6 - Gaussian Processes/Gaussian Processes.ipynb

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    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Creative Commons License\" align=\"left\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/80x15.png\" /></a>&nbsp;| [Emmanuel Rachelson](https://personnel.isae-supaero.fr/emmanuel-rachelson?lang=en) | <a href=\"https://supaerodatascience.github.io/machine-learning/\">https://supaerodatascience.github.io/machine-learning/</a>"
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    "<div style=\"font-size:22pt; line-height:25pt; font-weight:bold; text-align:center;\">Bayesian models for Machine Learning<br>Gaussian Processes</div>\n",
    "\n",
    "Suppose we want to predict the probability that sample $x$ has label $y$. This is a probability estimation problem that can be written:\n",
    "$$\\mathbb{P}(Y=y|X=x)$$\n",
    "\n",
    "According to Bayes' theorem, we have:\n",
    "$$\\mathbb{P}(Y=y|X=x) =\\frac{\\mathbb{P}(X=x|Y=y)\\cdot\\mathbb{P}(Y=y)}{\\mathbb{P}(X=x)}$$\n",
    "$$\\textrm{posterior} = \\frac{\\textrm{likelihood}\\cdot\\textrm{prior}}{\\textrm{evidence}}$$\n",
    "\n",
    "<div class=\"alert alert-success\">\n",
    "    \n",
    "**Bayesian inference** is the problem of estimating this **posterior distribution**.<br>\n",
    "In plain words, it consists in estimating the probability of label $y$, given an input $x$, using previously seen data to estimate the **likelihood** of an $x$ input associated to label $y$ and the general **prior** probability of observing label $y$.\n",
    "</div>\n",
    "\n",
    "Note that Bayesian inference applies both to classification and regression.\n",
    "\n",
    "The goal of Bayesian inference is to estimate the label distribution for a given $x$ and use them to predict the correct label, so it is a *probabilistic approach to Machine Learning*.\n",
    "\n",
    "The Bayesian predictor (classifier or regressor) returns the label that maximizes the posterior probability distribution.\n",
    "\n",
    "In this (second) notebook on Bayesian modeling in ML, we will explore Gaussian Processes.\n",
    "\n",
    "1. [A reminder on Gaussian distributions](#sec1)\n",
    "2. [Back to the regression problem](#sec2)\n",
    "3. [Gaussian Processes for classification](#sec3)\n",
    "4. [Examples](#sec4)\n",
    "    1. [Spam or ham?](#sec4-1)\n",
    "    2. [NIST](#sec4-2)"
   ]
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    "Suppose we want to learn a certain phenomenon $f(x)$, given some measurements $y = f(x)$ + noise.\n",
    "\n",
    "For example, that could be learning the pressure $P$ across the wingspan of a plane as a function of the position $l$ on the wing, the Mach value $M$, and the temperature $T$ (so $x=(l,M,T)$).\n",
    "\n",
    "Let's suppose that for a given value of $x$, the corresponding observation $y$ follows a Gaussian distribution of mean $\\mu$ and variance $\\sigma^2$.\n",
    "\n",
    "Need a reminder on Gaussian distributions?\n",
    "\n",
    "# 1. <a id=\"sec1\"></a>A reminder on Gaussian distributions\n",
    "\n",
    "A Gaussian (or Normal) distributed variable has the following probability density function. The mean $\\mu$ is the most frequent value observed for this variable, while the variance $\\sigma^2$ indicates the diversity of values that $y$ often takes (how the distribution is spread-out along $y$).\n",
    "\n",
    "We say that $y$ is drawn from the Gaussian distribution of mean $\\mu$ and variance $\\sigma^2$ and write:\n",
    "$$y \\sim \\mathcal{N}\\left(\\mu,\\sigma\\right)$$"
   ]
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",
      "text/plain": [
       "<Figure size 640x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "mu = 0.0\n",
    "sigma = 2.0\n",
    "x = np.linspace(-10., 10, 100)\n",
    "fig=plt.figure(figsize=(8, 8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(x, norm(mu,sigma).pdf(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, take two values $x_1$ and $x_2$. The value taken by $y$ in $x_1$ is not independent of the value in $x_2$; we shall say that $y_1$ and $y_2$ are **correlated**. For example, the pressures $P$ in close $(l,M,T)$ values take values that are linked together.\n",
    "\n",
    "Let's still suppose the pair $(y_1,y_2)$ follows a Gaussian distribution in $x_1$ and $x_2$, with mean $(\\mu_1,\\mu_2)$. While the variance in the monovariate case was given by a single scalar $\\sigma^2$, now it is given by a covariance matrix $\\Sigma = \\left[\\begin{array}{cc} \\sigma_{11} & \\sigma_{12}\\\\ \\sigma_{12} & \\sigma_{22} \\end{array}\\right]$ that depicts how the distribution spreads in the $(y_1,y_2)\\in\\mathbb{R}^2$ plane.\n",
    "\n",
    "$$\\left[\\begin{array}{c}y_1\\\\y_2\\end{array}\\right] \\sim \\mathcal{N}\\left( \\left[\\begin{array}{c} \\mu_1\\\\\\mu_2\\end{array}\\right], \\Sigma\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T12:46:08.327088Z",
     "start_time": "2019-10-21T12:46:07.879181Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu = [0.0, 0.0]\n",
      "sigma:\n",
      "[[2.  0.4]\n",
      " [0.4 0.5]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "x,y = np.mgrid[-1:1:.01, -1:1:.01]\n",
    "pos = np.dstack((x, y))\n",
    "mu = [0.0, 0.0]\n",
    "sigma = np.array([[2.0, 0.4], [0.4, 0.5]])\n",
    "fig=plt.figure(figsize=(8, 8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.contourf(x, y, multivariate_normal(mu, sigma).pdf(pos));\n",
