cdd9i+x1avXq3uuOMOpZRSjz/+uOrXr5+6++67VWpqar32nPV9qJQCtqrzxDRXTz+jEOKKhXi5ML1/ONP7h1NaWcO6A7msTMti1d5svt+ZjoNBIzHCl5HRgYzqHiSJiluLXQsg7xBa0lNU1ViosVhwdZQf+81pzpw5fPPNNwCcOHGCAwcO0L9/fzp27MimTZvo0qULe/fuZdCgQbz11lts27aNxMREQO9BCgwMBMBoNHLjjTfa6l29ejV/+9vfKCsrIz8/n5iYGIYMGUJxcTEDBgwA4JZbbmHhwoUALFu2jJSUFBYsWIDFYqG4uJgDBw4QGRlpq3P9+vVMmjQJNzf958ENN9zAunXruO666wgLC7NtHD99+nTmzJnDo48+irOzM3fffTfjx49n/PjxAKxYsYI9e/bY6i0qKrJtjXXdddfh4qInZr755psZPXo0f/rTn/jiiy+YPHmyra3ff/89r7/+OgAVFRUcP36ctWvX8sgjjwAQHx9PfHz8Zf1b9OzZk+zsbNLT08nJycHHx4ewsDCqq6t59tlnWbt2LQaDgYyMDLKysgAIDw+nf//+F637H//4x2W15ULkf6wQbYybkwPJscEkxwZjtih2nChgZVoWK9OyeWVRGq8sSqNzoLsetEUH0bODD0bZHeHqdGIzbPuQ0/F3k/TGdh4a3pl7h3Zs7la1HDMW1T43muqXHV3rl5296pfd/OqXPYIu+nZr1qxhxYoVbNy4EVdXV5KSkqioqABg6tSpfPHFF0RFRTFp0iQ0TUMpxR133MGrr756Vl3Ozs62eWkVFRU88MADbN26lbCwMGbNmmWr93yUUrzxxhuMGTOG4uJiPDw8Ltr+un4711XTNBwcHNi8eTMrV65kwYIFvPnmm6xatQqLxcKmTZtwdj57juSZIBAgNDQUPz8/UlJSmD9/Pu+8846trV999RXdunW7rDZeiptuuokFCxaQmZnJlClTAPj000/Jyclh27ZtmEwmwsPDbfezbnubisxRE6INMxo0eof78H/JUSx9bCjr/m84L07oTpCnE++tO8LkdzaS+OcVPPHFThbvyqCksqa5mywuR/zNYK7E59gSwnz1vT9F8yksLMTHxwdXV1f27t3Lpk2bbOcmTZrEd999x+eff87UqVMBGDlyJAsWLCA7W8+dmJ+fz7Fjx86q90wQ4e/vT0lJCQsWLAD0HQc8PDz45ZdfAJg3b57tNWPGjOHtt9+muroagP3791NaWlqv3iFDhvDtt99SVlZGaWkp33zzDUOGDAHg+PHjtk3iP/vsMwYPHkxJSQmFhYWMGzeOf/7zn+zcuROA0aNH88Ybb9jq3bFjx3nv0ZQpU/jb3/5GYWGhrYdszJgxvPHGG7Z5d7/++isAQ4cO5bPPPgMgNTWVlJSU89Z7ofebN28eCxYs4KabbgL0f6fAwEBMJhOrV6/m+PHjl12vPUmPmhDCJszXlRmDIpkxKJKiimp+2pdj3dYqi6+2n8TRaJAN5K8mob3BJxJSvmB8/D95bfFejueV0cHPtblb1iYlJyfzzjvvEB0dTbdu3eoNofn4+BAdHc2ePXvo27cvAN27d+eVV15h9OjRWCwWTCYTb731FuHh4fXq9fb25t577yU2Npbg4GDbUCnAe++9x7333ovBYGDYsGF4eXkBcM8993D06FF69eqF2WwmKCiIb7/9tl69vXr14s4777S155577qFnz562SfVvvfUWd911F927d2fmzJkUFhZy/fXXU1FRgVKK2bNnA/pw74MPPkh8fDw1NTUMHTrU1lv2W5MnT+b3v/89zz//vO3Y888/z6OPPkp8fDwWi4XIyEgWLlzIzJkzmTFjBtHR0URHR9O7d+/L/jeJiYmhuLiY0NBQQkJCALj11luZMGECcXFx9OnTh65du152vfYkgZoQ4pw8nU1M6NGOCT3aUWO2sPXYadtepHU3kB9lDdpkA/kWSNMgfgr89FeuHW7kNWDhrnQeSOrc3C1rk5ycnFi8ePF5z5+ZP1bXlClTbENydZ2Z43XGK6+8wiuvvHLWdTExMbaeptdee40+ffoAYDAY+Mtf/sJf/vKXCw59Pv744zz++OP1jkVERLB3796zrnV1dWXz5s1nHff392f+/PlnHZ81a9ZZx4KCgqipqd9z7+Lics5VqS4uLvV6Ca/Url276pX9/f1tvYVAvfuTmpra4Pe7XBKoCSEuysFooH9HP/p39OO5a7vXbiC/J5s3Vx9kjnUD+WuiAxkZJRvItyjxN8PB5YSZCkkI82bhzgwJ1NqQRYsW8eqrr1JTU0N4eLgt8au4ekigJoS4bL/dQH71vmxWpmXzw84MPt98AmeTgcGdZQP5FsGvE9y7CoD/S87FZJSpyW3J+Xrk2pKkpCS8vb0BfZj4zO4B9jBx4kQiIiIAvadx4sSJdqv7DAnUhBAN4uPmyA292nNDL30D+V+O5LEyLZvle+pvIH9NdBAjZQP55lNewMAQA7heeYZ0Ia5GdbeMaoxA7YyIiAhb0GZPEqgJIezG0cHAkC4BDOkSwIsTurMvq5gV1oBt9or9/GP5fkK9XRhpndfWv6MvTg4yRNroKothdjT0f4Dd0Y+wMi2bR0Z2ae5WCSEugQRqQohGcWYD+ahgTx4a0YXs4gpW781mRVo2X2w9wccbj+HmaGRo1wBGRgcxIioQXzfH5m526+TkAR36w64v2eo8ndnL95McG0zXoMvLnSWEaHoSqAkhmkSghzNTEjswJbEDFdVmfj6Uy4q07LM2kL+mexDXROsbyAs7irsZvv0dY/0y+ZMGC3em8/ho+ycQFULYlwRqQogm52wyMiIqiBFRQaiJsaSeKmJ5WhYr07J4bfFeXlu8l3A/Vzq7VXHa6yTx7b2J9HOT9B8NET0eFroQeGgB/SJvYmFKBo+N6irzBYVo4WT5jxCiWWmaRlx7Lx4f1ZVFjwzh56dH8PLEWCL93Vh3qobH5u9k5D9+osdLy7jlv5t4bfFeFu/K4FRBuS1TubgETh7QbSykfs34uCAO55ayJ6OouVslmsCOHTv48ccfL/t1SUlJbN269azjs2bNsqX5OHr0aL3J+g115513smbNGkDfcuvMxP9PPvmEmTNnMnbsWPLz8+32flcD6VETQrQo7bxduK1/OLf1D2flqtWEdu9NyolCdp4sIOVkIe+tP0y1WQ/Q/N2diG/vRXx7L3qEedOjvbfMc7uQpKch6RnGuobyz5UHOZ5XRkw7r+ZulWhkO3bsYOvWrYwbN665m3JeSqkL/uE1ffp0pk+fzm233UZZWRm+vm1n9bL0qAkhWiyjQV+QcHNiGH+eFMcPDw9m16wxfPvgIP50XQxDu/pzPL+Mf688wIwPttDr5eUM/usqHvx0O3N/OsTGQ3myP2ldAd0goCu+bo788uw1jI0Lae4WNaspczfy5dYTAFSbLUyZu5Fvfj0JQHmVmSlzN/LDTn1/1KKKaqbM3ciS1AwA8kurmDJ3Iyv2ZAGQXXzhTdDP+OSTT+jbty8JCQncf//9mM1mtmzZQnx8PBUVFZSWlhITE0Nqaipr1qxh6NChXHvttXTr1o3f/e53WCwWAJYtW8aAAQPo1asXN910k22ngi1btjBw4EB69OhB3759KSws5IUXXmD+/PkkJCQwf/58SktLueuuu+jbty89e/Zk0SJ9c/ny8nKmTp1KdHQ0kyZNory8/LLu59NPP81bb71lK8+aNYvXX3+dkpISRo4cSa9evYiLi+O7774DsG1FdfvttxMbG8uJEyfOW7fFYuG5557j1ltvpX379pfVrqud9KgJIa4qziYjCWHeJIR5244VV1STeqqIFGuv286TBSzapf9C1TQ9QW98ey96tPcmvr0X0SGeOJvaaFqQzF2wYQ7G8bNRju5U1lja7r1oYmlpacyfP58NGzZgMpl44IEH+PTTT7n99tu57rrr+OMf/0h5eTnTp08nNjaWNWvWsHnzZvbs2UN4eDjJycl8/fXXJCUl8corr7BixQrc3Nz461//yuzZs3n66aeZMmUK8+fPJzExkaKiIlxdXXnppZfYunUrb775JgDPPvssI0aM4P3336egoIA+ffowYcIE5s6di6urK2lpaaSkpNCrV6/L+nxTpkzh0Ucf5cEHHwTgiy++YOnSpTg7O/PNN9/g6elJbm4u/fv357rrrgPgwIEDfPTRR/X2PT2XJ598kg0bNpCVlUVYWBgxMTFX8C9wdZJATQhx1fNwNjGgkx8DOvnZjuWVVJJyqpCUE4WknCxg7f5cvt5+CgCTUaNbsAfx7b3p0d6L+PbedAl0x6EtZO2vLIFdX1DTcSRjV4cwPCqQZ8dFN3ermsX8+wfYnpuMhnplF0djvbKns6le2dfNsV450OPiu2+sXLmSbdu22TZNLy8vJzAwEIAXXniBxMREnJ2dmTNnju01ffv2pWPHjgBMmzaN9evX4+zszJ49exg0aBAAVVVVDBgwgH379hESEmKr39PT85ztWLZsGd9//z2vv/46AJWVlRw/fpy1a9fyyCOPABAfH098fPxFP1NdPXv2JDs7m/T0dHJycvDx8SEsLIzq6mqeffZZ1q5di8Fg4NSpU2Rl6T2R4eHhFw3SAP7xj39cVltak0YL1DRNCwM+BoIABbyrlPq3pmm+wHwgAjgK3KyUOq3pS4/+DYwDyoA7lVLbrXXdAfzRWvUrSqmPGqvdQojWwc/dieHdAhneTf9FqJQio7CClJMF7DypB28/7Ezns1+OA+BiMhLTzlMP3sL04C3Cz7X1rYoM6wdeHXBI/YIOvs+wcGc6TydHyYraJqCU4o477uDVV18961xeXh4lJSVUV1dTUVGBm5sbwFnff5qmoZRi1KhRfP755/XO/XZz8Qu146uvvqJbNz09y4U2Zb9cN910EwsWLCAzM9O2ddWnn35KTk4O27Ztw2QyERERQUWFPlR85nOK82vMPx9rgCeUUt2B/sCDmqZ1B54GViqlugArrWWAsUAX6+M+4G0Aa2D3ItAP6Au8qGmaTyO2WwjRCmmaRjtvF5JjQ3gqOYpP7+nPzhdGs+qJYfxrSgJT+4ahgE9/Ocbv5+1g+Otr6PGnZUz/f7/wtyV7WZKaSUZhK1hpajBA3GQ4vJpru7qRXljBrydON3er2oSRI0eyYMECsrP1rdXy8/M5duwYAPfffz8vv/wyt956K0899ZTtNZs3b+bIkSNYLBbmz5/P4MGD6d+/Pxs2bODgwYMAlJaWsn//frp160ZGRgZbtmwB9ACspqYGDw8PiouLbXWOGTOGN954w/a9vHPnTgCGDh3KZ599BkBqaiopKSmX/RmnTJnCvHnzWLBgATfddBMAhYWFBAYGYjKZWL16te0zi0vTaD1qSqkMIMP6vFjTtDQgFLgeSLJe9hGwBnjKevxjpX/nbNI0zVvTtBDrtcuVUvkAmqYtB5KB+n9KCCHEZTIYNDoGuNMxwJ2JPUMBqDFb2J9VUq/nbe7aw5gt+i+1AA8n23DpmXlvPlfbStP4m2H9bEaZ1+Ho0IEfdmbQO7ztrKJrLt27d+eVV15h9OjRWCwWTCYTb731Fj/99BMmk4lbbrkFs9nMwIEDWbVqFQaDgcTERB566CEOHjzI8OHDmTRpEgaDgQ8//JBp06ZRWVkJwCuvvELXrl2ZP38+Dz/8MOXl5bi4uLBixQqGDx/Oa6+9RkJCAs888wzPP/88jz76KPHx8VgsFsLCwliyZAkzZ85kxowZREdHEx0dTe/evS/7M8bExFBcXExoaCghIfpilVtvvZUJEyYQFxdHnz59iIqKsut9be20pvjrUNO0CGAtEAscV0p5W49rwGmllLemaQuB15RS663nVqIHcEmAs1LqFevx54FypdTrv3mP+9B74ggKCuo9b968Rv9cJSUluLtL9vTzkftzcXKPLqyl3J8qs+J4kYUjhRYOF5k5Umghs7T2Z2eAi0akl4FILyORXgYiPA04OzTNUOKV3qPYXX8mz68Pz2QO43ChhdlJLhha2zAv9e+Pl5cXnTt3buYWXbp169YxZ84cvvzyy0Z9H7PZjNF46QtK/vKXvxAeHs6tt97KsWPHmDlz5hXlaTuX3/3ud9x6660MGTKEdevW8emnn/LOO+/Ype4rdbn352IOHjxIYWFhvWPDhw/fppTqc67rG30xgaZp7sBXwKNKqaK64+1KKaVpml0iRaXUu8C7AH369FH2TMB3PmvWrLFror/WRu7Pxck9urCWfH+KKqpJPVlo63VLOVnI5kw9nYFBg86B7vUWK0SFeDTKBvRXfI+SkvAHnj2aT3ZxJUO7B7XKxRR1709aWprd5mI1BVdXVxwcHBq9zZc7R83JyQlnZ2c8PDxwd3fHaDTarY0mkwlXV1c8PDxwdXXFZDI1+7+ZPefwATg7O9OzZ89Lvr5RAzVN00zoQdqnSqmvrYezNE0LUUplWIc2s63HTwFhdV7e3nrsFLVDpWeOr2nMdgshxMV4OpsY2NmfgZ39bcdySyr1IVPrStPVe7NZsE3Py2UyakSHeFoT9OrJeTsHumNszkn85mr6eBZARMfma4M4r6SkpBb5h0pSUhLe3t4AeHt723YPsIeJEycSEREBQEREBBMnTrRb3Verxlz1qQHvAWlKqdl1Tn0P3AG8Zv36XZ3jD2maNg994UChNZhbCvylzgKC0cAzjdVuIYS4Uv7uTrY9TEFfXXeqoNyW2y3lRCHf/prOJ5v0laaujkZi2+k7K8SH6b1vHXybcKXpl3dC9h5O3baBH1IyuGdwZKvsVatLKdX6VvI2sbrBY2MEamdERETYgrbW4kqmmzVmj9og4DZgl6ZpO6zHnkUP0L7QNO1u4Bhws/Xcj+ipOQ6ip+eYAaCUytc07WVgi/W6l84sLBBCiJZM0zTa+7jS3seVcdZdACwWxeHc0nrJeT/edIyq9UcA8HY1ERdam5y3R5g3QZ4Xz9F1RbqOgb0L2ZXyK68tLiC2nReDu/hf/HVXKWdnZ/Ly8vDz85NgTTQ5pRR5eXk4O1/e/+fGXPW5Hjjf/4SR57heAQ+ep673gfft1zohhGgeBoNG50B3Oge6c0MvfSucarOFfZnFtl63nScLePunQ7aVpkGeTvXmu8W398Lb1Q4rTaOvg0VPkFS8EDfHYSxMSW/VgVr79u05efIkOTk5zd2UFqWiouKyg4e2xJ73x9nZ+bK3wJKdCYQQopmZjAZiQ72IDfXi1n76sfIqM7vT6y9WWG7dVxIg3M+VnmHeDPO2XPkbu3hD1zE4p33JqOibWLI7k5cnxmJqpcOfJpOJyMjI5m5Gi7NmzZrLmtze1jT3/ZFATQghWiAXRyN9InzpE1Gb36ywrJpdp6zz3U4W8OOuTIpCDUxqyBvF3QxpP3BtUB7f7qxm/cFc224OQojm1zr/bBJCiFbIy9XE4C7+PDi8M3Nv68PI6EC2Z5mxWBqQ5ajLaLhjIUMHJ+Hn5sih7BL7NVgI0WASqAkhxFUqOTaYgkrVsC2gTM4QOQQnRxM/PzOCe4ZIqg4hWhIJ1IQQ4io1IioQBw0W78psWEWVJbDkGZwOLQewLWIQQjQ/CdSEEOIq5eFsoru/kSW7Mxu2WbzJFXZ/C9s+4N6Pt/KHL3farY1CiIaRQE0IIa5ifYKMnDxdzu70oiuvxGCAuBvh4Ar8nRTLdmdSUW22XyOFEFdMAjUhhLiK9Qx0wGjQWJLawOHPuJvBUsN49zRKq8ys3pt98dcIIRqdBGpCCHEV83DU6Bfpy+LUjIZVFBwHAVH0y/gMf3dHFqY0sD4hhF1IoCaEEFe55NhgDuWUcjC7+Mor0TToPQMH/06MjQli5d4sSitr7NdIIcQVkUBNCCGucmNiggE7rP7s/zuY+BZT+obzzNhoO7RMCNFQEqgJIcRVLsjTmV4dvFmyu4GBGoBSxDqc4o4B4bg5yeY1QjQ3CdSEEKIVGBsbwu70Io7nlTWsopQv4O0BFB7byfwtxymuqLZPA4UQV0QCNSGEaAWSY/Xhz6UN7VXrMgoMDhzcsoSnvtpVbyN4IUTTk0BNCCFagTBfV2LaeTZ89aerL3QeRa9jHxHq7SyrP4VoZhKoCSFEK5EcE8z24wVkFVU0rKL4m9BK0rm2g5l1B3IoLJPhTyGaiwRqQgjRSoyNs9PwZ9ex4OjOeNZRbVYNr08IccUkUBNCiFaic6AHnQLcGr5LgaMr3PYNcTc+RbifK7vTC+3TQCHEZZO110II0YqMjQ3h7Z8OkV9aha+b45VXFNYXDfjh4cF4Opvs1j4hxOWRHjUhhGhFkmODMVsUy/fYYbhy6wd4rn0JAKVUw+sTQlw2CdSEEKIViWnnSXsfl4YPfwLk7INf3uHP3/3K3R9tbXh9QojLJoGaEEK0IpqmkRwTzPqDuRQ1NFlt/M1grsKl4CBr9mWTXdzA1aRCiMsmgZoQQrQyY+OCqTYrVu/NblhF7XqCX2cmVHyPRdlhL1EhxGWTQE0IIVqZnmE+BHo4NTyw0jSIu5kuGT/QLcCZhSnp9mmgEOKSSaAmhBCtjMGgMSYmmDX7symvMjessviboNMIxndxYcvR02QUltunkUKISyKBmhBCtEJjY4OpqLbw0/4GDn/6doTbvua6QT14eERnjAbNPg0UQlwSCdSEEKIV6hvpi4+ryT6rP4FwUyFPDPQh0MPZLvUJIS6NBGpCCNEKORgNjOoexMq0bCprGjj8WVEI/+5B1c/vsGpvVsP3EhVCXDIJ1IQQopVKjg2muLKGnw/lNawiZy+IHErmzpXc9eFWvvn1lH0aKIS4KAnUhBCilRrU2R93JweW2COtRtzNdCjdQY9Ao6z+FKIJSaAmhBCtlJODkRFRgSxPy6LGbGlYZVHXgsmVCa57SD1VxNHcUvs0UghxQRKoCSFEKzY2Npj80io2H81vWEVO7tBtHONOfwIgvWpCNBEJ1IQQohUb1i0AZ5OBpfZY/TniOdo9uIg+4T78cqSBgZ8Q4pI4NHcDhBBCNB5XRweGdQ1gye5MXpwQg6EhedB8OwLwzm2++Lo62qmFQogLkR41IYRo5ZJjg8kqqmTHyYKGV3ZyK/7f346hqrjhdQkhLkoCNSGEaOVGRAVhMmr2SX6rLLB/CR99v4yp725EKdXwOoUQ5yWBmhBCtHJeLiYGdvJnSWpmwwOr9ongE4EhfRubDuezN1N61oRoTBKoCSFEGzA2Npjj+WXsyShqWEWaBnE3MbbgMwyarP4UorFJoCaEEG3AqO5BGDTss/oz7mb8KWCgfzkLUzJk+FOIRiSBmhBCtAF+7k70jfRlsT0CtYCuEHcz4yMNHMsrI/VUA3vphBDnJYGaEEK0EckxwRzILuFgdknDK7vxvyQnj2dqYhgujsaG1yeEOCcJ1IQQoo0YExsMwNLdduhVA7wdqnltsJHOge52qU8IcTYJ1IQQoo0I8XIhIczbPmk6AL6cgfr8FnadLOB4Xpl96hRC1COBmhBCtCFjY4PZdaqQE/l2CKy6X0fJ6Sxu/M8GPvz5aMPrE0KcRQI1IYRoQ5LtOfwZPQEPBwtDfXL5cVcGFous/hTC3iRQE0KINiTcz43oEE/7DH86e0G3ZCZULCKzqIKtx043vE4hRD0SqAkhRBuTHBPMtuOnyS6qaHhlcTczsuYnnIyS/FaIxiCBmhBCtDFj44JRCpbuyWp4ZV1G4f675YyIDuan/TmS/FYIO3No7gYIIYRoWl0C3eno78aS1Axu6x/esMocnCAknhcnVODtakLTNPs0UggBNGKPmqZp72ualq1pWmqdY7M0TTuladoO62NcnXPPaJp2UNO0fZqmjalzPNl67KCmaU83VnuFEKKt0DSN5NhgNh3O53RpVcMrrCgkeNVjOB9Y1PC6hBD1NObQ54dA8jmO/1MplWB9/AigaVp3YCoQY33NfzRNM2qaZgTeAsYC3YFp1muFEEI0wNjYEMwWxfI0Owx/OnrAkbUs+2kNN8/dSLXZ0vA6hRBAIwZqSqm1QP4lXn49ME8pVamUOgIcBPpaHweVUoeVUlXAPOu1QgghGiA21JNQbxf7bNJuMEDcZMhIYfORfDYczG14nUIIoHnmqD2kadrtwFbgCaXUaSAU2FTnmpPWYwAnfnO837kq1TTtPuA+gKCgINasWWPnZp+tpKSkSd7naiX35+LkHl2Y3J+La8g9ivWqZuW+bBavWI2LQ8PmlrlVRjJMexNXQw3vLfsVMpwaVJ+9yPfQxck9urDmvj9NHai9DbwMKOvXfwB32aNipdS7wLsAffr0UUlJSfao9oLWrFlDU7zP1Uruz8XJPbowuT8X15B75BaRz9J3NlId0I2xPdo1vDHH3yX59H5W5MUzcPBQHB2aP7GAfA9dnNyjC2vu+9Ok/4uUUllKKbNSygL8F31oE+AUEFbn0vbWY+c7LoQQooF6d/AhwMOJJakZ9qmw771MiICiihrWHcixT51CtHFN2qOmaVqIUurMT4RJwJkVod8Dn2maNhtoB3QBNgMa0EXTtEj0AG0qcEtTtlkIIVorg0FjdPcgvt5+iopqM84mY8Mq7DODQQkWrtV24Olisk8jhWjjGjM9x+fARqCbpmknNU27G/ibpmm7NE1LAYYDjwEopXYDXwB7gCXAg9aetxrgIWApkAZ8Yb1WCCGEHYyNDaG82sxP++3TA+ZogLcGV5EY7mOX+oRo6xqtR00pNe0ch9+7wPV/Bv58juM/Aj/asWlCCCGs+nX0xcvFxNLUTMbEBDe8wp2fw3cPkD5tJRW+UXQMcG94nUK0Yc0/01MIIUSzMRkNjOoexPK0LKpq7JD/rNtYLJoj131ygn8s39/w+oRo4yRQE0KINi45Jpjiiho2Hs5reGWuvhi6jmKMcQur0rIpq6ppeJ1CtGESqAkhRBs3uIs/bo5G+63+jL+J8eZVlFebWZmWbZ86hWijJFATQog2ztlkZHhUIMt2Z2G2qIZX2DWZvs6nCDBVsijFTsGfEG2UBGpCCCEYGxtCXmkVW45e6s5/F2BywXjPUq7t04W1B3KoqDY3vE4h2qgLrvrUNO2GS6ij4szm6kIIIa5OSd0CcHIwsCQ1k/4d/RpeYVB3fpdUwQMjujQ8P5sQbdjF0nP8F/gOPfHs+QxF0mcIIcRVzc3JgaFdA1i6O5MXxnfHYGjY3p8Awbv/C6ePwrX/aHgDhWijLhaoLVZKXXAvTk3TPrFje4QQQjST5Jhglu/JIuVUIQlh3g2vsDiTXzev41/pG5gzvS9esluBEJftgnPUlFLTL1bBpVwjhBCi5bsmOggHg8Zie63+jLsJTdXw06EClu3OtE+dQrQxFwzUNE3rdbEKLuUaIYQQLZ+Xq4kBnfxYmpqJUnZY/RnSgx4BRsJMhSyU1Z9CXJGLrfr8QNM0H03TfM/34ALbQgkhhLi6jI0N4WheGXszixtemaahxd/MtZaf2HAwh9OlVQ2vU4g25mKBmhew7SKP6sZsoBBCiKYzqnsQmgaLU+00VBk3mfFdXamxwBIZ/hTisl1wMYFSKqKJ2iGEEKIFCPBwIjHCl6WpmTw+qmvDK/SNJOb22Yz9dDuezrKYQIjLJQlvhRBC1JMcE8y+rGIO55TYpT5N03h7jAfXhtth03ch2hgJ1IQQQtSTHBsM2HGosvw0vD2Akp//y5HcUvvUKUQbIYGaEEKIetp5u9CjvRdL7DVPzcUHOo1g2oYQnlqw0z51CtFGXCw9x/Q6zwf95txDjdUoIYQQzSs5NoSUk4WcKii3T4VxN3MNG9ly9DRZRRX2qVOINuBiPWqP13n+xm/OXXDHAiGEEFcv2/CnvXrVosYx3mknClgkOdWEuGQXC9S08zw/V1kIIUQrEenvRlSwB0vtFag5utEpJpFo4ykWpqTbp04h2oCLBWrqPM/PVRZCCNGKjIkJZsuxfLKL7TRUOfJFxicNZPvxAjIK7TSkKkQrd7FALUrTtBRN03bVeX6m3K0J2ieEEKKZjI0LRilYvifLPhV6hXJz/y4sfXQowZ7O9qlTiFbugglvgegmaYUQQogWp1uQB5H+bixJzeTWfuF2qTMgbwsBq/4Mt8wDZy+71ClEa3bBHjWl1LG6D6AE6AX4W8tCCCFaKU3TGBMTzMZDeRSU2WmfTgdnjh49xGMfrORYnuRUE+JiLpaeY6GmabHW5yFAKvpqz/9pmvZo4zdPCCFEcxobG0yNRbEiLds+FYb2xuQdwjfHnFgoqz+FuKiLzVGLVEqlWp/PAJYrpSYA/ZD0HEII0erFt/einZez/dJ0aBqhPcfQS9vPwl+P26dOIVqxiwVq1XWejwR+BFBKFQOyaZsQQrRymqYxJjaYtQdyKKmssU+lcTcz3riJtOxyDtlpP1EhWquLBWonNE17WNO0Sehz05YAaJrmApgau3FCCCGaX3JMMFU1Ftbss9Pwp39nru0ZgYZi4U4Z/hTiQi4WqN0NxAB3AlOUUgXW4/2BDxqvWUIIIVqKPhG++Ls7sthew59A0I1/5bqEUNycjHarU4jW6ILpOZRS2cDvznF8NbC6sRolhBCi5TAaNEZ1D+a7HaeoqDbjbLJPcPXvCR3g9FG71CVEa3XBQE3TtO8vdF4pdZ19myOEEKIlGhsbzOebj7PuQC6jugfZp9Jv7sOcc5D0O34mzNfNPnUK0cpcLOHtAOAE8DnwC7K/pxBCtEn9O/rh6ezAktRM+wVqsZN5+Is00uauZdXTyWia/IoR4rcuNkctGHgWiAX+DYwCcpVSPymlfmrsxgkhhGgZHB0MXNM9iBVpWVSb7bToP3o8Q0x7OVJoYXd6kX3qFKKVudjOBGal1BKl1B3oCwgOAms0TXuoSVonhBCixUiOCaawvJpNh/PsU6GTB8lRPjhgZuHOk/apU4hW5mI9amia5qRp2g3AJ8CDwBzgm8ZumBBCiJZlaNcAXB2Ndl396dNrIoMMu1j463GUUnarV4jW4mJbSH0MbETPofYnpVSiUuplpdSpJmmdEEKIFsPZZGR4t0CW7c7CbLFTUNVpJOOTx3Gy2MLOk4X2qVOIVuRiPWrTgS7A74GfNU0rsj6KNU2TCQVCCNHGJMcGk1tSybZjp+1ToYMjY/rG8snd/Yht52mfOoVoRS42R82glPKwPjzrPDyUUvI/Sggh2pjhUYE4OhhYnGq/HQU8VQmDtz6Cw56v7VanEK3FReeoCSGEEGe4OzkwtIs/S1Mz7TenzMmL/PRD/GXJAVJOFtinTiFaCQnUhBBCXJYxMcGkF1aQYq85ZQYDppjxfJQXxde/HLBPnUK0EhKoCSGEuCyjugdhNGgs2W2/1Z8evSYz3LCDRSkZ9luoIEQrIIGaEEKIy+Lt6siAjn4ssefwZ2A0431PkVNpZPORfPvUKUQrIIGaEEKIy5YcG8yR3FL2Z5XYrc4RSSNwMVpYuFMyQAlxhgRqQgghLtvomCA0Dbuu/nTtcwvX9wrH5GC0W51CXO0kUBNCCHHZAj2c6RPuwxI77lIA8Nr13ZgVdQpklwIhAAnUhBBCXKExMcHszSzmaG6p/SpN+QI+u4mcg1vsV6cQVzEJ1IQQQlyR5NhgALuu/iR6Aq+ab2XkR+lU1VjsV68QVykJ1IQQQlyR9j6uxIV62XWTdly8SWzvTlGNifX7suxXrxBXKQnUhBBCXLHk2GB2niggvaDcbnUOGTgID0pZuGmH3eoU4molgZoQQogrNtY6/LnUjsOfTlFjGGPayfLDVVRUm+1WrxBXo0YL1DRNe1/TtGxN01LrHPPVNG25pmkHrF99rMc1TdPmaJp2UNO0FE3TetV5zR3W6w9omnZHY7VXCCHE5esY4E7XIHf7rv40OTN+4lSKzQ6s3Z9jv3qFuAo1Zo/ah0Dyb449DaxUSnUBVlrLAGOBLtbHfcDboAd2wItAP6Av8OKZ4E4IIUTLkBwbwpaj+eSWVNqtzkEJMfxrSgIDOvnZrU4hrkaNFqgppdYCv90H5HrgI+vzj4CJdY5/rHSbAG9N00KAMcBypVS+Uuo0sJyzgz8hhBDNKDkmGIuC5XvsN/nfZDQwseAjPBY/Yrc6hbgaOTTx+wUppc6ksc4EgqzPQ4ETda47aT12vuNn0TTtPvTeOIKCglizZo39Wn0eJSUlTfI+Vyu5Pxcn9+jC5P5cXEu4R0opAl01Pl27h5Cyw3arN/TgQVYfq4DK7+ka7HlFdbSE+9PSyT26sOa+P00dqNkopZSmaXZLPa2Uehd4F6BPnz4qKSnJXlWf15o1a2iK97layf25OLlHFyb35+Jayj2aVJ7Ge+uP0LPfILxcTHap09zFh2lvpJKYU8V9U5OuqI6Wcn9aMrlHF9bc96epV31mWYc0sX7Nth4/BYTVua699dj5jgshhGhBkmODqbEoVqbZb/jT2C6ece77WZVuoqSyxm71CnE1aepA7XvgzMrNO4Dv6hy/3br6sz9QaB0iXQqM1jTNx7qIYLT1mBBCiBakR3tvgj2d7bv6U9O4NjaISuXAyq277VevEFeRxkzP8TmwEeimadpJTdPuBl4DRmmadgC4xloG+BE4DBwE/gs8AKCUygdeBrZYHy9ZjwkhhGhBDAaN5NhgftqfQ6kde78Sh11LkGMFP6QV2q1OIa4mjTZHTSk17TynRp7jWgU8eJ563gfet2PThBBCNIIxMcF8+PNRftqfw7i4ELvUafAJZ0LfUg7mlKCUQtM0u9QrxNVCdiYQQghhF30jffFzc7Tv3p/Ac+Oi+PAaDa3guF3rFeKilN3WPF4xCdSEEELYhdGgMap7EKvSsuy69ZNWUQAfJFO8UQZXRBMoy4fN/wVzNSiFZmnebcwkUBNCCGE3ybHBlFaZ2XAw136Vuvrymc9M+qztyekS+23+LoRNWT7s+hIW3A2zo+HHP8CRtWAwoJp5uF0CNSGEEHYzsJM/Hs4Odh/+jIvvRSUmlq7dYNd6hWD1X+BvkfDVPXB4NcROhpEvQsQQ/bzWvKFSsyW8FUII0fo4Ohi4JjqIFWlZVJstmIz2+SUX238M4Uu+YOFOA1PH2aVK0RZVlcH+pbDiBegyBq59HYLjIDgeet4Gfe4CY8sKjVpWa4QQQlz1xsQE882vp/jlcD6Du/jbpU7NyY3xIYW8nd6J3KJy/D1d7FKvaAOqK2Dt32Hfj3D6KFSXgdEJKqwpX6In6I8WSoY+hRBC2NWwrgG4mIws2Z1x8Ysvw/hrJ2HBwOI92Re/WLRtJTmw7UN91WZlMax7HXL2QtxNcPv38Gw63Pjf5m7lJZEeNSGEEHbl4mgkqVsAS3dn8dJ1sRgM9pmMHdWxA3+ZpDE8KsAu9YlWpiQHDq2CfYtg32IwV0Fob31o887F+nOTU3O38rJJoCaEEMLukmODWZyayfbjp+kT4WuXOjVN4xa/A/DpVJixCFx87FKvaAV++L3egwbgFghxN0NQDAR2149FDGy2pjWUDH0KIYSwuxFRgTgaDXZf/amcvfkuw4tVKxfbtV5xFaksgZT5ehqNdbP1Y8E9ICgOrn8LntgLE9+CAQ+Awdi8bbUD6VETQghhdx7OJgZ38WdJaiZ/vDbabls/aaG9eFtNxm1bGSPG26VKcTWoKoVVf4ajayH3ANRU6AsCSqzzFRPv0h+tkPSoCSGEaBTJMcGcKign9VSR/SrVNMZHamwrDyH9xBH71StanqIMSPlCf15wHDa9BdlpehqNO3+E5zJg7GvN28YmID1qQgghGsU13YMwfqOxZHcGce297Fbv+GEDeP3AYRatXsu9t0farV7RAhRl6DsCpH2vLwhQZj3xbGA03PYthA8GB1Nzt7JJSaAmhBCiUfi6OdIv0pfFqZn8YXQ3uw1/RnSOJtYjhYU5AdxrlxpFizDvVti7UH/uEQI9pukrNd2D9GOdhjdf25qRDH0KIYRoNGNjgzmcU8rB7BK71jt+cB/KDW6UVtbYtV7RRCqKYOsH+oKAHZ/rx4Lj9VQaN74Pj+3RFwQk3gWGth2qSI+aEEKIRjM6Jpjnv9vN4tRMugR52K3eewZH8rt4B0jfCJFD7FavaEQVRbDyT3Bis5581lwFRkcoOqWfT3pKf4h6JFATQgjRaII8nekd7sOS1EweGdnFbvU6GA2w6HEqsw/i9Oivbb7XpcUqOA4ZKRA9HtJ/hS3/Tw/OEu+B7hOhfWKL+7dTSpFXWsXB7BLmbznBtQGWZm2PBGpCCCEa1djYYF5ZlMbxvDI6+Lnard41ftN4KFXxw64NRPaQXrUWo+AkHF0He76FA8tAM8DTxyF8ENz6FXRMahEbn1ssiu3HT7Mno4ixsSEEeDhx8zsb2XGygKqa2uAsul/z7mbQ/HdKCCFEqzYmRg/UluzO4L6hnexWb7fewyn5aRMLN2znYQnUWob3x8Lxn/XnXmH6goDwQeDgovecdbmmyZtUXmUG9K3N/t/aw3y57QQORgOHc0opr9bP+bg6MqFHOyL8XSmvNjOxZyidA90J9HDiVNrWJm9zXRKoCSGEaFRhvq7EhnqyODXTroFaSKAfie65LDzpwsM1VeDgaLe6xSUoPw2/fgab/gPXvwGdRkBAN6gug2H/B93GgZ1W+l6qfZlFfLrpOG7ODhzMLmHLkXwKyqv547XR3DOkI6kZhRzOKWVAZ3/6RfphMmqE+bqS1E3fP/Zvk3ucVWfWvuYdmpVATQghRKNLjgnm9WX7ySysINjL2W71jo8N5MVNFvanbqNrwgC71SvOoywPlr0AWan6w1IDBhMUWhcETPhXo769Uor9WcXklVRxOLeUNfuy2XrsNHcOCOfRUd34cVcmH286hlGDyAB3Ovq7YTBo9AjzBmD2TQn8a0rPRm2jvUmgJoQQotElx4bw+rL9LN2dyR0DI+xW79ikIfzpl59YmO3L43arVdSTdxgKjul5zA6uhB2fgMkV+s+EmEnQrpfde84sFsWpgnJ+OZLHktRMEiN8uX9YJ77dcYrH5u+0XefoYMCoaZiVXr6lXwd6h3vTN9IPZ9PZ+3waDE3bw2cPEqgJIYRodJ0D3ekc6M6SVPsGaoHe7vzpuhh6h/varU6BviDg8CrY/S0cWgWO7vqCgG7jYPpX0HGEXVZrllXWsP5gLhalSI4NYX9WMTe98zPlVWaqzkRfwIn8cu4f1oneHXyZ3Ks9w7oF0DvchxAv53qJlIM8nQnytF+PbUsggZoQQogmMTY2mLdWHySvpBI/d/utpLuthyfMnwa9boMeU+1Wb5tkMcM7QyB7t172DtfvaedReq+Zkzt0vvwFASUV1bg7myiprOGRz3+loKyagrIqjuaVYlHg7GAg7eVgvF1M+Lk7ER3syeAu/oT7uRLs6UzHAHcAOvi58vrNZ88ja80kUBNCCNEkxsQE88aqg6xIy2JKYgf7Veziw6YcBwrXbWSMBGqXpzSPDkfnw78ehimfQkg8+EaAyQVGPAcdh1/2sOY3209yILuEsiozB7KK2Xg4D4uC3X8ag5ODgXUHcvByMZEY4cu4uGAKyqoZER0IQKCnM6ueSLL/57yKSaAmhBCiScS08yTM14XFqZn2DdQ0jbe0qRw7Vc7ookw0z2D71d1aWCxgrtQDsF1fwbJn9d6z0hw6gr4goOiUHqhN/eyCVdXUWNifXUxWUSUHs0v4attJiitr+PSefkT4u/Hi97spqqjBzdFIp0B9Qn9sqBdmpTAZDex9eSzGq3CuWHORQE0IIUST0DSN5JhgPvz5KEUV1Xg6m+xW94Tenfm/ZdnsWr+Q+HH32K3eq1JNlb65ee5+qCjUdwY4tgF63wET/g3FGVB2GgKjoN/9bC30o8/4GWf1nFXWmDmaW8bClHQOZJXw2KiudAv2YNwb69ifVbt3q6NRw9vVkTJrvrJ3pvfG3dmBuFCvevPHzpAg7fJIoCaEEKLJJMeG8N91R1iVls3EnqF2q3dM/wSeW7aYH3aeJH6c3apt+cryIXMXbP8I/Lvpe2WmfQ9f3a2fd3CBoBho1xNC++jHBjwIAx+yVXFiySpO7kinZwdvwv3cePXHND7eeIwqswWzpXZC/4joQLoFe3D7gHBSTxVxY+/2dA5wx8etfv66gZ39G/1jtyUSqAkhhGgyPcO8CfJ0YnFqhl0DNS9XE0PawaLTPXmmxozB4ezUDFc1cw0UngDfSH3/zI8n6kOVNRW11/h10QO1iMEw/FkITYSOw8BgxGKxUFljwQX4+XAeryxMw8fVxKGcUjKLKoAd3D+0I8+MiybAwwkvFxOTe4fSJcgDPzdHuod44euuB2TT+0c0ww1ouyRQE0II0WQMBo0xMcF8sfUEZVU1uDra79fQ+MG92LkojVNFlYT52m9P0SZnsUDaD7B/CTi66j1mp7br6TCeywInT6gsBo8Q6HMXBMeCX1fwbg9AgdGXj2tuwHAcju9IZcvRfI7kljE2Npi3p/fmSG4paRlFRIV4MLCTH0V5WXSJDGda3zAA7hnSkXuGdGzOOyDqkEBNCCFEk0qOCebjjcf4aV8OY+NC7Fbv+Ph2XNfNHYfDP4LPjU2+fdFlUwqKs/QM/3sXQsZOuHMhODjDV/eApUrPXxYcD93G6ntnWszg4k3xw3s4mlvG8fwyNqfmszxtPwnts/jP9N78eryA2cv3A+Dv7kiwpzNdAt0Z0MkPgJv7hDEtMQyDNQ/amjVrSEqKarbbIC5MAjUhhBBNqm+kLz6uJpbszrRroOboYIBdC1HfPgje4WhhiXaru8GqK+DEJj2Lv7MnfHKjnuWf2jlgOLhAUQb4d4bJ74OrD8WBfdidWco3v57CrdqBF4wOHMwu5prZa+tVbzRoFJXrvYi9I3z499QE+kb4EuLtclZTTMbm3btSXB4J1IQQQjQpB6OBUd2DWLwrk8oaM052nE+2x2c491bNYfa6ZfS7pRkDtWMb4Zd39L0wi05BZipYqmHKJxA9ATza6fPNuk/E0nE4e7VIjhQbGesbQnWNmTGL3MkrLaW4YqWtSqNB45lxUbT3ceW6Hu2ICvFgaJcAOgW44+JYew89nU1cn2C/+X+ieUmgJoQQosmNjQ3hi60n+flgHsOjAu1Wb3hIEHl4s3BfGv3M1Xar95wsFsg/BLkH9DlkOz6BkbMgYSrs+BT2fKvvidk+EfrcjaWmEhXSCyPwisNMUp1voWq/hQPriimuTAFg3f95E+bripODkS6B7lzTPYjOAe64mIwkRvhgMhowGWHOtKtrY3Fx5SRQE0II0eQGdvbDw8mBxakZdg3U3JwcGNnByOJj8bx4cDXgeNHXXJIzuck82kF4f9jxOXw7k3pDl0YnvfcM+LXLw2xWN1DuGsrB3FJ++iWH0qoa5se7kOgNS1IzyS6upFcHb67vGUp5lZn49l74W7fWWvrYUPu0W1z1JFATQgjR5JwcjIyIDmT5nixqzBYc7DhvavzAeBYd28UvO3dD4BX2PBVlwNLnoOCYngIjZ58+dBnaG+5dBb4dOR3Yn3yfOLb7TWDhcQcO51fwUmAsw4E//5TH1mPlaNpBQr1d8PdwIsrdAx9XPXBc/thQXOy44lW0XvJdIoQQolkkxwTz3Y50Nh/Jt2uS1OHdQ3Fz3M1Ch5GMIf/8F5pr4ORmKMnWU2Ds/gacPOD+n6A0G3Z/hTI4khOWzE/h09hR6MwNcZ3oDfxxuyufHH8YjgMUY9D0xQwllTUA/PHaaE4WlDMyKqje/LEzJEgTl0q+U4QQQjSLYd0CcDYZWLI7066BmrPJyNNjown3c8NyKk8/WFUGB5ZDThokPQ3lp+HvXfReMqBKmUhziiPU0Q1/YEVeAI9aPgdloGSf2VZ3xQkfeveH0d2DOZFfzpTEMKKCPejg61qvVzChgw8JHXzs9plE2yWBmhBCiGbh6ujAsK4BLEnNZNaEGAx23APytgER8MWd1OxbArvawekjoCz6yT53caLKnVdNfyLWcJxFhqHsPa1hrlT08vHha8DkaMLZ0cTgzv70CPMm2NOZUG8XYkM9ARjaNYChXQPs1l4hzkcCNSGEEM1mbGwIS3dn8euJAnqHN7AHqvCknhKjz11UeUawprQj4dW+/FRxDauce7G9wJVu7hX84BZA3ulCfiyMYLN7V+JCvYjv5ExVjYVJPfXs/sO6BrD1j6Ps8AmFaBgJ1IQQQjSb4VGBmIwaS1IzLjtQU1XlVKd8hWNINGUBPXht6QmG797I8NDeFDi04759vYHeOBYa6ODriq9nDTFdI0DTiG3nSeqsMbg7y69B0bLJd6gQQohm4+ViYlBnf5bszuTZcdFoF9j2afW+bDyKDtEnSMPSvh99/7qeydWbeHpQGs6jerH4QCkdkt5ieEwUAUrxn1t7kXFoD3dMGH7WqlIHowF3ydAvrgISqAkhhGhWyTHBPP31Ln49XkA7bxeCvZwBmPX9btyNNfwhwQyhvfjT97uJKd9Knw4/YbhzIbcNiCDO+3fQOwaDprH52ZG2QE/TNMbFhbAmb59dU38I0dQkUBNCCNEsVu/N5mRBOeNig3n2m108/PmvBHk68fW0UPCJoKyqBsPxlbD3v/D4Hv7fHYkElPlC4N0A/P6aLvXqu1BvnBBXK/kzQwghRKPIL61i69HaPGZvrT7I9W+ut5UXp2bw9uqD+DnW0D/CB4tS3B+QCnN6QXkBf5vcgxemDoebPgSgc6A7XhE9wNW3qT+KEM1GAjUhhBBXzGxRKKVvo/TL4Tye/HIn1WY9DcaHPx/l5rkbqajW85AFeTrTJcgDs0WBUjw/vjvrJgN/jWRaeCEZhRVExfWB8bPBYB3wadcTOvQD6S0TbZQEakIIIS5JXkklP+xMp7BMTxK7KCWD6BeWcPJ0OQAnTpezZn8OOcWVAEzqGcr/7u6H0ZofbXLv9rw+2h/jf/pC6ld4OJswhsRD4t30j44E4Id0T+h9Jzi5N/0HFKIFkkBNCCGETWF5NaXWbZAO5ZRw14dbSDlZAMDezGIe/vxXUtMLAX0o8s6BEZisk/Vv7BXKlueuoZ23CwCR/m4M6uiD6asZsGGO/gYewRAQBS7eetk9AJJfJSA8ip4dvFmyO7PJPqsQVwMJ1IQQoo0qq6rho5+P2gKxo7ml9PjTMhan6sGSk4OB9IJyisr1wC0hzJsfHxlCnwg931m3YA+eHRdtW6Vpm8y/8S1Y9Yr+3GAEVO2uAAYjTPkfdL7mrPaMjQ0m9VQRJ/LLGucDC3EVapZATdO0o5qm7dI0bYemaVutx3w1TVuuadoB61cf63FN07Q5mqYd1DQtRdO0Xs3RZiGEuBodzS3leJ4e+FSbLUz6zwbeW38EAKNB408/7GbNvhwA2vu48PTYKHq097KWXVny6FAGd9H34XRzcqB7O0+cHH6zyfjhn2Dly7Xl7DTITK0t3/wxDH70om1NjgkBYKn0qglh05w9asOVUglKqT7W8tPASqVUF2CltQwwFuhifdwHvN3kLRVCiBbMYlG253N/OsS8zcdt5cnv/Mybqw8AYDIaCPV2wcvFBICTg5Ffnr2Gh0d0BvQksL8b1okuQR4XfsPTx2D9v8Csz1Xj1FbY9gFUFuvlCXPglnmX/Tk6+LnSPcTT1qMnhGhZQ5/XAx9Zn38ETKxz/GOl2wR4a5oW0gztE0KIZrcnvYh1B3Js5X9vr+Cuj7bYysv3ZPHzoTxb+e+Te3D34I628pu39GJy7/a2coCH08Xzj1WXw77FUGJ934ydsOJFyEzRy/1mwh8OgJM1wDNc+a+W5Nhgth07TXZRxRXXIURrop1ZVt2kb6ppR4DTgALmKqXe1TStQCnlbT2vAaeVUt6api0EXlNKrbeeWwk8pZTa+ps670PvcSMoKKj3vHmX/9fc5SopKcHdXVYmnY/cn4uTe3RhbfH+KKUorgZPRz14WnOimkMFFu6OcwLgrR0VHCuy8LehrgAs2l+Co6MToyL0XjKLUhjskMrCpSwDi8GBSucAXEuP03fLw+zr+iAZ7UZjMFfiUFNClZNfg9/nt06VWHhufTm3dXdkZAdTg+tri99Dl0vu0YU1xf0ZPnz4tjojjPU0184Eg5VSpzRNCwSWa5q2t+5JpZTSNO2yIkil1LvAuwB9+vRRSUlJdmvs+axZs4ameJ+rldyfi5N7dGFt4f6kZRSx/kAu9wyJRNM0Xv0xjY82HmXPn5IxGDR2rTzAnrJchg3rj6ZpdIgpwWjQCPdzs9Zgp3tUUwVleeAZAlWl8NcI6HsfJP0ZlILukXQL60c3B8eGv9cFKKV4b99PHKp05uWk/g2ury18DzWU3KMLa+770yxDn0qpU9av2cA3QF8g68yQpvVrtvXyU0BYnZe3tx4TQogWr6LazJ70IlvS1xV7shjzz7WcLq0CYPORfP78Yxo5JXrusVHdg3h2XDQ11nlnD4/swhf3D7ANT3YMcK8TpDVQVZ3Vlf8dDgsf0587usGN70Hfe/WypkHkEGjkIE1/K42xscH8ciSffOs9EqIta/JATdM0N03TPM48B0YDqcD3wB3Wy+4AvrM+/x643br6sz9QqJTKaOJmCyHEBZ2ZRnIiv4w/L9rDsbxSAH7an8O4OevYl6lPtPdwdqC9jwulVXrKixt6hZIyazSBHnqKiz4Rvtw+IAJHh0b48Vx3qsuiP8DcobXlIY9D4j215e7XgU+E/dtwCZJjQjBbFCv2ZDXL+wvRkjRHj1oQsF7TtJ3AZmCRUmoJ8BowStO0A8A11jLAj8Bh4CDwX+CBpm+yEELoKqrNrD+Qa8v1dSinhD6vrGDpbj2oKKms4aONxzicowdqvcN9ePOWnoT76XPK+nX04707E2nvo5c9nE14Ojd8LtZF7ZwH/4yp7UXrOAwSbgGzHjASeyN0OTu3WXOIDfUk1NtFkt8KQTPMUVNKHQZ6nON4HjDyHMcV8GATNE0IIQCoMVuoqLHg7uRARbWZZ7/ZxcioIK6ND6Gi2sz0937h2XFR3De0E8GezgzvFkCgpz7Zv1uQB2kvJdu2TfJ3d2J8fLum/xDpO2DxU3D9m+DfBbzaQ8QQqCwCR1eIntD0bbpEmqaRHBvM/zYeo7iiGo+mCGSFaKFaUnoOIYRoFj/uymDtfj31hFKKPn9ewT+W7QP07PwpJwvJtKaL8HZ1ZN59/bmptz511s3Jgb/f1INeHfRs/QaDZgvSmlRZPnz/CBxeo5ddfKCmXD8OEDEYbpirb+F0FRgbG0yV2cKqvdkXv1iIVqy5Vn0KIUSTKSyrJr+sikh/fRL+s9/swtFoYNZ1MQD8e8UBwnxdGdo1AE3TeHhEF7oG6cvxNU1jxePD6tXXv6P901JckU3v4J+TDyTpCwAOLIN2CdAxCXzC4f61zdu+BujVwYcADyeWpGZyfUJoczdHiGYjgZoQotVZujuTI7ml/G5YJwAenvcreSWVLHpkCADODkZMxtperw9mJOLrVrui8e7BkU3b4POpKITSXPDTPwdf36cHZOP/qZe3fYi/wZr/28EJHtvToGSzLYnBoDEmJoivtp2ivMqMi6Px4i8SohVqHf+jhRBtSmZhBav31Q6JvbHyAEl/X20rrz+QyyebjtnKvxvWkaeSo2zlFyZ055lx0bZyO28XnE0tIBA4uAJ+ebe2/OWdsGBGbdkjBNzrDF3es4K90b+vLbeSIO2M5JgQyqvN/LQ/5+IXC9FKta7/1UKIVqOi2ozFmk7i50O5PPDpNlsusq+2n2TGB1soqdRXLHYOdGdY1wCqzRYA/jg+mnX/N9xW18BO/gztGtDEn+AczNWQd6i2/Mu78N7o2vLeH2Ht32rTaAx6FEa+UHt+1J8g6anaslPrzibfr6Mv3q4m2aRdtGkSqAkhml12cQXzNh8n15r09cddGUS/sITMUj1gKSirZk96ETnF+vnrE9rx7YODcLLmGhsbF8Kfro/FZNTLTg7Gi+9f2RRy9sO62VCjt5sN/4I3etVuXu7kAe5BteeveREe36snmAU9hUbnlpEyozmYjAauiQ5iRVoWVTWW5m6OEM1CAjUhRKNTSpFRWE5hWTUAh3NKmDJ3I1uO6isSj+eV8fTXu0g5WQBA9xBPHh3ZFRfrLNpxcSGseXI4Yb567rH2Pq4khHnbArNmoxSUZOublgMc3wT/HVnba5a1C1b+CfIP6+Wo8TBpLmjWdidMgyn/0+eXATh7gVGmDtc1NjaY4ooafj6U29xNEaJZSKAmhLC78iozb60+yOYjeiB28nQ5A15dxaJd+qYi7s4OVJsttl6S2FAv1j45nGFdAwGI8Hfj99d0wce5hf2IKi+Are9D7gG9fOIXeL0LHF2vlx3dwOQC1daksl3HwtPHIdA6Hy4wGnpM1a8Tl2RQZ3/cHI0sSZXhT9E2tbCfgkKIq8Xu9EL2Z+lDeBaLIvlfa3ljpR7AmIwa/15xgE2H8wAI9Xbh5Ymx9O/oC0CghzNfPzCIQZ39AXA2Geng59o8+cd+q7pcD8hA//rJjZD6lV6uqdD3wzxkXbgQGA3JfwX/rno5OA7uXKh/BT2xrLNXU7a+1XE2GRkRHcSyPVmYLeriLxCilZFATQhxXmcm74O+svK99Uds5fs+3sZbqw8CeiqFnh186GDdJsnBaGDHi6N4ZGQX2/nb+ofTMaAFTn7f/S0cseYbM9fAXyP0uWQATp56igyzPmSLexA8uqt2s3JnL+j/Oz1nmWg0yTHB5JdW2XpohWhLZDKEEAKAX4+fJquokuRYPf3DXR9uobSyhvn3DwBg+/HT+LjW5hqbfXMPAj2dbeVXb4irV5+rYwv58WKxQGWhnqkfYMkz+tDjiD/q5ZV/0nvAIofq88NGvVzbI2YwwD0rauvSNPDu0LTtFyR1C8DJwcDS3ZkM6NRCkg0L0URayE9SIURjqzFbyCissE3I/3jjUTYczGXubX2s5WNsOpxnC9TGxYXUW2n3wYy+9err11Ky8//WqW1QcAJiJurlTyfrqyzvWa6XKwpB1VlBeNs3ek/ZGf3ua7Kmikvj5uTA0K4BLEnN5IXx3TG0hCFyIZqIBGpCtFKppwpZtieLR0d2wWDQmL18P++uPUzay8mYjAZqzIryagsWi8Jg0PjDmG441llFObl3+2Zs/UVUltTmENvxORxYCjd9qJe3vg/7ltQGar1uq01/ATDxP/Xr8olo5MYKexgbG8zyPVnsPFlAT+u+qkK0BTJHTYirVGllDVuO5lNWpSd9XbEni8F/XUVmob55+K5Thby56oBtM/FxcSH89cZ4WxLZuwZH8vFdfW29E6HeLgR4ODXDJ7mIwpOw4zN9/hjA+n/Bax2gWv9cVBRC4SmoqdLLSc/CA5tqXx8zSV9pKa5qI6ODcDBosvpTtDkSqAnRgimlqLFm2z+eV8az3+zigHWl5eaj+dz0zkZSTxUBEODhRK8OPrbs/JN6hpL2cjLtvF0APQXGjb3b4+TQArZKqstihtNHocqa0uLEFvjfDVBwXC8fWQffzqzNRRYxGEY+DxbrBP/+v9OHNR2s8+e8QsG9BexCIOzKy8XEwM7+LNmdiVKy+lO0HRKoCdFCVFSbWZKaycHsEgCO5pYS++JSW+6xGouFRSkZnDitBzS9wnz44M5EugV7ANAjzJs503ra5qA5m4wtJyhTqrZHrCgDlj0PWbv18rEN8O8ecHJz7fVleXpPGUDXMfDQ1tqNydv3gcGP6Vn9RZsyNjaYY3llpGUUN3dThGgyEqgJ0YTKqmrIL9WH6KrNFt74tYIvt54AwGxR/O6TbSxJ1QOzEG9nbuoTRoSfnhw10t+NHS+MYkSUPvHdy9XE8KhAvFxMzfBJLqC6AnbOh8xderngBLzaHlLm62VzFfwyF3L26eWgWJgwpzYXWVgi3P9T7cpLV1/w7wKGFhJ0imYzqnsQBg2WyN6fog2RQE2IRvT19pP15tQMem0V/1imBygmo4GiSkWpdWNxNycHFj48mBmDIgF9v8pZ18XQI8wbAE3TWsb+lQCZqbXZ+S1meG8MbLRO0tc0+PZ3kPaDXvYIhp7T9WAL9PQWz2VA7A162dUXet8Bnu2a9jOIq46/uxOJEb62P2aEaAskUBOiATILK9idXmgrP/nlTh7/Yoet/MGGo8zfctxWfmZsNBN61AYkz/V34U5rYAb6PDI3pxawGLumCkrr7K24/MXaQAzgkxv0Sf2g93R5BNcORTo46UOVQ57Qy0YTjP0rhFnTe2ia9I6JK5YcG8z+rBIO5ZQ0d1OEaBIt4DeCEC2b2aJsWxstTEknLaOIJ8dEAfDHb1M5llfK8seHARDi7VJvovPHd/WtNzR5c2JYE7b8IpTSgybQs/OX50Ofu/TyB2P1wOv2b/Vy9h6oqvOL8Yb/1u8Bu/mj+nWfmU8mhJ2NiQnmTz/sYUlqJg8O79zczRGi0UmPmhB1nMgv44ed6bbyv1ccoM8ry23B147jBSzeVbvq7MHhnfhLnYz8j4/qyhOju9nKPm6OLSM5Z3Ya7Pm+trz4aZg7tLa851vY/N/a8sCHIPHu2vKtX8K1/6gtdxxWO5QpRBNq5+1CjzBvSdMh2gwJ1ESbk19aZUt5seFgLne8v5niCj3Vw9LdmTz8+a+2Cf/xYV5M69uBKuv1z46LZtUfkmxzxXp28CExwrcZPsVvVJZA+q96LxnAznnw/tja8q+fwNf36tspAYT0gM4ja19/3Zsw8+facswkiJ7QNG0X4jKNjQ1m16lCTlpXQAvRmkmgJlq1rKIK3lt/xJYEdklqBr1eXs7+LH0Yr8psIbekktOleqB2XUI7lj821DZcObxbIP+XHGVLc9GsvWPV5frEfYCT2+C7h2pTWGz/GN5N0tNaAKDpc8XODFf2nwkPbKwd6kyYBtfMqq3byb32nBAtXHKMvs2Z9KqJtkACNXFVM1sUB7OLyS3Rtwg6mlvKhDfWs3Z/DqAHai8v3EPKyQIA4tt788dro/Fz15OjDu8WyKJHhtDBT889FujhTJcgD9uctGZTnAmb3tEz7oO+JdKfQyArVS+XZML+pfp1AN2SYconYNKT29Jjij6/7MwEf6/24NtRgjHRKkT4uxEV7MFSSdMh2gAJ1MRV4cycsIpqM39futcWiOWVVnLN7LW2eWU+ro54u5pwsAZa0SGebPvjNYy2/gXeztuFe4Z0JMjTuWk/gMUCJdlQoe8iQE0lHFyBU4X+Ocg9CG/0gf3L9HJxJix5CtK36+XAaEh6Glysw6zdxsGTByDAOh/Ot6M+VOno1nSfSYhmlBwbzNZjp8kurmjupgjRqCRQEy3O1qP5th4wpRTDX1/DX5foucecHAz8b+Mxdp7Qzwe4O/HvqQlcE12bBPZ/d/djYGd/QM9V5ud+iftXWsz1N+/O2g2nj9WWU77Utzc6Y9nzsG+x9bUW+Ph6+PVTvVxdAX/vXJvSoqoYXu+iD1GCPqfskxvxz7XuSenmB4FRtRuNB8XAk4cgarxe9gnXAzVv66pR6RkTbdzY2BCUgmW7s5q7KUI0KgnURJOzWBSFZdW28j+W7WPOygO28pMLUnh7zSFAT/I6OiaI2FBPW3n786N4eGQXKM1FK87g+oRQfduk47/A8Tqbcf/6CexaUFte9kfYMKe2/MmNsPS52vK/4mHR47Xlj6+H9f+sLf/4B9j1ZW155zw4Ze3xMhj03GMW6zZJDk56kHUm276ju75qsmOSXnb2gruWkh2op/XAxUcfugwfqJeNJnDzl4BMiPPoGuROpL+bzFMTrZ7kURONRrOYoaKIX9KrOXG6nMkda6A0lxnLLBSWV/PtOAsUneJ4fjf+f3t3Hp11dedx/P3NRhKWBNkSE5QIyBYXNEJxQUDUYN3q2FHautaDPaOOSx2LnTNOpTN1bJ1Wz8yIZUSmi0Wty0gdRLTCIIyKgsoSoCJEkkCCbIFAINudP+6PLCgJAnl+vyf5vM7JOc/34SHPN/eE8Mnv3t+9XZISfLDatYl/m3yHX0P2559CZSkPXvNr/wlfuAmqtpJ0a3AV68VboL4Wbp3n67d+4jdSvfk1X384C1J7wGnX+nr7hpZXzHqfChnN9jU77+6mK1YA33oKumc31bcv8gHroL9rCpcAHOwLfMC64vGmOiERzrmtqU5MgpO+Qe2GhW2Mooh8FTOjMD+LGYs2sGtfDZnpKWG3JNIuFNTkmO2rqePz7fsY1jcNylcyq7gnb6wu5zF7BpbewiuDX+PNogquHTkXiuZw3aTFVNfUw4p/gfVv8cQP1/pP9KdZUL6C/PE/9nVisg80Bw2cAAeaHcZ87t3gGprqK55oueP9LXMhsdkP78l/aNl44SMt69FTWtaDJrase57c9mCISMwUjshi+sLPeLOogm8XRGgzaZHjSEFNjphzDjPj45JdzPl4Mw9eNpTkveXMeG83Tyz4jDWF60ld8BDpFy0hMy2Fiq6jyT19LPePGMI/XD4cKnNhxDVclhdcpRo2DSY+3PQGza9AgV+T1dzZN7WsBx8SpPqc2rJOOsK1aSISl07PzeDEjFTeWF2uoCYdltaoyZfs3l/LwnVbqaz268jeKqpg5LT5lOyohvpaNpTvZPbSTZSveBt+OYxv9q5g+nfPguFXwl//jutGn8JTN5zNnhNOh9G307tbF39+Zd9hkHdB0xuln+AX0YuIHAUz49L8LBZ9uo2qA3VhtyPSLhTUOqmaugb21/rNUzdt38c9z33EqjK/eeqqskpunvUBK0t9nZvZhcL8bGxvBTyaxxVuIasfvpT+w0bBxIcZPHAQhfnZpPbJ82EtJT20r0tEOpdJ+dnU1DWwYO3WsFsRaRcKap3A/tp6Xl5eyurNPniV7NjH8IfmMSfYeywx0figuGk/otNzM3nh9jGMzO0BM8YzdOUveOSa0+jffwAU3Exydr7foT+1B5x/D2TkhPSViUhnd/bJPendLUV3f0qHpaDWQWyrOsCWymrA79Z/4zNL+e27xYC/AfH+P37S+IMsOyOVH1w4kOHZfsuLnMw0lkydwISh/eD1H9HttR8wKu8EuqalwIDz/Z5eBz/RJf8E/c+J+dcnIvJVEhOMS0ZksWDd1sZZApGOREEtTs1euolXPiptrCc98Q7/Ov8vgP/BlZxgjQeHd0lK5O0fjuNvLxoMQFJiAvdfOoT8nAy/QevsyU2fOL0XdO3TVF/yUzjzO+3/BYmIHKXCEVnsq6lvPLFEpCPRXZ8RVbxtL9uqDlAwwB8ZdN/zH7PnQB3/eWMBAC8tKyUjLZlvjcwF4OErR5CV0XQs0sybW171GtA7OFqoZCm8++9w9VN+LVn9AX9w94Eqvyv+hQ/E4KsTETl+xgzsRY/UJOatLm88Lk6ko1BQC9H+2npSk/2+X//9URnLN+1k2lX5ADw2fx0rSitZ9MB4AIZmd+dAbdOeYb/7/mjSUpr2DLvstGYbszZXWQbvPwVn3wy9Bvp9yEqXwc5i6DccCm71HyIicSo5MYGJw/vxVlEFNXUNpCRpskg6Dn03x8iGL6r4w/ubGg8Xf/ytv3DmtPnUN/h647a9LN24g4agvnPCIJ787lmNf3/K2IH+2KRA85DWQm2135G/9ENfu3p4bzps+cTXp4yHe1f5kCYi0kFMys9m9/463tuwPexWRI4rBbXjpKHBUbJjHwfq/GLWxZ9u49rp/8f2Kn9k0ZL12/jxKyup2O3r0Xm9uGvCYGrr/VWyey8+lXn3jPV3UwJDs3r4NWRHYuMi2PiOf2yJ/kzLold9nXkSTP0c8q/xdUKCzo8UkQ7ngsG9SU9J5HXd/SkdjILaUdpSWc2cz2rYtH0fAH9eu5ULfr6A1Zt3A35Bf0KCsWe/34TxijNOZMnUCfTt7nfLHzOwF3eMH9Q49fm17CqB4sVN9etTYdEv/OOkFLhjKVw8renPU7p+/fcQEYkjqcmJjB/alzeLyhtnKkQ6AgW1o7S7uo6XP62laIvfm+yM/hk8cs1p5PZMA3wQe+H2MY2L+DPTU8jJTGu8Yva11B2AsmVN9fy/h5dug2AalW/PguubnWOZkaOrZiLS6UzKz2JbVQ0fFu8IuxWR40ZB7SgN6tuNX09MpzDfL+Lv2z2VyaNOom/31Db+5hHaVQINwc0Dix6DpydC