linear_models_for_classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models for Classification \n",
    "## CS175 Discussion #2,  Jan. 17th, 2018\n",
    "Author: [Eric Nalisnick](http://www.ics.uci.edu/~enalisni/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Goals of this Lesson\n",
    "- Extend the regression framework to support classification\n",
    "    - Logistic Regression\n",
    "    - Training with Gradient Descent\n",
    "    \n",
    "- Implement... \n",
    "    - An instantiation of SciKit-Learn's Logistic regression class\n",
    "\n",
    "### References \n",
    "- Chapter 4 of [*Elements of Statistical Learning* by Hastie, Tibshirani, Friedman](https://web.stanford.edu/~hastie/Papers/ESLII.pdf) \n",
    "- [SciKit-Learn's Logistic Regression Documentation](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html)\n",
    "- [A Few Useful Things to Know about Machine Learning](https://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf)\n",
    "\n",
    "## 0.  Python Preliminaries\n",
    "As usual, first we need to import Numpy, Pandas, MatPlotLib..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import time\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've created two functions that we'll use later to visualize which datapoints are being assigned to which classes.  They are a bit messy and not essential to the material so don't worry about understanding them.  I'll be happy to explain them to anyone interested during office hours.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "# A somewhat complicated function to make pretty plots\n",
    "def plot_classification_data(data1, data2, beta, logistic_flag=False):\n",
    "    plt.figure()\n",
    "    grid_size = .2\n",
    "    features = np.vstack((data1, data2))\n",
    "    # generate a grid over the plot\n",
    "    x_min, x_max = features[:, 0].min() - .5, features[:, 0].max() + .5\n",
    "    y_min, y_max = features[:, 1].min() - .5, features[:, 1].max() + .5\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, grid_size), np.arange(y_min, y_max, grid_size))\n",
    "    # color the grid based on the predictions \n",
    "    if logistic_flag:\n",
    "        Z = logistic(np.dot(np.c_[xx.ravel(), yy.ravel(), np.ones(xx.ravel().shape[0])], beta))\n",
    "        colorbar_label=r\"Value of f($X \\beta)$\"\n",
    "    else:\n",
    "        Z = np.dot(np.c_[xx.ravel(), yy.ravel(), np.ones(xx.ravel().shape[0])], beta)\n",
    "        colorbar_label=r\"Value of $X \\beta$\"\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    background_img = plt.pcolormesh(xx, yy, Z, cmap=plt.cm.coolwarm)\n",
    "    \n",
    "    # Also plot the training points\n",
    "    plt.scatter(class1_features[:, 0], class1_features[:, 1], c='b', edgecolors='k', s=70)\n",
    "    plt.scatter(class2_features[:, 0], class2_features[:, 1], c='r', edgecolors='k', s=70)\n",
    "    plt.title('Data with Class Prediction Intensities')\n",
    "    plt.xlabel('Feature 1')\n",
    "    plt.ylabel('Feature 2')\n",
    "    color_bar = plt.colorbar(background_img, orientation='horizontal')\n",
    "    color_bar.set_label(colorbar_label)\n",
    "    plt.xlim(xx.min(), xx.max())\n",
    "    plt.ylim(yy.min(), yy.max())\n",
    "    plt.xticks(())\n",
    "    plt.yticks(())\n",
    "    plt.show()\n",
    "\n",
    "# Another messy looking function to make pretty plots of basketball courts\n",
    "def visualize_court(log_reg_model, court_image = './data/nba_experiment/nba_court.png'):\n",
    "    two_class_cmap = ListedColormap(['#FFAAAA', '#AAFFAA']) # light red for miss, light green for make\n",
    "    x_min, x_max = 0, 50 #width (feet) of NBA court\n",