    "print(\"mu =\",mu)\n",
    "print(\"sigma:\")\n",
    "print(sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance matrix indicates how the values of $y_1$ are centered around $\\mu_1$ (through $\\sigma_{11}$) and correlated with the value of $y_2$ (through $\\sigma_{12}$). In particular, $\\sigma_{12}$ indicates how similar the evolution of $y_1$ and $y_2$ are. Suppose we measure a sample $(\\hat{y}_1, \\hat{y}_2)$:\n",
    "- having $\\sigma_{12}>0$ indicates that if $\\hat{y}_1>\\mu_1$ then it is likely that $\\hat{y}_2>\\mu_2$ in a proportional fashion,\n",
    "- conversely $\\sigma_{12}<0$ indicates that $\\hat{y}_1$ and $\\hat{y}_2$ evolve in opposite directions relatively to their respective means,\n",
    "- $\\sigma_{12}=0$ means that $y_1$ and $y_2$ are independent: a sample of the former gives no information about how likely it is that the latter is greater or smaller than its mean.\n",
    "\n",
    "If there are $N$ such points $x_i$, and we assume again a Gaussian distribution of $y$, we end up with a mean $(\\mu_1,\\ldots,\\mu_N)$ and a covariance matrix $\\Sigma = \\left[\\begin{array}{ccc} \\sigma_{11} & \\ldots & \\sigma_{1N}\\\\ \\vdots & \\ddots & \\vdots \\\\ \\sigma_{1N} & \\ldots & \\sigma_{NN} \\end{array}\\right]$.\n",
    "\n",
    "$$\\left[\\begin{array}{c}y_1\\\\ \\vdots\\\\y_N \\end{array}\\right] \\sim \\mathcal{N}\\left( \\left[\\begin{array}{c} \\mu_1\\\\ \\vdots \\\\ \\mu_N\\end{array}\\right], \\Sigma\\right)$$\n",
    "\n",
    "Let's generalize to any number of points:\n",
    "- The mean becomes $\\mu(x)$\n",
    "- The covariance matrix can be obtained through a **covariance kernel** $k(x,x')$\n",
    "\n",
    "For a finite set of points $(x_1,\\ldots,x_N)$, the corresponding $(y_1,\\ldots,y_N)$ follow a Gaussian distribution of mean $(\\mu(x_1),\\ldots,\\mu(x_N))$ and of covariance matrix $\\Sigma = \\left[\\begin{array}{ccc} k(x_1,x_1) & \\ldots & k(x_1,x_N)\\\\ \\vdots & \\ddots & \\vdots \\\\ k(x_1,x_N) & \\ldots & k(x_N,x_N) \\end{array}\\right]$.\n",
    "\n",
    "$$\\left[\\begin{array}{c}y_1\\\\ \\vdots\\\\y_N \\end{array}\\right] \\sim \\mathcal{N}\\left( \\left[\\begin{array}{c} \\mu(x_1)\\\\ \\vdots \\\\ \\mu(x_N)\\end{array}\\right], \\Sigma\\right)$$\n",
    "\n",
    "The information of $\\mu(x)$ and $k(x,x')$ defines a **Gaussian Process**. If we were able to learn a certain hidden function $f$ as a Gaussian Process, not only would we have the average function that fits $f$ best, but we would also have the probability that any other function fits $f$. In other words, in any new point $x$, we would have the average prediction $\\mu(x)$ but also an **uncertainty estimation** through the variance estimate $\\sigma(x)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <a id=\"sec2\"></a>2. Back to the regression problem\n",
    "\n",
    "So we assume that $y$ is drawn from a Gaussian Process.\n",
    "\n",
    "Recall that $\\mu(x)$ is the mean of the distribution in $x$ and that $k(x,x')$ describes how similar the values of $y$ and $y'$ (resp. in $x$ and $x'$) are likely to be spread around their respective means.\n",
    "\n",
    "To make things simple, assume that the Gaussian Process describing $f$ has mean zero, so $\\mu(x)=0$ everywhere. So what relates an observation to another is just the covariance function $k(x,x')$.\n",
    "\n",
    "A common covariance function is the so-called **squared exponential**:\n",
    "$$k(x,x') = \\sigma^2 e^{-\\frac{(x-x')^2}{2 l^2}}$$\n",
    "\n",
    "With this covariance function, the correlation between $y$ and $y'$ is high when $x$ and $x'$ are close. As $x$ and $x'$ get further from each other, $y$ and $y'$ tend to become independent.\n",
    "\n",
    "Since we assume that the observed data $\\left\\{(x_i,y_i)\\right\\}_{i=1...N}$ are drawn from a Gaussian distribution and that any new point $(x,y)$ should be drawn from that distribution too, we can write:\n",
    "\n",
    "$$\\left[\\begin{array}{c}y_1\\\\ \\vdots\\\\y_N \\\\y \\end{array}\\right] \\sim \\mathcal{N}\\left( 0_{N+1}, \\left[\\begin{array}{cccc}\n",
    "k(x_1,x_1) & \\ldots & k(x_1,x_N) & k(x_1, x)\\\\ \n",
    "\\vdots     & \\ddots & \\vdots     & \\vdots \\\\\n",
    "k(x_1,x_N) & \\ldots & k(x_N,x_N) & k(x_N,x)\\\\\n",
    "k(x_1, x)  & \\ldots & k(x_N,x)   & k(x,x)\n",
    "\\end{array}\\right] \\right)$$\n",
    "\n",
    "(where $0_{N+1}$ is the $N+1$ dimensional zero vector)\n",
    "\n",
    "The line above simply states that all points, both the observed data points and the new points on which we wish to make a prediction, are drawn according to the same Gaussian Process. Let's simplify the writing using vector notation. Let's write:\n",
    "- the data points $\\mathbf{y} = \\left[y_1,\\ldots,y_N\\right]$ and $\\mathbf{x} = \\left[x_1,\\ldots,x_N\\right]$, \n",
    "- the data covariance matrix $K = \\left[\\begin{array}{ccc}\n",
    "k(x_1,x_1) & \\ldots & k(x_1,x_N)\\\\ \n",
    "\\vdots     & \\ddots & \\vdots\\\\\n",
    "k(x_1,x_N) & \\ldots & k(x_N,x_N)\n",
    "\\end{array}\\right]$\n",
    "- The cross-covariance vector $K_*(x) = \\left[k(x_1, x), \\ldots, k(x_N,x)\\right]$\n",
    "\n",
    "Then we have:\n",
    "$$\\left[\\begin{array}{c}\\mathbf{y}\\\\y \\end{array}\\right] \\sim \\mathcal{N}\\left( 0_{N+1}, \\left[\\begin{array}{cc}\n",
    "K & K_*(x)^T\\\\ \n",
    "K_*(x) & k(x,x)\n",
    "\\end{array}\\right] \\right)$$\n",
    "\n",