9U5fXzgVbny16bV9hvg7NkVEOrFxQ/qSkpTAvNWa/pSOQ0HtKCUmGF2SjuNVq7oD/gNgzZ/g8XwoD24AOON6uO5ZSA6OZuo33IczXTUTEWnUrUsSYwf34Y1V5Y03bonEOwW1MDUEu2hv/wwezYOiOb4+aQxc8s/Q/URf9xoIQy+DpC7h9CkiEicK87PYXLmfFcFZxSLxTkEtDHU18OQY+N+f+7pnnt/nrPcgX3ftDefeCd37hdaiiEg8mjisL0kJprs/pcNQUIuVOXfBq3f6x0kpcMo46HOqrxMSoPBncOLI0NoTEekIMtNTGDOwF/NWbdH0p3QICmrt5YOZ8MJNTXV675ZnaBY+Avl/Ffu+REQ6uML8LIq372NdxZ6wWxE5Zgpqx8vGd3wwq6/1dW21P66prsbXE//Rf4iISLu6eHg/zOD1lZr+lPinoHa0dhYzcP1Mf5Ym+K0zNn8ElSW+PvdOuOFlP80pIiIx07d7KuecfAJvaJsO6QDiJqiZWaGZrTOz9WY2Nex+qK0mp+x1qFjl66GXw92fwAmnhNuXiIhwaX4Wa8v3UL63IexWRI5JXAQ1M0sE/gOYBAwHJptZuKeK9xnK4vOfhVMv9bXO0BQRiYzC/CwAllXUhdyJyLFJCruBIzQKWO+c2wBgZs8BVwFFoXVkRkOi9jUTEYminMw0Ts/NYO7GStY/uSTsdiJtd2U1TxRpjA4npWY/48aF9/7xEtRygJJmdSkwuvkLzGwKMAWgX79+LFy4sN2bqqqqisn7xCuNT9s0Rq3T+LRNY3R4E/rWUVPlqN2ruz9bk2z1GqNWpCXVhfpvLF6CWpucczOAGQAFBQVuXAzi78KFC4nF+8QrjU/bNEat0/i0TWN0eOOAMzU+bdL3UOvCHp+4WKMGlAH9m9W5wXMiIiIiHVa8BLUPgMFmlmdmKcD1wJyQexIRERFpV3Ex9emcqzOzO4E3gETgGefc6pDbEhEREWlXcRHUAJxzc4G5YfchIiIiEivxMvUpIiIi0ukoqImIiIhElIKaiIiISEQpqImIiIhElIKaiIiISEQpqImIiIhElIKaiIiISEQpqImIiIhElIKaiIiISESZcy7sHo47M/sC+DwGb9Ub2BaD94lXGp+2aYxap/Fpm8aodRqftmmMWheL8TnZOdfnq/6gQwa1WDGzD51zBWH3EVUan7ZpjFqn8Wmbxqh1Gp+2aYxaF/b4aOpTREREJKIU1EREREQiSkHt2MwIu4GI0/i0TWPUOo1P2zRGrdP4tE1j1LpQx0dr1EREREQiSlfURERERCJKQe0omNkzZrbVzFaF3UsUmVl/M1tgZkVmttrM7g67pygxs1QzW2pmnwTj83DYPUWVmSWa2Udm9lrYvUSNmRWb2Uoz+9jMPgy7nygys0wze9HM1prZGjMbE3ZPUWFmQ4LvnYMfu83snrD7ihozuzf4Ob3KzGabWWrMe9DU59dnZmOBKuC3zrn8sPuJGjPLBrKdc8vNrDuwDLjaOVcUcmuRYGYGdHXOVZlZMrAYuNs5917IrUWOmd0HFAA9nHOXh91PlJhZMVDgnNP+V4dhZr8B3nHOPW1mKUC6c25XyG1FjpklAmXAaOdcLPYgjQtmloP/+TzcOVdtZi8Ac51z/xXLPnRF7Sg45xYBO8LuI6qcc1ucc8uDx3uANUBOuF1Fh/OqgjI5+NBvTIcws1zgm8DTYfci8cfMMoCxwEwA51yNQtphXQR8ppD2lZKANDNLAtKBzbFuQEFN2pWZDQBGAu+H3EqkBFN6HwNbgTedcxqfL3sceABoCLmPqHLAfDNbZmZTwm4mgvKAL4BZwfT502bWNeymIup6YHbYTUSNc64MeAzYBGwBKp1z82Pdh4KatBsz6wa8BNzjnNsddj9R4pyrd86dCeQCo8xMU+jNmNnlwFbn3LKwe4mw851zZwGTgDuCJRnSJAk4C5junBsJ7AWmhttS9ARTwlcCfwy7l6gxs57AVfjQfyLQ1cy+F+s+FNSkXQRrr14CnnXOvRx2P1EVTMUsAApDbiVqzgOuDNZhPQdMMLPfh9tStAS/7eOc2wq8AowKt6PIKQVKm12tfhEf3KSlScBy51xF2I1E0ERgo3PuC+dcLfAycG6sm1BQk+MuWCw/E1jjnPtl2P1EjZn1MbPM4HEacDGwNtSmIsY596BzLtc5NwA/LfO2cy7mv8lGlZl1DW7UIZjOuwTQXejNOOfKgRIzGxI8dRGgG5q+bDKa9jycTcA3zCw9+H/tIvya65hSUDsKZjYbeBcYYmalZvb9sHuKmPOAG/BXQQ7e+n1Z2E1FSDawwMxWAB/g16hp+wn5OvoBi83sE2Ap8D/OuXkh9xRFdwHPBv/WzgR+Fm470RKE/IvxV4rkEMHV2BeB5cBKfGaK+SkF2p5DREREJKJ0RU1EREQkohTURERERCJKQU1EREQkohTURERERCJKQU1EREQkohTUREQOw8zyzOx9M1tvZs8Hu7gf+pqfmFmZmU0L6uuC12vLFRE5ZgpqIiKH9yjwK+fcIGAncLg9E3/lnHsIwDn3PHBbjPoTkQ5OQU1EOjUzG2Bma83sWTNbY2YvNtuJfAJ+w0uA3wBXh9aoiHRKCmoiIjAEeNI5NwzYDfwN0AvY5ZyrC15TCuSE1J+IdFIKaiIiUOKcWxI8/j1wfpjNiIgcpKAmIgKHnqXngO1AppklBc/lAmUx7UpEOj0FNREROMnMxgSPvwMsdv4g5AXAtcHzNwGvhtGciHReCmoiIrAOuMPM1gA9genB8z8C7jOz9fg1azND6k9EOqmktl8iItLh1Tnnvnfok865DcCoEPoREQF0RU1E5FhVAVOab3gLPInfd01E5JiYX4YhIiIiIlGjK2oiIiIiEaWgJiIiIhJRCmoiIiIiEaWgJiIiIhJRCmoiIiIiEaWgJiIiIhJR/w9ribxpt4q8sAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 14;\n",
       "                var nbb_unformatted_code = \"linestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\nlinestyle_total = \\\"--\\\"\\ncolor_expected_val = \\\"tab:blue\\\"\\ncolor_observed_mean = \\\"tab:orange\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_list,\\n    label=\\\"average observed MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_list,\\n    label=\\\"expected MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bias_list,\\n    label=\\\"||biases||\\u00b2\\\",\\n    linestyle=linestyle_bias,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_var_list,\\n    label=\\\"average observed ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_var_list,\\n    label=\\\"expected ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_expected_val,\\n)\\nax.set_xlabel(\\\"p0 []\\\")\\nax.set_ylabel(\\\"MSE []\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_formatted_code = \"linestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\nlinestyle_total = \\\"--\\\"\\ncolor_expected_val = \\\"tab:blue\\\"\\ncolor_observed_mean = \\\"tab:orange\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_list,\\n    label=\\\"average observed MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_list,\\n    label=\\\"expected MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bias_list,\\n    label=\\\"||biases||\\u00b2\\\",\\n    linestyle=linestyle_bias,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_var_list,\\n    label=\\\"average observed ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_var_list,\\n    label=\\\"expected ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_expected_val,\\n)\\nax.set_xlabel(\\\"p0 []\\\")\\nax.set_ylabel(\\\"MSE []\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linestyle_bias = \"-\"\n",
    "linestyle_var = \":\"\n",
    "linestyle_total = \"--\"\n",
    "color_expected_val = \"tab:blue\"\n",
    "color_observed_mean = \"tab:orange\"\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_mean_observed_list,\n",
    "    label=\"average observed MSE\",\n",
    "    linestyle=linestyle_total,\n",
    "    color=color_observed_mean,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_expected_list,\n",
    "    label=\"expected MSE\",\n",
    "    linestyle=linestyle_total,\n",
    "    color=color_expected_val,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_bias_list,\n",
    "    label=\"||biases||²\",\n",
    "    linestyle=linestyle_bias,\n",
    "    color=color_expected_val,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_mean_observed_var_list,\n",
    "    label=\"average observed ||var||²\",\n",
    "    linestyle=linestyle_var,\n",
    "    color=color_observed_mean,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_expected_var_list,\n",
    "    label=\"expected ||var||²\",\n",
    "    linestyle=linestyle_var,\n",
    "    color=color_expected_val,\n",
    ")\n",
    "ax.set_xlabel(\"p0 []\")\n",
    "ax.set_ylabel(\"MSE []\")\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown on the figure, the bias term of MSE decreases when new variables are added. Conversely the variance term increases. When increasing the number of experimentations, the average of observed values converge to the expected one. Surprisingly, even when an useless variable is added, the bias decreases and the variance increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian approach\n",
    "In the bayesian approach, the results are the following:\n",
    "$$\\hat{\\beta_{0}}=(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}Y$$\n",
    "$$\\hat{Y_{0}}=X_{0}\\hat{\\beta_{0}}=X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}Y$$\n",
    "The expected value of $\\hat{Y_{0}}$ is then:\n",
    "$$E[\\hat{Y_{0}}]=X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}X\\beta$$\n",
    "\n",
    "Since $X_{0}^{T}X_{0}$ is symmetric, positive and definite (since all variables are assumed to be linearly independent), it can be diagonalized by an orthogonal matrix: $X_{0}^{T}X_{0}=PDP^{T}$. Thus, we can perform similarly on $X_{0}^{T}X_{0}+\\alpha I$ by means of the same orthogonal matrix: $X_{0}^{T}X_{0}+\\alpha I=P(D+\\alpha I)P^{T}$.\n",
    "\n",
    "___\n",
    "* **$MSE_{var}$**\n",
    "\n",
    "Let's compare the variance term in the bayesian approach vs in the frequentist approach.\n",
    "$$\\begin{align}\n",
    "\\hat{Y_{0}} - E[\\hat{Y_{0}}] &= X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}Y - E[\\hat{Y_{0}}]\\\\\n",
    "&= X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}\\epsilon\\\\\n",
    "&= X_{0}P(D+\\alpha I)^{-1}P^{T}X_{0}^{T}\\epsilon\n",
    "\\end{align}$$\n",
    "\n",
    "Then:\n",
    "$$\\begin{align}\n",
    "||\\hat{Y_{0}} - E[\\hat{Y_{0}}]||^{2} &= (X_{0}P(D+\\alpha I)^{-1}P^{T}X_{0}^{T}\\epsilon)^{T}(X_{0}P(D+\\alpha I)^{-1}P^{T}X_{0}^{T}\\epsilon)\\\\\n",
    "&=\\epsilon^{T}X_{0}P(D+\\alpha I)^{-1}D(D+\\alpha I)^{-1}P^{T}X_{0}^{T}\\epsilon\n",
    "\\end{align}$$\n",
    "\n",
    "Hence, the expected value is (because $E[\\epsilon_{i}\\epsilon_{j}]=\\delta_{ij}\\sigma^{2}$):\n",
    "$$\\boxed{\n",
    "\\begin{align}\n",
    "E[||\\hat{Y_{0}} - E[\\hat{Y_{0}}]||^{2}]&=\\sum_{i=1}^{p_{0}}\\frac{D_{i,i}}{(D_{i,i}+\\alpha)^{2}}E[((P^{T}X_{0}^{T}\\epsilon)_{i})^{2}]\\\\\n",
    "&=\\sum_{i=1}^{p_{0}}\\frac{D_{i,i}}{(D_{i,i}+\\alpha)^{2}}\\sum_{j=1}^{m}((P^{T}X_{0}^{T})_{i,j})^{2}E[\\epsilon_{j}^{2}]\\\\\n",
    "&=\\sum_{i=1}^{p_{0}}\\frac{D_{i,i}}{(D_{i,i}+\\alpha)^{2}}\\sum_{j=1}^{m}((P^{T}X_{0}^{T})_{i,j})^{2}\\sigma ^{2}\n",
    "\\end{align}\n",
    "}$$\n",
    "\n",
    "In the frequentist approach we had:\n",
    "$$\\begin{align}\n",
    "||\\hat{Y_{0}} - E[\\hat{Y_{0}}]||^{2} &= (X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\\epsilon)^{T}(X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}\\epsilon)\\\\\n",
    "&= \\epsilon^{T}X_{0}PD^{-1}P^{T}X_{0}^{T}\\epsilon\n",
    "\\end{align}$$\n",
    "\n",
    "And the expected value was:\n",
    "$$\\boxed{\n",
    "\\begin{align}\n",
    "E[||\\hat{Y_{0}} - E[\\hat{Y_{0}}]||^{2}] &= \\sum_{i=1}^{p_{0}}\\frac{1}{D_{i,i}}E[((P^{T}X_{0}^{T}\\epsilon)_{i})^{2}] \\\\\n",
    "&= \\sum_{i=1}^{p_{0}}\\frac{1}{D_{i,i}}\\sum_{j=1}^{m}((P^{T}X_{0}^{T})_{i,j})^{2}\\sigma ^{2}\n",
    "\\end{align}\n",
    "}$$\n",
    "\n",
    "Moreover:\n",
    "$$\\begin{align}\n",
    "\\forall i: \\frac{D_{i,i}}{(D_{i,i}+\\alpha)^{2}}-\\frac{1}{D_{i,i}} = \\frac{D_{i,i}^{2}-(D_{i,i}+\\alpha)^{2}}{(D_{i,i}+\\alpha)^{2}D_{i,i}} < 0\n",
    "\\end{align}$$\n",
    "\n",
    "**Thus the variance term of the MSE is lower in the bayesian approach than in the frequentist one.** It seem to increase when adding new feature. However I wasn't able to proove it.\n",
    "$$\\boxed{MSE_{var}^{bayesian}<MSE_{var}^{frequentist}}$$\n",
    "\n",
    "___\n",
    "* **$MSE_{bias}$**\n",
    "\n",
    "Let derive the bias term of the MSE:\n",
    "$$\\begin{align}\n",
