Linear Regression Implementation from scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression Implementation using numpy\n",
    "\n",
    "In linear regression we want to model the relationship between a **scalar dependent variable** $y$ and one or more **independent (predictor) variables** $\\boldsymbol{x}$.\n",
    "\n",
    "**Given:** \n",
    "- dataset $\\{(\\boldsymbol{x}^{(1)}, y^{(1)}), ..., (\\boldsymbol{x}^{(m)}, y^{(m)})\\}$\n",
    "- with $\\boldsymbol{x}^{(i)}$ being a $d-$dimensional vector $\\boldsymbol{x}^i = (x^{(i)}_1, ..., x^{(i)}_d)$\n",
    "- $y^{(i)}$ being a scalar target variable\n",
    "\n",
    "The linear regression model can be interpreted as a very **simple neural network:**\n",
    "- it has a real-valued weight vector $\\boldsymbol{w}= (w^{(1)}, ..., w^{(d)})$\n",
    "- it has a real-valued bias $b$\n",
    "- it uses the identity function as its activation function\n",
    "\n",
    "![title](figures/linear_regression.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training\n",
    "A linear regression model can be trained using either  \n",
    "a) gradient descent or  \n",
    "b) the normal equation (closed-form solution): $\\boldsymbol{w} = (\\boldsymbol{X}^T \\boldsymbol{X})^{-1} \\boldsymbol{X}^T \\boldsymbol{y}$ \n",
    "\n",
    "where $\\boldsymbol{X}$ is a matrix of shape $(m, n_{features})$ that holds all training examples.  \n",
    "The normal equation requires computing the inverse of $\\boldsymbol{X}^T \\boldsymbol{X}$. The computational complexity of this operation lies between $O(n_{features}^{2.4}$) and $O(n_{features}^3$) (depending on the implementation).\n",
    "Therefore, if the number of features in the training set is large, the normal equation will get very slow. \n",
    "\n",
    "* * *\n",
    "The training procedure of a linear regression model has different steps. In the beginning (step 0) the model parameters are initialized. The other steps (see below) are repeated for a specified number of training iterations or until the parameters have converged.\n",
    "\n",
    "**Step 0: ** \n",
    "\n",
    "Initialize the weight vector and bias with zeros (or small random values)\n",
    "\n",
    "**OR**\n",
    "\n",
    "Compute the parameters directly using the normal equation\n",
    "* * *\n",
    "\n",
    "**Step 1: ** (Only needed when training with gradient descent)\n",
    "\n",
    "Compute a linear combination of the input features and weights. This can be done in one step for all training examples, using vectorization and broadcasting:\n",
    "$\\boldsymbol{\\hat{y}} = \\boldsymbol{X} \\cdot \\boldsymbol{w} + b $\n",
    "\n",
    "where $\\boldsymbol{X}$ is a matrix of shape $(m, n_{features})$ that holds all training examples, and $\\cdot$ denotes the dot product.\n",