    "Let's take a step back. What we have written so far is the probability $\\mathbb{P}(\\mathbf{y},y|\\mathbf{x},x)$. But what we are interested in is the posterior distribution $\\mathbb{P}(y|\\mathbf{x},\\mathbf{y},x)$; that is \"the probability of the prediction $y$, given the data $(\\mathbf{x},\\mathbf{y})$\". So let's use Bayes theorem:\n",
    "\n",
    "$$\\mathbb{P}(y|\\mathbf{x},\\mathbf{y},x) = \\frac{\\mathbb{P}(\\mathbf{y},y|\\mathbf{x},x)}{\\mathbb{P}(\\mathbf{y}|\\mathbf{x},x)}$$\n",
    "\n",
    "It appears that because we have assumed that the values were drawn from a Gaussian Process, this posterior follows a Gaussian distribution too:\n",
    "$$\\mathbb{P}(y|\\mathbf{x},\\mathbf{y},x) = \\mathcal{N}\\left( K_*(x)K^{-1} \\mathbf{y}, k(x,x) - K_*(x) K^{-1} K_*(x)^T\\right)$$\n",
    "\n",
    "Consequently, our best estimate for $y$ is the mean of this distribution:\n",
    "$$\\bar{y} = K_*(x) K^{-1} \\mathbf{y}$$\n",
    "\n",
    "And the uncertainty in this estimate is captured by the variance:\n",
    "$$\\sigma(y)^2 = k(x,x)- K_*(x)K^{-1}K_*(x)^T$$\n",
    "\n",
    "<div class=\"alert alert-success\"> \n",
    "Given the input data $\\mathbf{y} = \\left[y_1,\\ldots,y_N\\right]$ and $\\mathbf{x} = \\left[x_1,\\ldots,x_N\\right]$, and given a covariance kernel $k(x,x')$, a Gaussian Process regressor estimates the distribution of $y(x)$ as a Gaussian $\\mathcal{N}(\\mu,\\sigma)$ with:\n",
    "<ul>\n",
    "<li> $\\mu = K_*(x)K^{-1} \\mathbf{y}$\n",
    "<li> $\\sigma(y)^2 = k(x,x) - K_*(x)K^{-1}K_*(x)^T$\n",
    "</ul>\n",
    "where:\n",
    "<ul>\n",
    "<li> $K = \\left[\\begin{array}{ccc}\n",
    "k(x_1,x_1) & \\ldots & k(x_1,x_N)\\\\ \n",
    "\\vdots     & \\ddots & \\vdots\\\\\n",
    "k(x_1,x_N) & \\ldots & k(x_N,x_N)\n",
    "\\end{array}\\right]$\n",
    "<li>$K_*(x) = \\left[k(x_1, x), \\ldots, k(x_N,x)\\right]$\n",
    "</ul>\n",
    "</div>\n",
    "\n",
    "Let's take a concrete example.\n",
    "\n",
    "Suppose the hidden function we want to learn is $f(x) = x \\sin(x)$.\n",
    "\n",
    "Suppose the observation is drawn as $y = f(x) + \\mathcal{N}(0, \\sigma_n^2)$.\n",
    "\n",
    "Let's draw 10 data samples and try to obtain the best fit function and confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:13:58.906230Z",
     "start_time": "2019-10-21T13:13:58.344239Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func(x):\n",
    "    return x*np.sin(x)\n",
    "\n",
    "sigma_noise = 0.3\n",
    "def observation(x):\n",
    "    return func(x) + np.random.normal(0,sigma_noise,x.shape[0])\n",
    "\n",
    "X = np.linspace(-5,10,10)\n",
    "N = X.shape[0]\n",
    "Y = observation(X)\n",
    "x = np.linspace(-5,10,100)\n",
    "\n",
    "\n",
    "fig=plt.figure(figsize=(8,8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(x, func(x), 'r:', label=u'$f(x) = x\\,\\sin(x)$')\n",
    "plt.plot(X, Y, 'r.', markersize=10, label=u'Observations')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.ylim(-6, 10)\n",
    "plt.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Covariance Kernels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we can implement the simplest quadratic kernel: \n",
    "$$k(x_1, x_2) = \\sigma_k^2\\  (x_1 . x_2^{\\top})$$\n",
    "\n",
    "Where $ \\sigma_k$ is the variance of the process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_kernel = 0.2\n",
    "def kernel(x1,x2,sigma_kernel,l,sigma_noise):\n",
    "    k = sigma_kernel**2*np.dot(x1,x2.T)\n",
    "    return k + sigma_noise*(x1==x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can have a variety of other kernels that are more complicated and more realistic to model the uncertainties, for example: \n",
    "\\begin{align}\n",
    "\\exp\\left( -\\frac12 \\left(\\frac{\\lVert x - y \\rVert}{l}\\right)^\\beta \\right)\n",
    "&\\qquad\\text{ for $0 < \\beta \\le 2$ ($\\beta = 2$ is square exponential, $\\beta = 1$ is absolute exponential)}\n",
    "\\\\\n",
    "\\lVert x - z_0 \\rVert + \\lVert y - z_0 \\rVert - \\lVert x - y \\rVert\n",
    "&\\qquad\\text{ for any $z_0$ (\"distance kernel\")}\n",
    "\\\\\n",
    "\\frac{1}{\\sqrt{\\lVert x - y \\rVert^2 + c}}\n",
    "&\\qquad\\text{ (inverse multiquadric)}\n",
    "\\\\\n",
    "\\left( 1 + \\frac{\\lVert x - y \\rVert^2}{2 \\alpha \\ell^2} \\right)^{-\\alpha}\n",
    "&\\qquad\\text{ (rational quadratic; $\\alpha \\to \\infty$ becomes Gaussian)}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our case, we will use the square exponential kernel because it is a smooth kernel.\n",
    "\n",
    "For our 1-dimensional example, this kernel writes as:\n",
    "$$k(x_1, x_2) =  \\sigma_k^2 \\exp\\left( -\\frac{1}{2 l^2} \\lVert x_1 - x_2 \\rVert^2 \\right).$$\n",
    "\n",
    "Where $ \\sigma_k$ is the variance of the process and $l$ is a correlation length."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "**Exercice:**<br>\n",
    "Your turn to play. Define the kernel above in the cell below. Afterwards, we also want to add a noise but for this exercice, you just need to code the non-noisy part.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the best function, we need a covariance kernel. We will take the square exponential kernel with arbitrary $\\sigma$ and $l$ parameters and will modify it slightly to account for the measurement noise $\\sigma_n$. Then we simply apply the formula above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:30:16.392768Z",