    "    y_min, y_max = 0, 47 #length (feet) of NBA half-court\n",
    "    grid_step_size = 0.2\n",
    "    grid_x, grid_y = np.meshgrid(np.arange(x_min, x_max, grid_step_size), np.arange(y_min, y_max, grid_step_size))\n",
    "    grid_predictions = log_reg_model.predict(np.c_[grid_x.ravel(), grid_y.ravel()])\n",
    "    grid_predictions = grid_predictions.reshape(grid_x.shape)\n",
    "    fig, ax = plt.subplots()\n",
    "    court_image = plt.imread(court_image)\n",
    "    ax.imshow(court_image, interpolation='bilinear', origin='lower',extent=[x_min,x_max,y_min,y_max])\n",
    "    ax.imshow(grid_predictions, cmap=two_class_cmap, interpolation = 'nearest',\n",
    "              alpha = 0.60, origin='lower',extent=[x_min,x_max,y_min,y_max])\n",
    "    plt.xlim(x_min, x_max)\n",
    "    plt.ylim(y_min, y_max)\n",
    "    plt.title( \"Make / Miss Prediction Boundaries\" )\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.  Classes as Targets\n",
    "\n",
    "We turn to classification: assigning a datapoint $\\mathbf{x}_{i}$ to one of multiple classes.  Let's define some helper functions that we'll use throughout---one for shuffling, one for calculating classification error.  Classification error is defined as: \n",
    "\\begin{eqnarray*}\n",
    "\\frac{\\sum_{i=1}^{N_{test}} g(\\hat y_{i}, y_{i})}{N_{test}} \\ \\  \\text{  where  } \\ \\ \n",
    "g(\\hat y_{i}, y_{i}) = \\begin{cases} 1, & \\text{if $y_{i}\\ne$ round($\\hat y_{i}$).}\\\\0, & \\text{otherwise}.\\end{cases}\n",
    "\\end{eqnarray*}\n",
    "where $\\hat y_{i} \\in (0, 1)$ is our model's prediction of label $y_{i} \\in \\{0,1\\}$ and round() sends $\\hat y_{i}$ to 0 or 1, whichever is closer..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "### function for shuffling the data and labels\n",
    "def shuffle_in_unison(a, b):\n",
    "    rng_state = np.random.get_state()\n",
    "    np.random.shuffle(a)\n",
    "    np.random.set_state(rng_state)\n",
    "    np.random.shuffle(b)\n",
    "    \n",
    "### calculate classification errors\n",
    "# return a percentage: (number misclassified)/(total number of datapoints)\n",
    "def calc_classification_error(predictions, class_labels):\n",
    "    n = predictions.size\n",
    "    num_of_errors = 0.\n",
    "    for idx in range(n):\n",
    "        if (predictions[idx] >= 0.5 and class_labels[idx]==0) or (predictions[idx] < 0.5 and class_labels[idx]==1):\n",
    "            num_of_errors += 1\n",
    "    return num_of_errors/n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's generate some artificial data, representing class \\#1 as $y_{i}=0$ and class \\#2 as $y_{i}=1$..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set the random number generator for reproducability\n",
    "np.random.seed(182)\n",
    "\n",
    "#### create artificial data\n",
    "N = 400\n",
    "D = 2\n",
    "\n",
    "# Sample the features from a Multivariate Normal Dist.\n",
    "mean1 = [13.,5.]\n",
    "mean2 = [5.,5.]\n",
    "covariance = [[13.,5.],[5.,13.]]\n",
    "class1_features = np.random.multivariate_normal(mean1, covariance, int(N/2))\n",
    "class2_features = np.random.multivariate_normal(mean2, covariance, int(N/2))\n",
    "features = np.vstack((class1_features, class2_features))\n",
    "\n",
    "# add column of ones for bias term\n",
    "features = np.hstack((features,np.ones((N,1))))\n",
    "\n",
    "# Set the class labels\n",
    "class1_labels = [0]*int(N/2)\n",
    "class2_labels = [1]*int(N/2)\n",
    "class_labels = class1_labels+class2_labels\n",
    "\n",
    "# shuffle the data\n",
    "shuffle_in_unison(features, class_labels)\n",