    "* * *\n",
    "\n",
    "**Step 2: ** (Only needed when training with gradient descent)\n",
    "\n",
    "Compute the cost (mean squared error) over the training set:\n",
    "\n",
    "$J(\\boldsymbol{w},b) = \\frac{1}{m} \\sum_{i=1}^m \\Big(\\hat{y}^{(i)} - y^{(i)} \\Big)^2$\n",
    "* * *\n",
    "\n",
    "**Step 3: **  (Only needed when training with gradient descent)\n",
    "\n",
    "Compute the partial derivatives of the cost function with respect to each parameter:\n",
    "\n",
    "$ \\frac{\\partial J}{\\partial w_j} = \\frac{2}{m}\\sum_{i=1}^m \\Big( \\hat{y}^{(i)} - y^{(i)} \\Big) x^{(i)}_j$\n",
    "\n",
    "$ \\frac{\\partial J}{\\partial b} = \\frac{2}{m}\\sum_{i=1}^m \\Big( \\hat{y}^{(i)} - y^{(i)} \\Big)$\n",
    "\n",
    "\n",
    "The gradient containing all partial derivatives can then be computed as follows: \n",
    "\n",
    "$\\nabla_{\\boldsymbol{w}} J = \\frac{2}{m} \\boldsymbol{X}^T \\cdot \\big(\\boldsymbol{\\hat{y}} - \\boldsymbol{y} \\big)$\n",
    "\n",
    "$\\nabla_{\\boldsymbol{b}} J = \\frac{2}{m} \\big(\\boldsymbol{\\hat{y}} - \\boldsymbol{y} \\big)$\n",
    "* * *\n",
    "\n",
    "**Step 4: ** (Only needed when training with gradient descent)\n",
    "\n",
    "Update the weight vector and bias:\n",
    "\n",
    "$\\boldsymbol{w} = \\boldsymbol{w} - \\eta \\, \\nabla_w J$  \n",
    "\n",
    "$b = b - \\eta \\, \\nabla_b J$  \n",
    "\n",
    "\n",
    "where $\\eta$ is the learning rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-26T14:37:06.920607Z",
     "start_time": "2018-03-26T14:37:06.906905Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "class LinearRegression:\n",
    "    \n",
    "    def fit(self, X, y, lr = 0.001, epochs=10000, verbose=True, batch_size=1):\n",
    "        X = self.add_bias(X)\n",
    "        self.weights = np.zeros(len(X[0]))\n",
    "        for i in range(epochs):\n",
    "            idx = np.random.choice(len(X), batch_size) \n",
    "            X_batch, y_batch =  X[idx], y[idx]\n",
    "            self.weights -= lr * self.get_gradient(X_batch, y_batch)\n",
    "            if i % 1000 == 0 and verbose: \n",
    "                print('Iterations: %d - Error : %.4f' %(i, self.get_loss(X,y)))\n",
    "                \n",
    "    def predict(self, X):\n",
    "        return self.predict_(self.add_bias(X))\n",
    "    \n",
    "    def get_loss(self, X, y):\n",
    "        return np.mean((y - self.predict_(X)) ** 2)\n",
    "    \n",
    "    def predict_(self, X):\n",
    "        return np.dot(X,self.weights)\n",
    "    \n",
    "    def add_bias(self,X):\n",
    "        return np.insert(X, 0, np.ones(len(X)), axis=1)\n",