     "start_time": "2019-10-21T13:30:16.385442Z"
    }
   },
   "outputs": [],
   "source": [
    "sigma_kernel = 0.2\n",
    "l=0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/code4.py\n",
    "# If you get stuck, uncomment the line above to load a correction in this cell (then you can execute this code).\n",
    "def kernel(x1,x2,sigma_kernel,l,sigma_noise):\n",
    "    ### WRITE YOUR CODE HERE\n",
    "    #k =  \n",
    "    return k + sigma_noise*(x1==x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "**Exercice:**<br>\n",
    "Define two functions `compute_K(X,sigma_kernel,l,sigma_noise)` (that returns the covariance matrix) and `GPpredict(x_new, x_data, y_data, Kinv)` (that returns the mean and standard deviation of the output value) below.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:30:17.235928Z",
     "start_time": "2019-10-21T13:30:17.229347Z"
    }
   },
   "outputs": [],
   "source": [
    "# %load solutions/code5.py\n",
    "### WRITE YOUR CODE HERE\n",
    "# If you get stuck, uncomment the line above to load a correction in this cell (then you can execute this code).\n",
    "\n",
    "def compute_K(X,sigma_kernel,l,sigma_noise):\n",
    "    ### FILL THE VALUES OF K\n",
    "    \n",
    "    return K\n",
    "\n",
    "def GPpredict(x_new, x_data, y_data, Kinv):\n",
    "    ### COMPUTE MEAN AND STANDARD DEVIATION\n",
    "    \n",
    "    return mu, sigma\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:30:19.432718Z",
     "start_time": "2019-10-21T13:30:19.095143Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Kinv = np.linalg.inv(compute_K(X,sigma_kernel,l,sigma_noise))\n",
    "\n",
    "x = np.linspace(-5,10,100)\n",
    "y = np.zeros(x.shape)\n",
    "sigma = np.zeros(x.shape)\n",
    "for i in range(x.shape[0]):\n",
    "    y[i], sigma[i] = GPpredict(x[i].reshape(-1,1), X, Y, Kinv)\n",
    "\n",
    "fig=plt.figure(figsize=(8,8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(x, func(x), 'r:', label=u'$f(x) = x\\,\\sin(x)$')\n",
    "plt.plot(X, Y, 'r.', markersize=10, label=u'Observations')\n",
    "plt.plot(x, y, 'b-', label=u'Prediction')\n",
    "plt.fill(np.concatenate([x, x[::-1]]),\n",
    "         np.concatenate([y - 1.9600 * sigma,\n",
    "                        (y + 1.9600 * sigma)[::-1]]),\n",
    "         alpha=.5, fc='b', ec='None', label='95% confidence interval')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.ylim(-6, 10)\n",
    "plt.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's quite disappointing. Indeed, the (blue) learned curve goes through the data points but it is far from the (red) original function. An interesting feature however is that the uncertainty reduces almost to zero around the data points and strongly increases elsewhere.\n",
    "\n",
    "What happened? It seems we made a poor arbitrary choice of kernel parameters. For instance taking $l=0.3$ implies that values $y$ and $y'$ for two points $x$ and $x'$ quickly tend to be independent and so the \"influence\" of a data point (a red point) does not extend far.\n",
    "\n",
    "Let's re-run this experiment with other parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:34:12.893293Z",
     "start_time": "2019-10-21T13:34:12.633219Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma_kernel = 3\n",
    "l=1\n",
    "\n",
    "Kinv = np.linalg.inv(compute_K(X,sigma_kernel,l,sigma_noise))\n",
    "\n",
    "def GPpredict(x_new, x_data, y_data, Kinv):\n",
    "    N = y_data.shape[0]\n",
    "    Kstar = np.zeros((1,N))\n",
    "    for i in range(N):\n",
    "        Kstar[0,i] = kernel(x_data[i], x_new, sigma_kernel, l, sigma_noise)\n",
    "    mu = Kstar @ Kinv @ y_data\n",
    "    sigma = kernel(x_new,x_new,sigma_kernel,l,sigma_noise) - Kstar @ Kinv @ Kstar.T\n",
    "    return mu, sigma\n",
    "\n",
    "x = np.linspace(-5,10,100)\n",
    "y = np.zeros(x.shape)\n",
    "sigma = np.zeros(x.shape)\n",
    "for i in range(x.shape[0]):\n",
    "    y[i], sigma[i] = GPpredict(x[i], X, Y, Kinv)\n",
    "\n",
    "fig=plt.figure(figsize=(8,8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(x, func(x), 'r:', label=u'$f(x) = x\\,\\sin(x)$')\n",
    "plt.plot(X, Y, 'r.', markersize=10, label=u'Observations')\n",
    "plt.plot(x, y, 'b-', label=u'Prediction')\n",
    "plt.fill(np.concatenate([x, x[::-1]]),\n",
    "         np.concatenate([y - 1.9600 * sigma,\n",
    "                        (y + 1.9600 * sigma)[::-1]]),\n",
    "         alpha=.5, fc='b', ec='None', label='95% confidence interval')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.ylim(-6, 10)\n",
    "plt.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This starts to look better. The blue curve fits the data points better but it's still not perfect and the uncertainty between data points is actually quite large.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "**Exercice:**<br>\n",
    "Test several values of $[l, \\sigma_f]$ with $l$ being geometrically the length-scale (of oscillations) and  $\\sigma_f$ the amplitude. Compare the square exponential and quadratic kernels and conclude.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We could wish for an automated way of tuning these kernel parameters. Let's call them $\\theta$.\n",
    "\n",
    "One way to do that is to search for the value of $\\theta$ that maximizes the probability of the observed $\\mathbf{y}$ given the inputs $\\mathbf{x}$. In other words, to find the best $\\theta$, we search for the one that explains best the data that we already know, and then use it to make predictions on new points. That is called **Marginal Likelihood Maximization**.\n",