    "||E[\\hat{Y_{0}}] - X\\beta||^{2} &= ||(X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}-I)X\\beta||^{2}\\\\\n",
    "&= ||X\\beta||^{2} - 2\\beta^{T}X^{T}X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}X\\beta + \\beta^{T}X^{T}X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}X_{0}(X_{0}^{T}X_{0}+\\alpha I)^{-1}X_{0}^{T}X\\beta\\\\\n",
    "&= ||X\\beta||^{2} + \\beta^{T}X^{T}X_{0}P((D+\\alpha I)^{-1}D(D+\\alpha I)^{-1}-2(D+\\alpha I)^{-1})P^{T}X_{0}X\\beta\\\\\n",
    "\\end{align}$$\n",
    "In the frequentist approach that was:\n",
    "$$||E[\\hat{Y_{0}}] - X\\beta||^{2} = ||X\\beta||^{2} + \\beta^{T}X^{T}X_{0}P(-D^{-1})P^{T}X\\beta$$\n",
    "\n",
    "Subtituing the frequentist term to the bayesian one gives:\n",
    "$$||E[\\hat{Y_{0}}] - X\\beta||^{2}_{bay} - ||E[\\hat{Y_{0}}] - X\\beta||^{2}_{freq} = \\beta^{T}X^{T}X_{0}P((D+\\alpha I)^{-1}D(D+\\alpha I)^{-1}-2(D+\\alpha I)-(-D^{-1})P^{T}X\\beta$$\n",
    "\n",
    "Moreover:\n",
    "$$\\begin{align}\n",
    "\\forall i: \\frac{D_{i,i}}{(D_{i,i}+\\alpha)^{2}} - 2\\frac{1}{D_{i,i}+\\alpha} - -\\frac{1}{D_{i,i}} &= \\frac{D_{i,i}^{2}-2D_{i,i}(D_{i,i}+\\alpha)+(D_{i,i}+\\alpha)^{2}}{(D_{i,i}+\\alpha)^{2}D_{i,i}} \\\\\n",
    "&= \\frac{\\alpha^{2}}{(D_{i,i}+\\alpha)^{2}D_{i,i}} > 0\n",
    "\\end{align}$$\n",
    "\n",
    "**Thus the bias term of the MSE is greater in the bayesian approach than in the frequentist one. It can increase when adding feature.**\n",
    "$$\\boxed{MSE_{bias}^{bayesian}>MSE_{bias}^{frequentist}}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 15;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha = 40  # since we are in a bayesian approach with regularization\\nn_exp = 10\\n\\n# initialization\\nmse_mean_observed_list = []\\nmse_expected_list = []\\nmse_bias_list = []\\nmse_mean_observed_var_list = []\\nmse_expected_var_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    p0_list.append(p0)\\n    mse_var = get_expected_mse_var_term(X0, alpha, p0)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_mean_observed_list.append(np.mean(mse_list))\\n    mse_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * mse_var)\\n    mse_bias_list.append(np.sum(biases ** 2))\\n    mse_mean_observed_var_list.append(np.mean(mse_list) - np.sum(biases ** 2))\\n    mse_expected_var_list.append(sigma_noise ** 2 * mse_var)\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha = 40  # since we are in a bayesian approach with regularization\\nn_exp = 10\\n\\n# initialization\\nmse_mean_observed_list = []\\nmse_expected_list = []\\nmse_bias_list = []\\nmse_mean_observed_var_list = []\\nmse_expected_var_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    p0_list.append(p0)\\n    mse_var = get_expected_mse_var_term(X0, alpha, p0)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_mean_observed_list.append(np.mean(mse_list))\\n    mse_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * mse_var)\\n    mse_bias_list.append(np.sum(biases ** 2))\\n    mse_mean_observed_var_list.append(np.mean(mse_list) - np.sum(biases ** 2))\\n    mse_expected_var_list.append(sigma_noise ** 2 * mse_var)\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha = 40  # since we are in a bayesian approach with regularization\n",
    "n_exp = 10\n",
    "\n",
    "# initialization\n",
    "mse_mean_observed_list = []\n",
    "mse_expected_list = []\n",
    "mse_bias_list = []\n",
    "mse_mean_observed_var_list = []\n",
    "mse_expected_var_list = []\n",
    "p0_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\n",
    "    p0_list.append(p0)\n",
    "    mse_var = get_expected_mse_var_term(X0, alpha, p0)\n",
    "\n",
    "    y_hat_list, mse_list = make_experimentation(\n",
    "        n_exp, sigma_noise, m, X_beta, X0, alpha\n",
    "    )\n",
    "\n",
    "    mse_mean_observed_list.append(np.mean(mse_list))\n",
    "    mse_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * mse_var)\n",
    "    mse_bias_list.append(np.sum(biases ** 2))\n",
    "    mse_mean_observed_var_list.append(np.mean(mse_list) - np.sum(biases ** 2))\n",
    "    mse_expected_var_list.append(sigma_noise ** 2 * mse_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.30113893e+00,  4.44247294e+00, -2.07992967e+02, -8.36648842e+01,\n",
       "       -1.74190485e+03, -5.22794376e-02, -1.75823544e-01])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 16;\n",
       "                var nbb_unformatted_code = \"np.diff(mse_bias_list)\";\n",
       "                var nbb_formatted_code = \"np.diff(mse_bias_list)\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
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       "<IPython.core.display.Javascript object>"
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   "source": [
    "np.diff(mse_bias_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 17;\n",
       "                var nbb_unformatted_code = \"linestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\nlinestyle_total = \\\"--\\\"\\ncolor_expected_val = \\\"tab:blue\\\"\\ncolor_observed_mean = \\\"tab:orange\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_list,\\n    label=\\\"average observed MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_list,\\n    label=\\\"expected MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bias_list,\\n    label=\\\"||biases||\\u00b2\\\",\\n    linestyle=linestyle_bias,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_var_list,\\n    label=\\\"average observed ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_var_list,\\n    label=\\\"expected ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_expected_val,\\n)\\nax.set_xlabel(\\\"p0 []\\\")\\nax.set_ylabel(\\\"MSE []\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_formatted_code = \"linestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\nlinestyle_total = \\\"--\\\"\\ncolor_expected_val = \\\"tab:blue\\\"\\ncolor_observed_mean = \\\"tab:orange\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_list,\\n    label=\\\"average observed MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_list,\\n    label=\\\"expected MSE\\\",\\n    linestyle=linestyle_total,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bias_list,\\n    label=\\\"||biases||\\u00b2\\\",\\n    linestyle=linestyle_bias,\\n    color=color_expected_val,\\n)\\nax.plot(\\n    p0_list,\\n    mse_mean_observed_var_list,\\n    label=\\\"average observed ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_observed_mean,\\n)\\nax.plot(\\n    p0_list,\\n    mse_expected_var_list,\\n    label=\\\"expected ||var||\\u00b2\\\",\\n    linestyle=linestyle_var,\\n    color=color_expected_val,\\n)\\nax.set_xlabel(\\\"p0 []\\\")\\nax.set_ylabel(\\\"MSE []\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linestyle_bias = \"-\"\n",
    "linestyle_var = \":\"\n",
    "linestyle_total = \"--\"\n",
    "color_expected_val = \"tab:blue\"\n",
    "color_observed_mean = \"tab:orange\"\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_mean_observed_list,\n",
    "    label=\"average observed MSE\",\n",
    "    linestyle=linestyle_total,\n",
    "    color=color_observed_mean,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_expected_list,\n",
    "    label=\"expected MSE\",\n",
    "    linestyle=linestyle_total,\n",
    "    color=color_expected_val,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_bias_list,\n",
    "    label=\"||biases||²\",\n",
    "    linestyle=linestyle_bias,\n",
    "    color=color_expected_val,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_mean_observed_var_list,\n",
    "    label=\"average observed ||var||²\",\n",
    "    linestyle=linestyle_var,\n",
    "    color=color_observed_mean,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_expected_var_list,\n",
    "    label=\"expected ||var||²\",\n",
    "    linestyle=linestyle_var,\n",
    "    color=color_expected_val,\n",
    ")\n",
    "ax.set_xlabel(\"p0 []\")\n",
    "ax.set_ylabel(\"MSE []\")\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When increasing the number of experimentations, the average of observed values converge to the expected one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison frequentist vs bayesian approaches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 18;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha_freq = 0\\nalpha_bay = 40\\nn_exp = 20\\n\\n# initialization\\nmse_freq_expected_list = []\\nmse_freq_bias_list = []\\nmse_freq_expected_var_list = []\\nmse_bay_mean_observed_list = []\\nmse_bay_bias_list = []\\nmse_bay_mean_observed_var_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    # frequentist approach\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha_freq, sigma_noise)\\n    p0_list.append(p0)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_freq_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * p0)\\n    mse_freq_bias_list.append(np.sum(biases ** 2))\\n    mse_freq_expected_var_list.append(sigma_noise ** 2 * p0)\\n\\n    # bayesian approach\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha_bay, sigma_noise)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_bay_mean_observed_list.append(\\n        np.sum(biases ** 2)\\n        + sigma_noise ** 2 * get_expected_mse_var_term(X0, alpha_bay, p0)\\n    )\\n    mse_bay_bias_list.append(np.sum(biases ** 2))\\n    mse_bay_mean_observed_var_list.append(\\n        sigma_noise ** 2 * get_expected_mse_var_term(X0, alpha_bay, p0)\\n    )\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha_freq = 0\\nalpha_bay = 40\\nn_exp = 20\\n\\n# initialization\\nmse_freq_expected_list = []\\nmse_freq_bias_list = []\\nmse_freq_expected_var_list = []\\nmse_bay_mean_observed_list = []\\nmse_bay_bias_list = []\\nmse_bay_mean_observed_var_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    # frequentist approach\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha_freq, sigma_noise)\\n    p0_list.append(p0)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_freq_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * p0)\\n    mse_freq_bias_list.append(np.sum(biases ** 2))\\n    mse_freq_expected_var_list.append(sigma_noise ** 2 * p0)\\n\\n    # bayesian approach\\n    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha_bay, sigma_noise)\\n\\n    y_hat_list, mse_list = make_experimentation(\\n        n_exp, sigma_noise, m, X_beta, X0, alpha\\n    )\\n\\n    mse_bay_mean_observed_list.append(\\n        np.sum(biases ** 2)\\n        + sigma_noise ** 2 * get_expected_mse_var_term(X0, alpha_bay, p0)\\n    )\\n    mse_bay_bias_list.append(np.sum(biases ** 2))\\n    mse_bay_mean_observed_var_list.append(\\n        sigma_noise ** 2 * get_expected_mse_var_term(X0, alpha_bay, p0)\\n    )\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha_freq = 0\n",