    "        \n",
    "    def get_gradient(self, X, y):\n",
    "        return -1.0 * np.dot(y - self.predict_(X), X) / len(X)\n",
    "    \n",
    "    def evaluate(self, X, y):\n",
    "        return self.get_loss(self.add_bias(X), y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations: 0 - Error : 29468.6469\n",
      "Iterations: 1000 - Error : 5222.0489\n",
      "Iterations: 2000 - Error : 4763.5437\n",
      "Iterations: 3000 - Error : 4468.1709\n",
      "Iterations: 4000 - Error : 4280.3568\n",
      "Iterations: 5000 - Error : 4161.9211\n",
      "Iterations: 6000 - Error : 4086.6240\n",
      "Iterations: 7000 - Error : 4039.2490\n",
      "Iterations: 8000 - Error : 4008.7785\n",
      "Iterations: 9000 - Error : 3989.7663\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "\n",
    "# Load the diabetes dataset\n",
    "diabetes = datasets.load_diabetes()\n",
    "\n",
    "\n",
    "# Use only one feature\n",
    "diabetes_X = diabetes.data[:, np.newaxis, 2]\n",
    "\n",
    "# Split the data into training/testing sets\n",
    "diabetes_X_train = diabetes_X[:-20]\n",
    "diabetes_X_test = diabetes_X[-20:]\n",
    "\n",
    "# Split the targets into training/testing sets\n",
    "diabetes_y_train = diabetes.target[:-20]\n",
    "diabetes_y_test = diabetes.target[-20:]\n",
    "\n",
    "# Create linear regression object\n",
    "regr = LinearRegression()\n",
    "\n",
    "# Train the model using the training sets\n",
    "regr.fit(diabetes_X_train, diabetes_y_train, lr=0.1, batch_size=len(diabetes_X_train))\n",
    "\n",
    "# Make predictions using the testing set\n",
    "diabetes_y_pred = regr.predict(diabetes_X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-26T14:37:08.615318Z",
     "start_time": "2018-03-26T14:37:08.519693Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Coefficients: \\n', array([152.84030657, 840.69507178]))\n",
      "Mean squared error: 2675.46\n",
      "Variance score: 0.45\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', regr.weights)\n",
    "# The mean squared error\n",
    "print(\"Mean squared error: %.2f\"\n",
    "      % mean_squared_error(diabetes_y_test, diabetes_y_pred))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % r2_score(diabetes_y_test, diabetes_y_pred))\n",
    "\n",
    "# Plot outputs\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  color='black')\n",
    "plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=3)\n",