    "$$\\max_\\theta \\mathbb{P}(\\mathbf{y}|\\mathbf{x})$$\n",
    "\n",
    "Fortunately for use, scikit-learn includes all these operations in a single procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:40:11.441931Z",
     "start_time": "2019-10-21T13:40:11.029020Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {color: black;background-color: white;}#sk-container-id-5 pre{padding: 0;}#sk-container-id-5 div.sk-toggleable {background-color: white;}#sk-container-id-5 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-5 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-5 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-5 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-5 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-5 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-5 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-5 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-5 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-5 div.sk-item {position: relative;z-index: 1;}#sk-container-id-5 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-5 div.sk-item::before, #sk-container-id-5 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-5 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-5 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-5 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-5 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-5 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-5 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-5 div.sk-label-container {text-align: center;}#sk-container-id-5 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-5 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GaussianProcessRegressor()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GaussianProcessRegressor</label><div class=\"sk-toggleable__content\"><pre>GaussianProcessRegressor()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "GaussianProcessRegressor()"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.gaussian_process import GaussianProcessRegressor\n",
    "gp = GaussianProcessRegressor()\n",
    "X=X.reshape(-1,1)\n",
    "Y=Y.reshape(-1,1)\n",
    "gp.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:48:38.030257Z",
     "start_time": "2019-10-21T13:48:37.766260Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Hyperparameter(name='k1__constant_value', value_type='numeric', bounds='fixed', n_elements=1, fixed=True), Hyperparameter(name='k2__length_scale', value_type='numeric', bounds='fixed', n_elements=1, fixed=True)]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5,10,100)\n",
    "#x = np.linspace(-25,40,100)\n",
    "y = np.zeros(x.shape)\n",
    "sigma = np.zeros(x.shape)\n",
    "for i in range(x.shape[0]):\n",
    "    y[i], sigma[i] = gp.predict(x[i].reshape(-1,1), return_std=True)\n",
    "\n",
    "fig=plt.figure(figsize=(8,8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(x, func(x), 'r:', label=u'$f(x) = x\\,\\sin(x)$')\n",
    "plt.plot(X, Y, 'r.', markersize=10, label=u'Observations')\n",
    "plt.plot(x, y, 'b-', label=u'Prediction')\n",
    "plt.fill(np.concatenate([x, x[::-1]]),\n",
    "         np.concatenate([y - 1.9600 * sigma,\n",
    "                        (y + 1.9600 * sigma)[::-1]]),\n",
    "         alpha=.5, fc='b', ec='None', label='95% confidence interval')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.ylim(-6, 10)\n",
    "plt.legend(loc='upper left');\n",
    "print(gp.kernel_.hyperparameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that's better. Although the correct function was not found exactly, given the few data points we had it's already a good fit.\n",
    "\n",
    "Let's summarize a few properties of Gaussian Processes.\n",
    "\n",
    "<div class=\"alert alert-success\">\n",
    "<ul>\n",
    "<li> Gaussian processes are an offline method\n",
    "<li> They are an optimal method (in the sense of Bayesian inference)\n",
    "<li> They provide a best fit function, but also error bounds\n",
    "<li> Given $N$ data points, they require the inversion of an $N\\times N$ covariance matrix (complexity in $O(N^3)$)\n",
    "<li> The kernel encodes the prior knowledge about the function's behaviour.\n",
    "<li> Careful choice / design of kernels can make GPs a very powerful tool... but can also make them very unstable computationally.\n",
    "</ul>\n",
    "</div>\n",
    "\n",
    "Let's illustrate this last property on a final example, with a periodic function and the \"Exp-Sine-Squared\" kernel that is commonly used for periodic functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T13:56:08.661819Z",
     "start_time": "2019-10-21T13:56:08.076898Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.gaussian_process.kernels import WhiteKernel, ExpSineSquared\n",
    "\n",
    "# Generate sample data\n",
    "rng = np.random.RandomState(0)\n",
    "X = 15 * rng.rand(100, 1)\n",
    "y = np.sin(X).ravel()\n",
    "y += 3 * (0.5 - rng.rand(X.shape[0]))  # add noise\n",
    "\n",
    "# GP training\n",
    "gp_kernel = ExpSineSquared(1.0, 5.0, periodicity_bounds=(1e-2, 1e1)) + WhiteKernel(1e-1)\n",
    "gpr = GaussianProcessRegressor(kernel=gp_kernel)\n",
    "#gpr = GaussianProcessRegressor()\n",
    "gpr.fit(X, y)\n",
    "\n",
    "# GP prediction\n",