    "alpha_bay = 40\n",
    "n_exp = 20\n",
    "\n",
    "# initialization\n",
    "mse_freq_expected_list = []\n",
    "mse_freq_bias_list = []\n",
    "mse_freq_expected_var_list = []\n",
    "mse_bay_mean_observed_list = []\n",
    "mse_bay_bias_list = []\n",
    "mse_bay_mean_observed_var_list = []\n",
    "p0_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    # frequentist approach\n",
    "    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha_freq, sigma_noise)\n",
    "    p0_list.append(p0)\n",
    "\n",
    "    y_hat_list, mse_list = make_experimentation(\n",
    "        n_exp, sigma_noise, m, X_beta, X0, alpha\n",
    "    )\n",
    "\n",
    "    mse_freq_expected_list.append(np.sum(biases ** 2) + sigma_noise ** 2 * p0)\n",
    "    mse_freq_bias_list.append(np.sum(biases ** 2))\n",
    "    mse_freq_expected_var_list.append(sigma_noise ** 2 * p0)\n",
    "\n",
    "    # bayesian approach\n",
    "    p0, X0, biases, _ = get_common_results(X, x_cols, X_beta, alpha_bay, sigma_noise)\n",
    "\n",
    "    y_hat_list, mse_list = make_experimentation(\n",
    "        n_exp, sigma_noise, m, X_beta, X0, alpha\n",
    "    )\n",
    "\n",
    "    mse_bay_mean_observed_list.append(\n",
    "        np.sum(biases ** 2)\n",
    "        + sigma_noise ** 2 * get_expected_mse_var_term(X0, alpha_bay, p0)\n",
    "    )\n",
    "    mse_bay_bias_list.append(np.sum(biases ** 2))\n",
    "    mse_bay_mean_observed_var_list.append(\n",
    "        sigma_noise ** 2 * get_expected_mse_var_term(X0, alpha_bay, p0)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 19;\n",
       "                var nbb_unformatted_code = \"color_freq = \\\"tab:blue\\\"\\ncolor_bay = \\\"tab:orange\\\"\\nlinestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\nlinestyle_total = \\\"--\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    mse_freq_expected_list,\\n    label=\\\"frequentist expected MSE\\\",\\n    color=color_freq,\\n    linestyle=linestyle_total,\\n)\\nax.plot(\\n    p0_list,\\n    mse_freq_bias_list,\\n    label=\\\"frequentist ||biases||\\u00b2\\\",\\n    color=color_freq,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    mse_freq_expected_var_list,\\n    label=\\\"frequentist expected ||var||\\u00b2\\\",\\n    color=color_freq,\\n    linestyle=linestyle_var,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bay_mean_observed_list,\\n    label=\\\"bayesian expected MSE\\\",\\n    color=color_bay,\\n    linestyle=linestyle_total,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bay_bias_list,\\n    label=\\\"bayesian ||biases||\\u00b2\\\",\\n    color=color_bay,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bay_mean_observed_var_list,\\n    label=\\\"bayesian expected ||var||\\u00b2\\\",\\n    color=color_bay,\\n    linestyle=linestyle_var,\\n)\\nax.set_xlabel(\\\"number of explanatory variables\\\")\\nax.set_ylabel(\\\"MSE\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_formatted_code = \"color_freq = \\\"tab:blue\\\"\\ncolor_bay = \\\"tab:orange\\\"\\nlinestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\nlinestyle_total = \\\"--\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    mse_freq_expected_list,\\n    label=\\\"frequentist expected MSE\\\",\\n    color=color_freq,\\n    linestyle=linestyle_total,\\n)\\nax.plot(\\n    p0_list,\\n    mse_freq_bias_list,\\n    label=\\\"frequentist ||biases||\\u00b2\\\",\\n    color=color_freq,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    mse_freq_expected_var_list,\\n    label=\\\"frequentist expected ||var||\\u00b2\\\",\\n    color=color_freq,\\n    linestyle=linestyle_var,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bay_mean_observed_list,\\n    label=\\\"bayesian expected MSE\\\",\\n    color=color_bay,\\n    linestyle=linestyle_total,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bay_bias_list,\\n    label=\\\"bayesian ||biases||\\u00b2\\\",\\n    color=color_bay,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    mse_bay_mean_observed_var_list,\\n    label=\\\"bayesian expected ||var||\\u00b2\\\",\\n    color=color_bay,\\n    linestyle=linestyle_var,\\n)\\nax.set_xlabel(\\\"number of explanatory variables\\\")\\nax.set_ylabel(\\\"MSE\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "color_freq = \"tab:blue\"\n",
    "color_bay = \"tab:orange\"\n",
    "linestyle_bias = \"-\"\n",
    "linestyle_var = \":\"\n",
    "linestyle_total = \"--\"\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_freq_expected_list,\n",
    "    label=\"frequentist expected MSE\",\n",
    "    color=color_freq,\n",
    "    linestyle=linestyle_total,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_freq_bias_list,\n",
    "    label=\"frequentist ||biases||²\",\n",
    "    color=color_freq,\n",
    "    linestyle=linestyle_bias,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_freq_expected_var_list,\n",
    "    label=\"frequentist expected ||var||²\",\n",
    "    color=color_freq,\n",
    "    linestyle=linestyle_var,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_bay_mean_observed_list,\n",
    "    label=\"bayesian expected MSE\",\n",
    "    color=color_bay,\n",
    "    linestyle=linestyle_total,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_bay_bias_list,\n",
    "    label=\"bayesian ||biases||²\",\n",
    "    color=color_bay,\n",
    "    linestyle=linestyle_bias,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    mse_bay_mean_observed_var_list,\n",
    "    label=\"bayesian expected ||var||²\",\n",
    "    color=color_bay,\n",
    "    linestyle=linestyle_var,\n",
    ")\n",
    "ax.set_xlabel(\"number of explanatory variables\")\n",
    "ax.set_ylabel(\"MSE\")\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown on the figure, the bias term of MSE of the regularized model is always greater than the one of the OLS. Conversely the variance term of MSE of the regularized model is always lower than the one of the OLS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Bias and variance analysis for a single estimator\n",
    "In this section, let's focus on a single estimator $\\hat{Y_{0}}=(X_{0}\\hat{\\beta})_{i} = X_{0i,.}\\hat{\\beta}$, and not the entire parameter estimator vector $X_{0}\\hat{\\beta}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frequentist approach\n",
    "I was only able to demonstrate that the variance of a single prediction increases when new variables are added. However, I cannot say anything about the bias. It can increase or decrease. Noting $u$ a vector with a single 1 for the desired index:\n",
    "$$\\hat{Y}_{0i}=u^{T}\\hat{Y_{0}} \\sim \\mathcal{N}(E[\\hat{Y}_{0i}], \\sigma^{2}u^{T}X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}u)$$\n",
    "Since $X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}$ is a projector (let's note it $P_{X_{0}}$, which verifies $P_{X_{0}}P_{X_{0}}=P_{X_{0}}=P_{X_{0}}^{T}$), then:\n",
    "$$u^{T}X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}u = u^{T}P_{X_{0}}u = u^{T}P_{X_{0}}^{T}P_{X_{0}}u = ||P_{X_{0}}u||^{2}$$\n",
    "Thanks to Pythagore, we know that:\n",
    "$$\\boxed{\\begin{align}\n",
    "||P_{X_{0}}u||^{2} &= ||u||^{2} - ||(I-P_{X_{0}})u||^{2}\\\\\n",
    "&= ||u||^{2} - \\min\\limits_{v\\in\\mathbb{R}^{p_{0}}}(||u-X_{0}v||^{2})\n",
    "\\end{align}}$$\n",
    "Thus, adding a new variables to $X_{0}$ can only lead to a decrease of the second term, $\\min\\limits_{v\\in\\mathbb{R}^{p_{0}}}(||u-X_{0}v||^{2})$, which is an increase of $||P_{X_{0}}u||^{2}$. **When adding a new variable, the variance of a single prediction increases.** This is actually true for any $u$ and if $X_{0}$ is full rank, then this is true any variable vector $x$ and not only the observation of the training dataset.\n",
    "$$\\forall x\\in {R}^{p_{0}} \\exists u\\in {R}^{m} : X_{0}^{T}u=x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 20;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha = 0  # since we are in a frequentist approach without regularization\\nindex = 2\\n\\n# initialization\\nbias_list = []\\nvariance_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    p0, X0, biases, cov_mat = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    p0_list.append(p0)\\n    bias_list.append(biases[index])\\n    variance_list.append(cov_mat[index, index])\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha = 0  # since we are in a frequentist approach without regularization\\nindex = 2\\n\\n# initialization\\nbias_list = []\\nvariance_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    p0, X0, biases, cov_mat = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\\n    p0_list.append(p0)\\n    bias_list.append(biases[index])\\n    variance_list.append(cov_mat[index, index])\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha = 0  # since we are in a frequentist approach without regularization\n",
    "index = 2\n",
    "\n",
    "# initialization\n",
    "bias_list = []\n",
    "variance_list = []\n",