    "\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z52fmksxcMm/evBHbrhcZSJKaomM0Nx4RnVRh4CuZeTlAZj7SMv9zwDfKyxXAkS2rLyxl7KZ8NdAdER3lLEHr8pIkaR+M5lUGAVwA3JmZH28pn9+y2G8Ct5XpK4CzImJSRCwGjgWuB24Aji1XFHRRdTy8IjMTuAZ4RVn/bODro7U/kiQ12WieIXg+8Drg1oi4uZT9KdVVAidQjQt0P/C7AJl5e0RcCtxBdYXCWzOzFyAi3gZcBbQDF2bm7WV77wYujogPAD+jCiBjyj4EkqQmGLVAkJk/Zugr867cwzofBD44RPmVQ62XmfdSXYUwTuxEIElqBu9UKEmSDAR12WIgSWoCA0ENXnYoSWoKA4EkSTIQ1JVeZiBJagADQQ22GEiSmsJAIEmSDASSJMlAUItXGUiSmsJAIEmSDAR1eZGBJKkJDAQ1hNcZSJIawkAgSZIMBHWloxlIkhrAQFCDVxlIkprCQCBJkgwEdXmVgSSpCQwENdhkIElqCgOBJEkyEEiSJANBbXYhkCQ1gYGgBu9UKElqCgOBJEkyENSVXncoSWoAA0EdthhIkhrCQCBJkgwEddlgIElqAgNBDbYYSJKawkAgSZIMBLXZZiBJagADQQ3h6EaSpIYwEEiSJANBXbYYSJKawEBQgw0GkqSmMBBIkiQDQV2OZSBJagIDQQ1eZCBJagoDgSRJMhDUZYOBJKkJDAQ12GIgSWoKA4EkSTIQ1OVFBpKkJjAQ1OBYBpKkpjAQSJIkA4EkSTIQ1JZeeChJagADQQ32IJAkNYWBQJIkGQjq8rJDSVITjFogiIgjI+KaiLgjIm6PiD8s5XMi4uqIuKc8zy7lERGfjIhlEXFLRDy7ZVtnl+XviYizW8pPjIhbyzqfjLG+DtA2A0lSQ4zmGYIe4I8y8zjgZOCtEXEccC7w3cw8FvhueQ3wEuDY8jgH+CxUAQJ4L/Bc4CTgvf0hoizz5pb1Th/F/ZEkqbFGLRBk5srMvKlMbwTuBBYAZwIXlcUuAl5eps8EvpiVa4HuiJgPnAZcnZlrMnMtcDVwepk3MzOvzcwEvtiyrTFjk4EkqQnGpA9BRCwCngVcBxyWmSvLrIeBw8r0AuDBltWWl7I9lS8fonzMhG0GkqSGGPVAEBHTga8B78jMDa3zyi/7Uf+NHRHnRMTSiFi6atWq0X47SZImnFENBBHRSRUGvpKZl5fiR8rpfsrzo6V8BXBky+oLS9meyhcOUf4EmXl+Zi7JzCXz5s2rt1OSJDXQaF5lEMAFwJ2Z+fGWWVcA/VcKnA18vaX89eVqg5OB9aVp4Srg1IiYXToTngpcVeZtiIiTy3u9vmVbY8KxjSRJTdExitt+PvA64NaIuLmU/SnwIeDSiHgT8ADwqjLvSuAMYBmwBXgjQGauiYi/BG4oy70/M9eU6bcAXwCmAN8qD0mStI9GLRBk5o/Z/ZX6Lx5i+QTeupttXQhcOET5UuDpNapZW3qZgSSpAbxTYQ22GEiSmsJAIEmSDAR12WAgSWoCA0ENXmUgSWoKA4EkSTIQ1OVFBpKkJjAQ1OBYBpKkpjAQSJIkA4EkSTIQ1JZeeChJagADQQ1edihJagoDgSRJMhDU5WWHkqQmMBDUYJOBJKkpDASSJMlAUJctBpKkJjAQ1GKbgSSpGQwEkiTJQFCXVxlIkprAQFCDVxlIkprCQCBJkgwE9dlmIEma+AwENdhiIElqCgOBJEkaXiCIiC8Np+xg5FUGkqQmGO4ZguNbX0REO3DiyFdnYvEqA0lSU+wxEETEeRGxEfjViNhQHhuBR4Gvj0kNJUnSqNtjIMjMv87MGcBHM3NmeczIzEMy87wxquMBzRYDSVITDLfJ4BsRMQ0gIv5PRHw8Io4axXpNCOF1BpKkhhhuIPgssCUingn8EfAL4IujVitJkjSmhhsIejIzgTOBT2Xmp4EZo1etiSO9zECS1AAdw1xuY0ScB7wO+O8R0QZ0jl61JgavMpAkNcVwzxC8GtgO/HZmPgwsBD46arWSJEljaliBoISArwCzIuI3gG2ZaR8CSZIaYrh3KnwVcD3wSuBVwHUR8YrRrNhEYQ8CSVITDLcPwXuA52TmowARMQ/4DnDZaFVsIrALgSSpKYbbh6CtPwwUq/dhXUmSdIAb7hmC/4iIq4CvltevBq4cnSpNLF51KElqgj0Ggog4BjgsM/84In4LeEGZ9VOqToYHtfC6Q0lSQ+ztDMHfAucBZOblwOUAEfGMMu+lo1o7SZI0JvbWD+CwzLx1cGEpWzQqNZpgvFOhJKkJ9hYIuvcwb8pIVkSSJI2fvQWCpRHx5sGFEfE7wI2jUyVJkjTW9taH4B3Av0bEa3k8ACwBuoDfHM2KTRQ2GEiSmmCPgSAzHwH+W0S8CHh6Kf5mZn5v1Gs2AXiRgSSpKYZ1H4LMvAa4ZpTrIkmSxol3G6zLNgNJUgMYCGoIRzOQJDWEgUCSJI1eIIiICyPi0Yi4raXsfRGxIiJuLo8zWuadFxHLIuLuiDitpfz0UrYsIs5tKV8cEdeV8ksiomu09mVPbDGQJDXBaJ4h+AJw+hDln8jME8rjSoCIOA44Czi+rPOZiGiPiHbg08BLgOOA15RlAT5ctnUMsBZ40yjuy5C8ykCS1BSjFggy84fAmmEufiZwcWZuz8z7gGXASeWxLDPvzcwdwMXAmVGNKnQKcFlZ/yLg5SO6A5IkHUTGow/B2yLiltKkMLuULQAebFlmeSnbXfkhwLrM7BlUPuYcy0CS1ARjHQg+CxwNnACsBD42Fm8aEedExNKIWLpq1aqR2+6IbUmSpPE1poEgMx/JzN7M7AM+R9UkALACOLJl0YWlbHflq4HuiOgYVL679z0/M5dk5pJ58+aNzM5IktQgYxoIImJ+y8vfBPqvQLgCOCsiJkXEYuBY4HrgBuDYckVBF1XHwyuyOk9/DfCKsv7ZwNfHYh8Gs8FAktQEw7p18f6IiK8CLwTmRsRy4L3ACyPiBKrv0fuB3wXIzNsj4lLgDqAHeGtm9pbtvA24CmgHLszM28tbvBu4OCI+APwMuGC09kWSpKYbtUCQma8Zoni3X9qZ+UHgg0OUXwlcOUT5vTze5DAuvOxQktQU3qlQkiQZCOryqkNJUhMYCGoI2wwkSQ1hIJAkSQaCutILDyVJDWAgqMEGA0lSUxgIJEmSgaAurzKQJDWBgaAO2wwkSQ1hIJAkSQaCumwxkCQ1gYGghrDNQJLUEAYCSZJkIKjNNgNJUgMYCGpwKANJUlMYCCRJkoGgLscykCQ1gYGgBlsMJElNYSCQJEkGgrocy0CS1AQGghq8ykCS1BQGAkmSZCCQJEkGglqCoM9OBJKkBjAQ1BDhnYslSc1gIKgh8CoDSVIzGAjq8DIDSVJDGAhq6I8D6WkCSdIEZyCooa2cITAPSJImOgNBDf0tBl5pIEma6AwENQw0GYxrLSRJqs9AUEP/GQJPEEiSJjoDQQ3R34fAcwSSpAnOQFCDZwgkSU1hIKgh8CoDSVIzGAhqGDhDYJOBJGmCMxDU8PiNica1GpIk1WYgqGHgxkTjXA9JkuoyENTgjYkkSU1hIBgB5gFJ0kRnIKghHu9VKEnShGYgqOHxWxebCCRJE5uBoIY2b0wkSWoIA0EN/U0GdiqUJE10BoIa7EIgSWoKA0EN3phIktQUBoIaHO1QktQUBoIaHO1QktQUBoIaHO1QktQUoxYIIuLCiHg0Im5rKZsTEVdHxD3leXYpj4j4ZEQsi4hbIuLZLeucXZa/JyLObik/MSJuLet8MgbuEjR2HO1QktQUo3mG4AvA6YPKzgW+m5nHAt8trwFeAhxbHucAn4UqQADvBZ4LnAS8tz9ElGXe3LLe4PcadXYqlCQ1xagFgsz8IbBmUPGZwEVl+iLg5S3lX8zKtUB3RMwHTgOuzsw1mbkWuBo4vcybmZnXZmYCX2zZ1phxtENJUlOMdR+CwzJzZZl+GDisTC8AHmxZbnkp21P58iHKx1b/aId9RgJJ0sQ2bp0Kyy/7MfkmjYhzImJpRCxdtWrVyG13xLYkSdL4GutA8Eg53U95frSUrwCObFluYSnbU/nCIcqHlJnnZ+aSzFwyb9682jvRb+A+BJ4gkCRNcGMdCK4A+q8UOBv4ekv568vVBicD60vTwlXAqRExu3QmPBW4qszbEBEnl6sLXt+yrTHjaIeSpKboGK0NR8RXgRcCcyNiOdXVAh8CLo2INwEPAK8qi18JnAEsA7YAbwTIzDUR8ZfADWW592dmf0fFt1BdyTAF+FZ5jKm2Eqc8QyBJmuhGLRBk5mt2M+vFQyybwFt3s50LgQuHKF8KPL1OHevqvzGRox1KkiY671RYg6MdSpKawkAwAjxBIEma6AwENbTF490KJUmayAwENfTnAe9LJEma6AwENTjaoSSpKQwENTjaoSSpKQwENTjaoSSpKQwENXjrYklSUxgIani8U6GJQJI0sRkIanC0Q0lSUxgIarDJQJLUFAaCGhztUJLUFAaCGhztUJLUFAaCGhztUJLUFAaCOhztUJLUEAaCGrwxkSSpKQwENTjaoSSpKQwENTjaoSSpKQwENTjaoSSpKQwENQyMdmgikCRNcAaCGuxBIElqCgNBDd66WJLUFAaCGmwykCQ1hYGgBpsMJElNYSCowSYDSVJTGAhqaC9Hr9dEIEma4AwENXSU4Q57evvGuSaSJNVjIKiho71qMtjZ6xkCSdLEZiCooau0GfT0eYZAkjSxGQhq6CiBYKdNBpKkCc5AUEOnTQaSpIYwENTQ6RkCSVJDGAhq6GirzhD0eIZAkjTBGQhq6OzwDIEkqRkMBDV0tvUHAs8QSJImNgNBDf2dCr0xkSRpojMQ1NBe+hDs7PMMgSRpYjMQ1BARdLaHfQgkSROegaCmzvY2dvQYCCRJE5uBoKZDpnexetP28a6GJEm1GAhqmj9zCivXbxvvakiSVIuBoKb53ZO5dcV6lq/dMt5VkSRpv3WMdwUmulcvOZKv3/wQL/jwNTx53jSeu3gOJy2ew3MXH8IR3VPGu3qSJA1LZB5cl8wtWbIkly5dOqLb/OkvVnPjA2u46ZfruOH+NWzc1gPAwtlTOGnxHJYcNYcTj5rNsYdOp61cqihJ0liIiBszc8nelvMMwQh43tGH8LyjDwGgty+56+ENXH/fGq6/bw0/uHsVl9+0AoCZkzt49lGzWXLUbE48ag7PPHIWU7v8J5AkjT+/jUZYe1tw/BGzOP6IWbzx+YvJTO5fvYWl96/hpl+uZen9a/n+3asGln3KYTM44chufnXhLJ65sJunHDadjna7dkiSxpZNBuNg3ZYd/OyX6/jZL9fyswfX8fMH17GhNDNM7mzjuPkzecaCWTxjYTfPWDCLo+dNMyRIkvbLcJsMDAQHgMzkgdVb+PnyddyyfD23Ll/PbQ+tZ8uOXgAmdbTxK4fP4GmHz+S4I6rHUw+fwYzJneNcc0nSgc5AsBsHYiAYSm9fct9jm7hl+XruXLmBO1Zu4I6HNrB2y86BZZ40ZyrHzZ/J0+ZXIeEph03niO4pdHo2QZJU2KlwgmtvC445dAbHHDpjoCwzeWTDdu5YuZ47V27kjoeqoHDVHQ/Tn+va24Kj503juIGQMIOj501nQfcUr3CQJO3WuASCiLgf2Aj0Aj2ZuSQi5gCXAIuA+4FXZebaiAjg74AzgC3AGzLzprKds4E/K5v9QGZeNJb7MdYigsNnTebwWZM55amHDZRv3t7DXQ9v5BePbuKBNZu5a+VGrr13Df9280MDy0zubGPx3Okcc+h0Fs6ewtPmz2TxIdM4au5UZtr0IEkHvXFpMiiBYElmPtZS9hFgTWZ+KCLOBWZn5rsj4gzg7VSB4LnA32Xmc0uAWAosARK4ETgxM9fu6b0nSpPBSFi7eQf3PLqJX6zaxC8e3cSyVdX0w+u3sbP38X/3Q6Z1sWjuNBYdMo1Fh0xl0dxpLJ47jaMOmWo/BUma4CZik8GZwAvL9EXA94F3l/IvZpVcro2I7oiYX5a9OjPXAETE1cDpwFfHttoHrtnTujip3Dmx1badvdy/ejP3P7alPG/m/tWb+cmyx/jaTbuOyzB3elcVFOY+HhYWHWJYkKSmGa9AkMC3IyKBf8zM84HDMnNlmf8w0H8sAC1qAAAQOUlEQVROfAHwYMu6y0vZ7sqfICLOAc4BeNKTnjRS+zBhTe5s56mHz+Sph898wrwtO3r45Zot3P/YZu57bMtAWPjRPau47MZdR3WcObmDhbOnsnD2FBbMnsLC2VNZ0D2FBd1TOKJ7MnOmdVG1+EiSDnTjFQhekJkrIuJQ4OqIuKt1ZmZmCQsjogSO86FqMhip7TbR1K6OPYaFB1ZXIeHBtVtYvnYry9du5f7Vm/nxsscGLpPsN6mjjSO6pzB/1mTmz5rC4bMmcUT3FA6fOZnDyuOQaV12dpSkA8C4BILMXFGeH42IfwVOAh6JiPmZubI0CTxaFl8BHNmy+sJStoLHmxj6y78/ylU/qE3t6uBp5TLHwTKTdVt2snztVh5av5WV67by0PptrFi3lYfWbeUnyx5j1abt9Pbtmsc62oJDZ0zi0JmTOWzmJA6fOZkFs6cwd/qklkcXc6Z1eXMmSRpFYx4IImIa0JaZG8v0qcD7gSuAs4EPleevl1WuAN4WERdTdSpcX0LDVcBfRcTsstypwHljuCtqERHMntbF7GldPGPhrCGX6entY9Wm7Ty8fhuPbNjOIxu28fCGbTyyfhuPbNzGvas285/LVrNxe88Q24fZU7s4onsyh82YzNzpkzhketcuz/3Ts6d20e5ZB0naJ+NxhuAw4F9L23IH8M+Z+R8RcQNwaUS8CXgAeFVZ/kqqKwyWUV12+EaAzFwTEX8J3FCWe39/B0MdmDra25g/awrzZ+1+WOjMZOP2HlZv2sFjm7bz2MbtPLZpO6vK6+Vrt7Jy/TZue2g9qzftoKfviS1A/eFhzrTymNrF7GmdzJnWtWv5tC66p3Qxa2onMyZ12HQh6aDmnQo1YfX1JRu27eSxTTtYvWk7j5XQsHpz9XrN5h2s3ryDdVt2sGbzDtZu2fmEJot+bQGzpnTSPbWrPHfSXV7PnNLJrCmdzJzcweypXXRP7WTG5E6mT+5gxuQOpncZJiQduCbiZYfSPmlrC7qndtE9tYtjDp2+1+Uzkw3belizeQdrNm9nzeadrN+6k3VbdpTnnawrr9ds3sG9qzazfutONmzbyd5y8/RJVTiYMbmjTHeW1+W5zJ8+UN7BjElVqJjW1c7USR1M7Ww3WEgaNwYCHTQiglnl1/7iudOGvV5vX7JpWw8btu1kzeYdrNu6k03beti4bSebtvewYVvPwOuN23rYtL2HdVt28OCaLWzcXpVv29k3rPea2tXO1K4Opk0qz13tzJjcwZSudqZ0djClq40pne1M6eqonjvbqnnldX/YmNZV1ulqZ3JHO53t4SWgkvbIQCDtRXtbMGtqJ7OmdnLknKn7tY0dPX1s3t7DxhIsNpXpTdt3smVHL5u397B5ey9bdvSweUcvW7ZXz5u29fDYph1s3dnL1h29bNvZy5YdvWzd2bv3N23RFjCls53J5TGpswSLgbI2JnW0M6mjjUmd1fO0Se1M6minq6ONrva26rmjjUmDXg932kAiHdgMBNIYqL4Yq6swRkJmsr2nbyAcbN1RPTaUsxRbd/ZU83b0sr2nbyBMbOvpZdvOPrbu7GXbjipcbNnRw9otfdX8nX3s6O0bCB6763OxP4YTHIYKG1O62ulqb6OjvY3O9qCjrY2O9hiY7uxoo6MtaI+gvS3oaC/PbUFb9L9uG/S6mt/e1jrdtktZ6zIdbW20tVE9B4YbNZKBQJqAImLg1/5o6u1LdvT0saOnj+29vQPTO3r7Hp/u6WP7oNe7zO/tY/su8564nf75m7b37LpeCS87e/vo6U129vXttT/HWBg6OLQNETL2HC52v1wJMLusF7S3V8FnYJn2YFJHG20lDLUNBKPqM9IWUQIMtJUQExEE1ZmvzvYq4LRFQHnuaAuqlzEQfsrsXabb4vHlorxH63RbeZ/qbVu21bIutCy7m221bicIoq2lLoO21Taoroa3fWMgkLRb7W0x0BcBDoyxK3r7sgoIfcnOnj529vXR1wc9Lc+9fUlPX9JbHj0Dz30DZbuWJ30Dr/t2WXeX5XqT3mxZpresm7nL696+PnqTarnesp1s2UZfsqWn54nLlOX6Xw9sa4j6at88IVwMChqtgYUYOlwwEFJawgstQWmIbQ1+r8HBrK2tNQhVZS975hH89gsWj/kxMhBImlCqX9LlzMik8a3LeOrry+oMS28ffS1hIhN6+pIs032Z9JXn6uxK9dwfPHad318GSUIyMJ3VS/rKRJL09VVlmfn4c/aXlW3uUl6eW+YNbKuUP75M7rqdZOht0bpv1XHpX69/uwzeVv/8QfVr3Vdofd/H5zMwveu+7rItyrYG7/+gfd1lWy31m