    "X_plot = np.linspace(0, 25, 10000)[:, None]\n",
    "y_gpr, y_std = gpr.predict(X_plot, return_std=True)\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(8,8))\n",
    "lw = 2\n",
    "plt.scatter(X, y, c='k', label='data')\n",
    "plt.plot(X_plot, np.sin(X_plot), color='navy', lw=lw, label='True')\n",
    "plt.plot(X_plot, y_gpr, color='darkorange', lw=lw,\n",
    "         label='GPR (%s)' % gpr.kernel_)\n",
    "plt.fill_between(X_plot[:, 0], y_gpr - y_std, y_gpr + y_std, color='darkorange',\n",
    "                 alpha=0.2)\n",
    "plt.xlabel('data')\n",
    "plt.ylabel('target')\n",
    "plt.xlim(0, 25)\n",
    "plt.ylim(-4, 4)\n",
    "plt.legend(loc=\"best\",  scatterpoints=1, prop={'size': 8})\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <a id=\"sec3\"></a>3. Gaussian Processes for classification ?\n",
    "\n",
    "It actually works exactly the same way. For binary classification problems, Gaussian Processes try to predict the probability of belonging to the first class (thus turning back to a regression problem).\n",
    "\n",
    "More precisely, they try to build a hidden function $f(x)$ so that: \n",
    "$$\\mathbb{P}(Y=0|X=x) = \\frac{1}{1+e^{f(x)}}$$\n",
    "Where $f$ is a Gaussian Process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <a id=\"sec4\"></a> 4. Examples\n",
    "\n",
    "## <a id=\"sec4-1\"></a> 4.1 Spam or ham?\n",
    "\n",
    "Let's illustrate that on the Ling-spam database."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:09:40.437397Z",
     "start_time": "2019-10-21T14:09:36.902587Z"
    }
   },
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'load_spam'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-21-94334f07a894>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msys\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mpath\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mpath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'../2 - Text data preprocessing'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mload_spam\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mspam_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mload_spam\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mspam_data_loader\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mspam_data\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mload_data\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'load_spam'"
     ]
    }
   ],
   "source": [
    "from sys import path\n",
    "path.append('../2 - Text data preprocessing')\n",
    "import load_spam\n",
    "spam_data = load_spam.spam_data_loader()\n",
    "spam_data.load_data()\n",
    "print(\"data loaded\")\n",
    "\n",
    "Xtrain, ytrain, Xtest, ytest = spam_data.split(2000)\n",
    "print(Xtrain.shape)\n",
    "print(Xtest.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have loaded a training set with 2000 examples. This means that the Gaussian Process training will require inverting a $2000\\times2000$ matrix. Although this is still feasible in a few seconds or minutes, we are touching here a limitation of Gaussian Processes in their ability to scale up to large datasets.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "**Exercice:**<br>\n",
    "Use scikit-learn to fit a [Gaussian Process classifier](http://scikit-learn.org/stable/modules/gaussian_process.html#gaussian-process-classification-gpc) to the spam data loaded above. Estimate the generalization score.<br>\n",
    "Hint: you can use the `.toarray()` method of sparse matrices to get the corresponding dense matrix.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:11:07.546628Z",
     "start_time": "2019-10-21T14:10:10.768404Z"
    }
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'toarray'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-22-d81097848ac0>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;31m# If you get stuck, uncomment the line above to load a correction in this cell (then you can execute this code).\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mspam_GP\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mGaussianProcessClassifier\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXtrain\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mytrain\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscore\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXtest\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mytest\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'toarray'"
     ]
    }
   ],
   "source": [
    "# %load solutions/code6.py\n",
    "### WRITE YOUR CODE HERE\n",
    "# If you get stuck, uncomment the line above to load a correction in this cell (then you can execute this code).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a fair comparison, we can also try the training on the word count features rather than Tf-Idf ones. Although it would probably be more beneficial to search for a better kernel than the default squared exponential one.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "**Exercice:**<br>\n",
    "Use scikit-learn to fit a Gaussian Process classifier to the raw word count data loaded below. Estimate the generalization score.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:12:51.210593Z",