    "p0_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    p0, X0, biases, cov_mat = get_common_results(X, x_cols, X_beta, alpha, sigma_noise)\n",
    "    p0_list.append(p0)\n",
    "    bias_list.append(biases[index])\n",
    "    variance_list.append(cov_mat[index, index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 21;\n",
       "                var nbb_unformatted_code = \"fig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(p0_list, np.abs(bias_list), label=\\\"|bias|\\\")\\nax.plot(p0_list, variance_list, label=\\\"variance\\\")\\nax.set_xlabel(\\\"p0 []\\\")\\nax.set_ylabel(\\\"bias / variance\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_formatted_code = \"fig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(p0_list, np.abs(bias_list), label=\\\"|bias|\\\")\\nax.plot(p0_list, variance_list, label=\\\"variance\\\")\\nax.set_xlabel(\\\"p0 []\\\")\\nax.set_ylabel(\\\"bias / variance\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.plot(p0_list, np.abs(bias_list), label=\"|bias|\")\n",
    "ax.plot(p0_list, variance_list, label=\"variance\")\n",
    "ax.set_xlabel(\"p0 []\")\n",
    "ax.set_ylabel(\"bias / variance\")\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown on the figure, the variance of a single estimation can only increase when adding new variables. Whereas there is not a similar rule for the bias. In this case the bias get worse when adding the second, third and fourth variables that are both useful and useless."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison frequentist vs bayesian approaches\n",
    "We can only demonstrate that the variance is lower than in the frequentist approach. Nothing can be said regarding the bias. Following the same notation, we have:\n",
    "$$\\hat{Y}_{0i}=u^{T}\\hat{Y_{0}} \\sim \\mathcal{N}(E[\\hat{Y}_{0i}], \\sigma^{2}u^{T}X_{0}(X_{0}^{T}X_{0} + \\alpha I)^{-1}X_{0}^{T}X_{0}(X_{0}^{T}X_{0} + \\alpha I)^{-1}X_{0}^{T}u)$$\n",
    "Like previously, we can show that:\n",
    "$$\n",
    "u^{T}X_{0}(X_{0}^{T}X_{0} + \\alpha I)^{-1}X_{0}^{T}X_{0}(X_{0}^{T}X_{0} + \\alpha I)^{-1}X_{0}^{T}u - u^{T}X_{0}(X_{0}^{T}X_{0})^{-1}X_{0}^{T}u = u^{T}X_{0}P(D(D+\\alpha I)^{-2}-D^{-1})P^{T}X_{0}^{T}u\n",
    "$$\n",
    "And:\n",
    "$$\\begin{align}\n",
    "\\forall i:(D(D+\\alpha I)^{-2}-D^{-1})_{i,i} &= \\frac{D_{i,i}}{(D_{i,i}+\\alpha)^{2}}-\\frac{1}{D_{i,i}}\\\\\n",
    "&= \\frac{D_{i,i}^{2}-(D_{i,i}+\\alpha)^{2}}{D_{i,i}(D_{i,i}+\\alpha)^{2}} < 0\n",
    "\\end{align}$$\n",
    "**The variance of a single prediction is then always lower in the bayesian approach than in the frequentist approach.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 22;\n",
       "                var nbb_unformatted_code = \"# parameters\\nalpha_freq = 0\\nalpha_bay = 40\\nindex = 2\\n\\n# initialization\\nbias_freq_list = []\\nvariance_freq_list = []\\nbias_bay_list = []\\nvariance_bay_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    # frequentist approach\\n    p0, X0, biases, cov_mat = get_common_results(\\n        X, x_cols, X_beta, alpha_freq, sigma_noise\\n    )\\n    p0_list.append(p0)\\n    bias_freq_list.append(biases[index])\\n    variance_freq_list.append(cov_mat[index, index])\\n\\n    # bayesian approach\\n    p0, X0, biases, cov_mat = get_common_results(\\n        X, x_cols, X_beta, alpha_bay, sigma_noise\\n    )\\n    bias_bay_list.append(biases[index])\\n    variance_bay_list.append(cov_mat[index, index])\";\n",
       "                var nbb_formatted_code = \"# parameters\\nalpha_freq = 0\\nalpha_bay = 40\\nindex = 2\\n\\n# initialization\\nbias_freq_list = []\\nvariance_freq_list = []\\nbias_bay_list = []\\nvariance_bay_list = []\\np0_list = []\\n\\n# loop over an increasing number of independent variables\\nfor nb_x in range(1, X.shape[1] + 1):\\n    x_cols = list(range(nb_x))\\n\\n    # frequentist approach\\n    p0, X0, biases, cov_mat = get_common_results(\\n        X, x_cols, X_beta, alpha_freq, sigma_noise\\n    )\\n    p0_list.append(p0)\\n    bias_freq_list.append(biases[index])\\n    variance_freq_list.append(cov_mat[index, index])\\n\\n    # bayesian approach\\n    p0, X0, biases, cov_mat = get_common_results(\\n        X, x_cols, X_beta, alpha_bay, sigma_noise\\n    )\\n    bias_bay_list.append(biases[index])\\n    variance_bay_list.append(cov_mat[index, index])\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "alpha_freq = 0\n",
    "alpha_bay = 40\n",
    "index = 2\n",
    "\n",
    "# initialization\n",
    "bias_freq_list = []\n",
    "variance_freq_list = []\n",
    "bias_bay_list = []\n",
    "variance_bay_list = []\n",
    "p0_list = []\n",
    "\n",
    "# loop over an increasing number of independent variables\n",
    "for nb_x in range(1, X.shape[1] + 1):\n",
    "    x_cols = list(range(nb_x))\n",
    "\n",
    "    # frequentist approach\n",
    "    p0, X0, biases, cov_mat = get_common_results(\n",
    "        X, x_cols, X_beta, alpha_freq, sigma_noise\n",
    "    )\n",
    "    p0_list.append(p0)\n",
    "    bias_freq_list.append(biases[index])\n",
    "    variance_freq_list.append(cov_mat[index, index])\n",
    "\n",
    "    # bayesian approach\n",
    "    p0, X0, biases, cov_mat = get_common_results(\n",
    "        X, x_cols, X_beta, alpha_bay, sigma_noise\n",
    "    )\n",
    "    bias_bay_list.append(biases[index])\n",
    "    variance_bay_list.append(cov_mat[index, index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 23;\n",
       "                var nbb_unformatted_code = \"color_freq = \\\"tab:blue\\\"\\ncolor_bay = \\\"tab:orange\\\"\\nlinestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    np.abs(bias_freq_list),\\n    label=\\\"frequentist |bias|\\\",\\n    color=color_freq,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    variance_freq_list,\\n    label=\\\"frequentist variance\\\",\\n    color=color_freq,\\n    linestyle=linestyle_var,\\n)\\nax.plot(\\n    p0_list,\\n    np.abs(bias_bay_list),\\n    label=\\\"bayesian |bias|\\\",\\n    color=color_bay,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    variance_bay_list,\\n    label=\\\"bayesian variance\\\",\\n    color=color_bay,\\n    linestyle=linestyle_var,\\n)\\nax.set_xlabel(\\\"number of explanatory variables\\\")\\nax.set_ylabel(\\\"bias / variance\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_formatted_code = \"color_freq = \\\"tab:blue\\\"\\ncolor_bay = \\\"tab:orange\\\"\\nlinestyle_bias = \\\"-\\\"\\nlinestyle_var = \\\":\\\"\\n\\nfig, ax = plt.subplots(figsize=(10, 6))\\nax.plot(\\n    p0_list,\\n    np.abs(bias_freq_list),\\n    label=\\\"frequentist |bias|\\\",\\n    color=color_freq,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    variance_freq_list,\\n    label=\\\"frequentist variance\\\",\\n    color=color_freq,\\n    linestyle=linestyle_var,\\n)\\nax.plot(\\n    p0_list,\\n    np.abs(bias_bay_list),\\n    label=\\\"bayesian |bias|\\\",\\n    color=color_bay,\\n    linestyle=linestyle_bias,\\n)\\nax.plot(\\n    p0_list,\\n    variance_bay_list,\\n    label=\\\"bayesian variance\\\",\\n    color=color_bay,\\n    linestyle=linestyle_var,\\n)\\nax.set_xlabel(\\\"number of explanatory variables\\\")\\nax.set_ylabel(\\\"bias / variance\\\")\\nax.legend()\\nax.grid()\\nplt.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "color_freq = \"tab:blue\"\n",
    "color_bay = \"tab:orange\"\n",
    "linestyle_bias = \"-\"\n",
    "linestyle_var = \":\"\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    np.abs(bias_freq_list),\n",
    "    label=\"frequentist |bias|\",\n",
    "    color=color_freq,\n",
    "    linestyle=linestyle_bias,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    variance_freq_list,\n",
    "    label=\"frequentist variance\",\n",
    "    color=color_freq,\n",
    "    linestyle=linestyle_var,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    np.abs(bias_bay_list),\n",
    "    label=\"bayesian |bias|\",\n",
    "    color=color_bay,\n",
    "    linestyle=linestyle_bias,\n",
    ")\n",
    "ax.plot(\n",
    "    p0_list,\n",
    "    variance_bay_list,\n",
    "    label=\"bayesian variance\",\n",
    "    color=color_bay,\n",
    "    linestyle=linestyle_var,\n",
    ")\n",
    "ax.set_xlabel(\"number of explanatory variables\")\n",
    "ax.set_ylabel(\"bias / variance\")\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown on the figure, the variance of a single estimation is always lower in when there is a L2 regularization. However, there is no order between the biases between the two approaches for a single target estimation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Conclusion\n",
    "\n",
    "In this notebook, I investigated the change of bias and variance of both a vector estimator and a scalar estimator of a linear regression model. When analyzing the vector estimators, two definitions have been considered (the scalar MSE and the matrix MSE). Finally, the results are summarized in the following table. The change of the bias and variance terms when adding explanatory variables are detailed in the table.\n",
    "\n",
    "| Estimator | Metric | Approach | Bias | Variance |\n",
    "| :---: | :---: | :---: | :---: | :---: |\n",
    "| vector | matrix | frequentist | - | $\\nearrow$ |\n",
    "| vector | matrix | bayesian | - | - |\n",
    "| vector | scalar | frequentist | $\\searrow$ | $\\nearrow$ |\n",
    "| vector | scalar | bayesian | > frequentist | < frequentist<br>$\\nearrow$? |\n",
    "| scalar | scalar | frequentist | - | $\\nearrow$ |\n",
    "| scalar | scalar | bayesian | - | < frequentist<br>$\\nearrow$? |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "# Appendix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bias and variance in function of model complexity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_8980/3347557311.py:4: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  bias = 1 / (1 * np.sqrt(x))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 24;\n",