9Q5PndlNRBI0gTU1hZMbhv9ZiMdPLw5vCRJMhBIkiQDgSRJwkAgSZIwEEiSJAwEkiQJA4EkScJAIEmSMBBIkiQMBJIkCQOBJEnCQCBJkjAQSJIkILJ/nMeDRESsAh4YwU3OBR4bwe0djDyG9XkMR4bHsT6PYX0jfQyPysx5e1vooAsEIy0ilmbmkvGux0TmMazPYzgyPI71eQzrG69jaJOBJEkyEEiSJAPBSDh/vCvQAB7D+jyGI8PjWJ/HsL5xOYb2IZAkSZ4hkCRJBoL9FhGnR8TdEbEsIs4d7/ocSCLiyIi4JiLuiIjbI+IPS/mciLg6Iu4pz7NLeUTEJ8uxvCUint2yrbPL8vdExNnjtU/jJSLaI+JnEfGN8npxRFxXjtUlEdFVyieV18vK/EUt2zivlN8dEaeNz56Mn4jojojLIuKuiLgzIp7nZ3HfRMQ7y//l2yLiqxEx2c/inkXEhRHxaETc1lI2Yp+7iDgxIm4t63wyIqJ2pTPTxz4+gHbgF8CTgS7g58Bx412vA+UBzAeeXaZnAP8FHAd8BDi3lJ8LfLhMnwF8CwjgZOC6Uj4HuLc8zy7Ts8d7/8b4WP5f4J+Bb5TXlwJnlel/AH6/TL8F+IcyfRZwSZk+rnw+JwGLy+e2fbz3a4yP4UXA75TpLqDbz+I+Hb8FwH3AlJbP4Bv8LO71uP0a8GzgtpayEfvcAdeXZaOs+5K6dfYMwf45CViWmfdm5g7gYuDMca7TASMzV2bmTWV6I3An1R+VM6n+OFOeX16mzwS+mJVrge6ImA+cBlydmWsycy1wNXD6GO7KuIqIhcD/Av6pvA7gFOCyssjgY9h/bC8DXlyWPxO4ODO3Z+Z9wDKqz+9BISJmUf1hvgAgM3dk5jr8LO6rDmBKRHQAU4GV+Fnco8z8IbBmUPGIfO7KvJmZeW1W6eCLLdvabwaC/bMAeLDl9fJSpkHK6cJnAdcBh2XmyjLrYeCwMr2743mwH+e/Bf4E6CuvDwHWZWZPed16PAaOVZm/vix/sB/DxcAq4POl6eWfImIafhaHLTNXAH8D/JIqCKwHbsTP4v4Yqc/dgjI9uLwWA4FGTURMB74GvCMzN7TOK6nWS1x2IyJ+A3g0M28c77pMcB1Up20/m5nPAjZTnaod4Gdxz0o795lU4eoIYBoH19mRUXEgfu4MBPtnBXBky+uFpUxFRHRShYGvZOblpfiRcqqL8vxoKd/d8TyYj/PzgZdFxP1UTVKnAH9HdSqxoyzTejwGjlWZPwtYzcF9DKH65bQ8M68rry+jCgh+Fofv14H7MnNVZu4ELqf6fPpZ3Hcj9blbUaYHl9diINg/NwDHll62XVQdZ64Y5zodMEp74QXAnZn58ZZZVwD9vWTPBr7eUv760tP2ZGB9Oa12FXBqRMwuv1JOLWWNl5nnZebCzFxE9fn6Xma+FrgGeEVZbPAx7D+2ryjLZyk/q/T8XgwcS9UZ6aCQmQ8DD0bEr5SiFwN34GdxX/wSODkippb/2/3H0M/ivhuRz12ZtyEiTi7/Jq9v2db+G++emBP1QdUr9L+oesq+Z7zrcyA9gBdQnQq7Bbi5PM6gakf8LnAP8B1gTlk+gE+XY3krsKRlW79N1floGfDG8d63cTqeL+TxqwyeTPVHdBnwL8CkUj65vF5W5j+5Zf33lGN7NyPQE3miPYATgKXl8/hvVL21/Szu2zH8C+Au4DbgS1RXCvhZ3PMx+ypVn4udVGeq3jSSnztgSfn3+AXwKcqNBus8vFOhJEmyyUCSJBkIJEkSBgJJkoSBQJIkYSCQJEkYCKQDWkRkRHys5fW7IuJ9I7TtL0TEK/a+ZO33eWVUowxeM6j8iIi4rEyfEBFnjOB7dkfEW4Z6L0lDMxBIB7btwG9FxNzxrkirljvUDcebgDdn5otaCzPzoczsDyQnUN2rYqTq0E016t5Q7yVpCAYC6cDWA5wPvHPwjMG/8CNiU3l+YUT8ICK+HhH3RsSHIuK1EXF9GT/96JbN/HpELI2I/yrjJxAR7RHx0Yi4oYzN/rst2/1RRFxBdae6wfV5Tdn+bRHx4VL251Q3qrogIj46aPlFZdku4P3AqyPi5oh4dURMi2o8+evLoERnlnXeEBFXRMT3gO9GxPSI+G5E3FTeu3/U0Q8BR5ftfbT/vco2JkfE58vyP4uIF7Vs+/KI+I+oxp7/SMvx+EKp660R8YR/C6kJ9iXlSxofnwZu6f+CGqZnAk+jGn71XuCfMvOkiPhD4O3AO8pyi6iGoD0auCYijqG6Der6zHxOREwCfhIR3y7LPxt4elbD1w6IiCOADwMnAmuBb0fEyzPz/RFxCvCuzFw6VEUzc0cJDksy821le39Fdcvb346IbuD6iPhOSx1+NTPXlLMEv5mZG8pZlGtLYDm31POEsr1FLW/51upt8xkR8dRS16eUeSdQjc65Hbg7Iv4eOBRYkJlPL9vq3suxlyYkzxBIB7isRor8IvAH+7DaDZm5MjO3U93atP8L/VaqENDv0szsy8x7qILDU6nul/76iLiZatjqQ6juOw9w/eAwUDwH+H5WA+D0AF8Bfm0f6jvYqcC5pQ7fp7od7pPKvKszs3+c+QD+KiJuoboV7AIeH1J2d14AfBkgM+8CHgD6A8F3M3N9Zm6jOgtyFNVxeXJE/H1EnA5sGGKb0oTnGQJpYvhb4Cbg8y1lPZRQHxFtQFfLvO0t030tr/vY9f/94HuXJ9WX7Nszc5fBeyLihVTDB4+FAP6