     "start_time": "2019-10-21T14:12:51.204740Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'spam_data' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-23-3ab43560e3a3>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mXtrain\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mytrain\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mXtest\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mytest\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mspam_data\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2000\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeat\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'wordcount'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'spam_data' is not defined"
     ]
    }
   ],
   "source": [
    "Xtrain, ytrain, Xtest, ytest = spam_data.split(2000, feat='wordcount')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:13:55.362716Z",
     "start_time": "2019-10-21T14:12:52.199856Z"
    }
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'toarray'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-24-2b7b5a9b1d2d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;31m# If you get stuck, uncomment the line above to load a correction in this cell (then you can execute this code).\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mspam_GP\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mGaussianProcessClassifier\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXtrain\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mytrain\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscore\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXtest\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mytest\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'toarray'"
     ]
    }
   ],
   "source": [
    "# %load solutions/code7.py\n",
    "### WRITE YOUR CODE HERE\n",
    "# If you get stuck, uncomment the line above to load a correction in this cell (then you can execute this code).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's keep this last classifier and identify which are the misclassified emails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'spam_data' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-25-8ee85b5ee9f3>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Retrain\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mXtrain\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mytrain\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mXtest\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mytest\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mspam_data\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2000\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeat\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'wordcount'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mspam_GP\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mGaussianProcessClassifier\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXtrain\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mytrain\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'spam_data' is not defined"
     ]
    }
   ],
   "source": [
    "# Retrain\n",
    "Xtrain, ytrain, Xtest, ytest = spam_data.split(2000, feat='wordcount')\n",
    "spam_GP = GaussianProcessClassifier()\n",
    "spam_GP.fit(Xtrain.toarray(),ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:15:29.874219Z",
     "start_time": "2019-10-21T14:15:13.010486Z"
    }
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'toarray'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-26-39a41ccaccef>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Find misclassified examples\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mypredict\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mXtest\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mmisclass\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnot_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mypredict\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mytest\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mXmisclass\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mXtest\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mmisclass\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mymisclass\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mytest\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mmisclass\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'toarray'"
     ]
    }
   ],
   "source": [
    "# Find misclassified examples\n",
    "ypredict = spam_GP.predict(Xtest.toarray())\n",
    "misclass = np.not_equal(ypredict, ytest)\n",
    "Xmisclass = Xtest[misclass,:]\n",
    "ymisclass = ytest[misclass]\n",
    "misclass_indices = [i for i, j in enumerate(misclass) if j == True]\n",
    "print(\"Misclassified messages indices:\", misclass_indices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:15:29.885441Z",
     "start_time": "2019-10-21T14:15:29.877155Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion matrix:\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'ypredict' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-27-a244db1bdd99>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmetrics\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mconfusion_matrix\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Confusion matrix:\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mconfusion_matrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mytest\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mypredict\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'ypredict' is not defined"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "print(\"Confusion matrix:\")\n",