       "                var nbb_unformatted_code = \"plt.rcParams.update({\\\"font.size\\\": 16})\\n\\nx = np.linspace(0, 1, 100)\\nbias = 1 / (1 * np.sqrt(x))\\nvar = np.exp(2 * x)\\n\\nfig, ax = plt.subplots(1, 1, figsize=(8, 6))\\nax.plot(\\n    x,\\n    bias,\\n    label=\\\"bias\\u00b2\\\",\\n    linestyle=\\\"-\\\",\\n)\\nax.plot(\\n    x,\\n    var,\\n    label=\\\"variance\\\",\\n    linestyle=\\\"-\\\",\\n)\\nax.plot(\\n    x,\\n    bias + var,\\n    label=\\\"total error\\\",\\n    linestyle=\\\"-\\\",\\n)\\nax.set_xlabel(\\\"Model complexity\\\")\\nax.set_ylabel(\\\"Error\\\")\\nax.set_xticks([])\\nax.set_yticks([])\\nax.legend()\\nplt.show()\";\n",
       "                var nbb_formatted_code = \"plt.rcParams.update({\\\"font.size\\\": 16})\\n\\nx = np.linspace(0, 1, 100)\\nbias = 1 / (1 * np.sqrt(x))\\nvar = np.exp(2 * x)\\n\\nfig, ax = plt.subplots(1, 1, figsize=(8, 6))\\nax.plot(\\n    x,\\n    bias,\\n    label=\\\"bias\\u00b2\\\",\\n    linestyle=\\\"-\\\",\\n)\\nax.plot(\\n    x,\\n    var,\\n    label=\\\"variance\\\",\\n    linestyle=\\\"-\\\",\\n)\\nax.plot(\\n    x,\\n    bias + var,\\n    label=\\\"total error\\\",\\n    linestyle=\\\"-\\\",\\n)\\nax.set_xlabel(\\\"Model complexity\\\")\\nax.set_ylabel(\\\"Error\\\")\\nax.set_xticks([])\\nax.set_yticks([])\\nax.legend()\\nplt.show()\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams.update({\"font.size\": 16})\n",
    "\n",
    "x = np.linspace(0, 1, 100)\n",
    "bias = 1 / (1 * np.sqrt(x))\n",
    "var = np.exp(2 * x)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
    "ax.plot(\n",
    "    x,\n",
    "    bias,\n",
    "    label=\"bias²\",\n",
    "    linestyle=\"-\",\n",
    ")\n",
    "ax.plot(\n",
    "    x,\n",
    "    var,\n",
    "    label=\"variance\",\n",
    "    linestyle=\"-\",\n",
    ")\n",
    "ax.plot(\n",
    "    x,\n",
    "    bias + var,\n",
    "    label=\"total error\",\n",
    "    linestyle=\"-\",\n",
    ")\n",
    "ax.set_xlabel(\"Model complexity\")\n",
    "ax.set_ylabel(\"Error\")\n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=\"8\">\n",
    "$$\\begin{align}\n",
    "\\mbox{bias} &= \\mathbb{E}(\\hat{\\theta}-\\theta) \\\\\n",
    "\\mbox{variance} &= \\mbox{Var}(\\hat{\\theta})\n",
    "\\end{align}$$\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visual illustration of bias and variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "            setTimeout(function() {\n",
       "                var nbb_cell_id = 25;\n",
       "                var nbb_unformatted_code = \"# parameters\\nfontsize = 20\\nn_pts = 30\\nbias_low = [0, 0]\\nbias_high = [2, 1]\\ncov_low = [[0.1, 0], [0, 0.1]]\\ncov_high = [[2, 0], [0, 2]]\\n\\nfig, axs = plt.subplots(2, 2, figsize=(10, 10))\\n\\nlines_kwargs = {\\\"linewidth\\\": 2, \\\"fill\\\": False, \\\"alpha\\\": 1, \\\"color\\\": \\\"k\\\"}\\nblue_circle_kwargs = {\\\"color\\\": \\\"b\\\", \\\"alpha\\\": 0.5, \\\"fill\\\": False, \\\"linewidth\\\": 26}\\nred_circle_kwargs = {\\\"color\\\": \\\"r\\\", \\\"alpha\\\": 0.5, \\\"fill\\\": True, \\\"linewidth\\\": 0}\\n\\nfor ii in range(2):\\n    for jj in range(2):\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 2.5, **blue_circle_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 1, **red_circle_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 1, **lines_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 2, **lines_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 3, **lines_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 4, **lines_kwargs))\\n        axs[ii, jj].set_xlim([-5, 5])\\n        axs[ii, jj].set_ylim([-5, 5])\\n        axs[ii, jj].xaxis.set_visible(False)\\n        axs[ii, jj].tick_params(left=False, labelleft=False)\\n        # axs[ii, jj].patch.set_visible(False)\\n        plt.setp(axs[ii, jj].spines.values(), visible=False)\\naxs[0, 0].set_ylabel(\\\"Low bias\\\", fontsize=fontsize)\\naxs[0, 0].set_title(\\\"Low variance\\\", fontsize=fontsize)\\naxs[1, 0].set_ylabel(\\\"High bias\\\", fontsize=fontsize)\\naxs[0, 1].set_title(\\\"High variance\\\", fontsize=fontsize)\\n\\n\\n# low bias / low variance\\npts = np.random.multivariate_normal(bias_low, cov_low, size=n_pts)\\naxs[0, 0].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\n# low bias / high variance\\npts = np.random.multivariate_normal(bias_low, cov_high, size=n_pts)\\naxs[0, 1].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\n# high bias / low variance\\npts = np.random.multivariate_normal(bias_high, cov_low, size=n_pts)\\naxs[1, 0].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\n# high bias / high variance\\npts = np.random.multivariate_normal(bias_high, cov_high, size=n_pts)\\naxs[1, 1].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\nplt.subplots_adjust(wspace=0, hspace=0)\";\n",
       "                var nbb_formatted_code = \"# parameters\\nfontsize = 20\\nn_pts = 30\\nbias_low = [0, 0]\\nbias_high = [2, 1]\\ncov_low = [[0.1, 0], [0, 0.1]]\\ncov_high = [[2, 0], [0, 2]]\\n\\nfig, axs = plt.subplots(2, 2, figsize=(10, 10))\\n\\nlines_kwargs = {\\\"linewidth\\\": 2, \\\"fill\\\": False, \\\"alpha\\\": 1, \\\"color\\\": \\\"k\\\"}\\nblue_circle_kwargs = {\\\"color\\\": \\\"b\\\", \\\"alpha\\\": 0.5, \\\"fill\\\": False, \\\"linewidth\\\": 26}\\nred_circle_kwargs = {\\\"color\\\": \\\"r\\\", \\\"alpha\\\": 0.5, \\\"fill\\\": True, \\\"linewidth\\\": 0}\\n\\nfor ii in range(2):\\n    for jj in range(2):\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 2.5, **blue_circle_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 1, **red_circle_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 1, **lines_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 2, **lines_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 3, **lines_kwargs))\\n        axs[ii, jj].add_patch(plt.Circle((0, 0), 4, **lines_kwargs))\\n        axs[ii, jj].set_xlim([-5, 5])\\n        axs[ii, jj].set_ylim([-5, 5])\\n        axs[ii, jj].xaxis.set_visible(False)\\n        axs[ii, jj].tick_params(left=False, labelleft=False)\\n        # axs[ii, jj].patch.set_visible(False)\\n        plt.setp(axs[ii, jj].spines.values(), visible=False)\\naxs[0, 0].set_ylabel(\\\"Low bias\\\", fontsize=fontsize)\\naxs[0, 0].set_title(\\\"Low variance\\\", fontsize=fontsize)\\naxs[1, 0].set_ylabel(\\\"High bias\\\", fontsize=fontsize)\\naxs[0, 1].set_title(\\\"High variance\\\", fontsize=fontsize)\\n\\n\\n# low bias / low variance\\npts = np.random.multivariate_normal(bias_low, cov_low, size=n_pts)\\naxs[0, 0].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\n# low bias / high variance\\npts = np.random.multivariate_normal(bias_low, cov_high, size=n_pts)\\naxs[0, 1].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\n# high bias / low variance\\npts = np.random.multivariate_normal(bias_high, cov_low, size=n_pts)\\naxs[1, 0].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\n# high bias / high variance\\npts = np.random.multivariate_normal(bias_high, cov_high, size=n_pts)\\naxs[1, 1].scatter(pts[:, 0], pts[:, 1], color=\\\"k\\\")\\n\\nplt.subplots_adjust(wspace=0, hspace=0)\";\n",
       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
       "                        }\n",
       "                        break;\n",
       "                    }\n",
       "                }\n",
       "            }, 500);\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters\n",
    "fontsize = 20\n",
    "n_pts = 30\n",
    "bias_low = [0, 0]\n",
    "bias_high = [2, 1]\n",
    "cov_low = [[0.1, 0], [0, 0.1]]\n",
    "cov_high = [[2, 0], [0, 2]]\n",
    "\n",
    "fig, axs = plt.subplots(2, 2, figsize=(10, 10))\n",
    "\n",
    "lines_kwargs = {\"linewidth\": 2, \"fill\": False, \"alpha\": 1, \"color\": \"k\"}\n",
    "blue_circle_kwargs = {\"color\": \"b\", \"alpha\": 0.5, \"fill\": False, \"linewidth\": 26}\n",
    "red_circle_kwargs = {\"color\": \"r\", \"alpha\": 0.5, \"fill\": True, \"linewidth\": 0}\n",
    "\n",
    "for ii in range(2):\n",
    "    for jj in range(2):\n",
    "        axs[ii, jj].add_patch(plt.Circle((0, 0), 2.5, **blue_circle_kwargs))\n",
    "        axs[ii, jj].add_patch(plt.Circle((0, 0), 1, **red_circle_kwargs))\n",
    "        axs[ii, jj].add_patch(plt.Circle((0, 0), 1, **lines_kwargs))\n",
    "        axs[ii, jj].add_patch(plt.Circle((0, 0), 2, **lines_kwargs))\n",
    "        axs[ii, jj].add_patch(plt.Circle((0, 0), 3, **lines_kwargs))\n",
    "        axs[ii, jj].add_patch(plt.Circle((0, 0), 4, **lines_kwargs))\n",
    "        axs[ii, jj].set_xlim([-5, 5])\n",
    "        axs[ii, jj].set_ylim([-5, 5])\n",
    "        axs[ii, jj].xaxis.set_visible(False)\n",
    "        axs[ii, jj].tick_params(left=False, labelleft=False)\n",
    "        # axs[ii, jj].patch.set_visible(False)\n",
    "        plt.setp(axs[ii, jj].spines.values(), visible=False)\n",
    "axs[0, 0].set_ylabel(\"Low bias\", fontsize=fontsize)\n",
    "axs[0, 0].set_title(\"Low variance\", fontsize=fontsize)\n",
    "axs[1, 0].set_ylabel(\"High bias\", fontsize=fontsize)\n",
    "axs[0, 1].set_title(\"High variance\", fontsize=fontsize)\n",
    "\n",
    "\n",
    "# low bias / low variance\n",
    "pts = np.random.multivariate_normal(bias_low, cov_low, size=n_pts)\n",
    "axs[0, 0].scatter(pts[:, 0], pts[:, 1], color=\"k\")\n",
    "\n",
    "# low bias / high variance\n",
    "pts = np.random.multivariate_normal(bias_low, cov_high, size=n_pts)\n",
    "axs[0, 1].scatter(pts[:, 0], pts[:, 1], color=\"k\")\n",
    "\n",
    "# high bias / low variance\n",
    "pts = np.random.multivariate_normal(bias_high, cov_low, size=n_pts)\n",
    "axs[1, 0].scatter(pts[:, 0], pts[:, 1], color=\"k\")\n",
    "\n",
    "# high bias / high variance\n",
    "pts = np.random.multivariate_normal(bias_high, cov_high, size=n_pts)\n",
    "axs[1, 1].scatter(pts[:, 0], pts[:, 1], color=\"k\")\n",
    "\n",
    "plt.subplots_adjust(wspace=0, hspace=0)"
   ]
  }
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