/zLx7UB2eO6gOrwXmASdm5s6oRoecXON9W49bL9CRmWsj4pnAacDvAa+iur+81CieIZAmgPKL+FKqDnr97qc6RQ/wMqBzPzb9yohoK/0Knkw16MxVwO9HNYQ1EfGUiJi2l+1cD/yPiJgbEe3Aa4Af7EM9NgIzWl5fBby9jORGRDxrN+vNAh4tYeBFVL/oh9peqx9RBQlKU8GTqPZ7SKUpoi0zvwb8GVWThdQ4BgJp4vgY0Hq1weeovoR/DjyP/fv1/kuqL/NvAb9XTpX/E9Xp8ptKR7x/ZC9nE7MajvVcqiFxfw7cmJn7MhzrNcBx/Z0Kgb+kCji3RMTt5fVQvgIsiYhbqfo+3FXqs5qq78NtgzszAp8B2so6lwBvKE0ru7MA+H5pvvgycN4+7Jc0YTjaoSRJ8gyBJEkyEEiSJAwEkiQJA4EkScJAIEmSMBBIkiQMBJIkCQOBJEkC/n9eawaLmwMECAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(np.arange(10000), regr.loss)\n",
    "plt.title(\"Development of cost during training\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-26T14:37:25.473465Z",
     "start_time": "2018-03-26T14:37:25.201638Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations: 0 - Error : 25.4396\n",
      "Iterations: 1000 - Error : 3.3716\n",
      "Iterations: 2000 - Error : 2.0538\n",
      "Iterations: 3000 - Error : 1.6314\n",
      "Iterations: 4000 - Error : 1.5079\n",
      "Iterations: 5000 - Error : 1.4654\n",
      "Iterations: 6000 - Error : 1.4769\n",
      "Iterations: 7000 - Error : 1.4498\n",
      "Iterations: 8000 - Error : 1.4945\n",
      "Iterations: 9000 - Error : 1.4789\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generating our data.\n",
    "\n",
    "X = np.linspace(1.0, 10.0, 100)[:, np.newaxis]\n",
    "Y = np.sin(X) + 0.1 * np.power(X, 2) + 0.5 * np.random.randn(100, 1)\n",
    "X /= np.max(X)\n",
    "\n",
    "X = np.hstack((np.ones_like(X), X))\n",
    "\n",
    "order = np.random.permutation(len(X))\n",
    "portion = 20\n",
    "\n",
    "\"\"\"\n",
    "    Split your data into train and test using the order and permutation variable\n",
    "\"\"\"\n",
    "test_idx = order[:portion]\n",
    "train_idx = order[portion:]\n",
    "\n",
    "train_x = X[train_idx]\n",
    "train_y = Y[train_idx]\n",
    "\n",
    "test_x = X[test_idx]\n",
    "test_y = Y[test_idx]\n",
    "\n",
    "train_y = train_y.reshape(-1,)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(train_x, train_y, lr=0.01)\n",
    "\n",
    "plt.plot(X[:,1], reg.predict(X), c='g', label='Model')\n",
    "plt.scatter(train_x[:,1], train_y, c='b', label='Train Set')\n",
    "plt.scatter(test_x[:,1], test_y, c='r', label='Test Set')\n",
    "plt.grid()\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-03-26T14:37:27.326617Z",
     "start_time": "2018-03-26T14:37:27.312972Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(np.arange(10000), reg.loss)\n",
    "plt.title(\"Development of cost during training\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "python3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.16"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}