    "print(confusion_matrix(ytest, ypredict))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:15:49.529641Z",
     "start_time": "2019-10-21T14:15:49.358830Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'misclass_indices' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-28-85201403e9a6>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Check some misclassified mails\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mindex\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmisclass_indices\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m2000\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Prediction:\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mspam_GP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mspam_data\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mword_count\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mspam_data\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprint_email\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'misclass_indices' is not defined"
     ]
    }
   ],
   "source": [
    "# Check some misclassified mails\n",
    "index = misclass_indices[0]+2000\n",
    "print(\"Prediction:\", spam_GP.predict(spam_data.word_count[index,:].toarray()))\n",
    "spam_data.print_email(index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <a id=\"sec4-2\"></a> 4.2 NIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:16:15.616110Z",
     "start_time": "2019-10-21T14:16:15.501553Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 8, 8)\n",
      "(1797,)\n",
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "digits = datasets.load_digits()\n",
    "print(digits.data.shape)\n",
    "print(digits.images.shape)\n",
    "print(digits.target.shape)\n",
    "print(digits.target_names)\n",
    "\n",
    "X = digits.data\n",
    "y = digits.target\n",
    "Xtrain,Xtest = np.split(X,[1000])\n",
    "ytrain,ytest = np.split(y,[1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:16:24.435470Z",
     "start_time": "2019-10-21T14:16:24.429540Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.utils import shuffle\n",
    "\n",
    "def shuffle_and_split(X,y,n):\n",
    "    X0,y0 = shuffle(X,y)\n",
    "    Xtrain,Xtest = np.split(X0,[n])\n",
    "    ytrain,ytest = np.split(y0,[n])\n",
    "    return Xtrain, ytrain, Xtest, ytest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-21T14:21:17.605159Z",
     "start_time": "2019-10-21T14:21:12.234639Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 64)\n",
      "(1000,)\n",
      "Generalization error: 0.8996235884567126\n",
      "Generalization score: 0.10037641154328733\n",
      "Confusion matrix:\n",
      "[[ 0  0  0  0  0  0  0  0  0 78]\n",
      " [ 0  2  0  0  0  0  0  0  0 77]\n",
      " [ 0  0  0  0  0  0  0  0  0 89]\n",
      " [ 0  0  0  0  0  0  0  0  0 79]\n",
      " [ 0  0  0  0  0  0  0  0  0 86]\n",
      " [ 0  0  0  0  0  0  0  0  0 75]\n",
      " [ 0  0  0  0  0  0  0  0  0 79]\n",
      " [ 0  0  0  0  0  0  0  0  0 76]\n",
      " [ 0  0  0  0  0  0  0  0  0 78]\n",
      " [ 0  0  0  0  0  0  0  0  0 78]]\n"
     ]
    }
   ],
   "source": [
    "Xtrain, ytrain, Xtest, ytest = shuffle_and_split(X,y,1000)\n",
    "print(Xtrain.shape)\n",
    "print(ytrain.shape)\n",
    "digits_gp = GaussianProcessClassifier()\n",
    "digits_gp.fit(Xtrain,ytrain)\n",
    "prediction = digits_gp.predict(Xtest)\n",
    "#print(\"Training error:\", np.sum(np.not_equal(prediction,ytest))/len(ytest))\n",
    "print(\"Generalization error:\", np.sum(np.not_equal(prediction,ytest))/len(ytest) )\n",
    "print(\"Generalization score:\", digits_gp.score(Xtest,ytest))\n",
    "print(\"Confusion matrix:\")\n",
    "print(confusion_matrix(ytest, prediction))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A perfect illustration that (often) ML methods don't work out-of-the-box and require some engineering knowledge just like any other modeling method. Here for example, a data scientist might investigate the kernel's properties, the marginal likelihood optimization procedure, the data distribution..., while the computer vision expert might question the use of pixel data as input.\n",
    "\n",
    "For instance, try `digits_gp = GaussianProcessClassifier(multi_class=\"one_vs_one\")` and try to explain what has changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <a id=\"sec4\"></a> 4.3 Cancer mortality Examples\n",
    "\n",
    "The OLS regression challenge tasks you with predicting cancer mortality rates for US counties. The dataset contains data from cancer.gov, clinicaltrials.gov, and the American Community Survey. It is in CSV format and includes the following information about cancer in the US: death rates, reported cases, US county name, income per county, population, demographics and more.  \n",
    "\n",
    "[Dataset for cancer mortality](https://data.world/nrippner/ols-regression-challenge)\n",
    "\n",
    "**Question** :\n",
    "- What is the main limitation in using GP with this dataset ?\n",
    "- Using GP, make a predictor on the target variable\n",
    "- What are the main possible improvements ?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "pd.read_csv(\"../data/cancer/cancer_reg.csv\",encoding = \"ISO-8859-1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
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