    "class_labels = np.array(class_labels)[np.newaxis].T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now visualize the data with color-codes for each class..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c5ec88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the data\n",
    "plt.scatter(class1_features[:, 0], class1_features[:, 1], c='b', edgecolors='k', s=70, label=\"Class #1\")\n",
    "plt.scatter(class2_features[:, 0], class2_features[:, 1], c='r', edgecolors='k', s=70, label=\"Class #2\")\n",
    "\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel(\"Feature 1\")\n",
    "plt.ylabel(\"Feature 2\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.  Logistic Regression: A Summary\n",
    "\n",
    "_**Data**_\n",
    "\n",
    "We observe pairs $(\\mathbf{x}_{i},y_{i})$ where\n",
    "\\begin{eqnarray*}\n",
    "y_{i} \\in \\{ 0, 1\\} &:& \\mbox{class label} \\\\\n",
    "\\mathbf{x}_{i} = (1, x_{i,1}, \\dots, x_{i,D}) &:& \\mbox{set of $D$ explanatory variables (aka features) and a bias term } \n",
    "\\end{eqnarray*}\n",
    "\n",
    "_** Parameters**_\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\mathbf{\\beta}^{T} = (\\beta_{0}, \\dots, \\beta_{D}) : \\mbox{values encoding the relationship between the features and label}\n",
    "\\end{eqnarray*}\n",
    "\n",
    "_** Transformation Function **_\n",
    "\n",
    "\\begin{equation*}\n",
    "f(z_{i}=\\mathbf{x}_{i} \\mathbf{\\beta} ) = (1+e^{-\\mathbf{x}_{i} \\mathbf{\\beta} })^{-1}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c837b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define the transformation function\n",
    "def logistic(z):\n",
    "    # return the output of the logistic function\n",
    "    return 1/(1+np.exp(-z))\n",
    "\n",
    "# graph the function \n",
    "z = np.linspace(-6,6,50)\n",
    "logistic_out = logistic(z)\n",
    "\n",
    "# TO DO: write the line of code to plot the function\n",
    "plt.plot(z, logistic_out, 'b-')\n",
    "\n",
    "plt.title(\"Logistic Function\")\n",
    "plt.xlabel('Input')\n",
    "plt.ylabel('Output')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_**Error Function**_\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\mathcal{L} = \\sum_{i=1}^{N} -y_{i} \\log f(\\mathbf{x}_{i} \\mathbf{\\beta} ) - (1-y_{i}) \\log (1-f(\\mathbf{x}_{i} \\mathbf{\\beta} ))\n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "### compute the cross-entropy error \n",
    "# labels: Numpy array containing the true class labels\n",
    "# f: column vector of predictions (i.e. output of logistic function)\n",
    "def cross_entropy(labels, f):\n",
    "    return np.sum(-1*np.multiply(labels,np.log(f)) - np.multiply((np.ones(N)-labels),np.log(np.ones(N)-f)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_** Learning $\\beta$ **_\n",
    "\n",
    "Learning (or *estimating*) a Logistic Regression model will entail minimizing the error function $\\mathcal{L}$ above.  $\\beta$ can't be solved for in closed form (i.e. exactly) so we use the Gradient Descent algorithm instead:  \n",
    "- Randomly initialize $\\beta$\n",
    "- Until $\\alpha || \\nabla \\mathcal{L} || < tol $:\n",
    "    - $\\mathbf{\\beta}_{t+1} = \\mathbf{\\beta}_{t} - \\alpha \\nabla_{\\mathbf{\\beta}} \\mathcal{L}$\n",
    "\n",
    "$\\alpha$ above denotes a *learning rate*, which says how far to step when doing each gradient update.  The derivative of $\\mathcal{L}$ with respect to $\\beta$ is calculated as:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\frac{\\partial \\mathcal{L}_{i}}{\\partial \\mathbf{\\beta}} &=& \\frac{\\partial \\mathcal{L}_{i}}{\\partial f(z_{i})} \\frac{\\partial f(z_{i})}{\\partial z_{i}} \\frac{\\partial z_{i}}{\\partial \\mathbf{\\beta}}\\\\\n",
    "&=& \\left[\\frac{-y_{i}}{f(\\mathbf{x}_{i} \\mathbf{\\beta})} - \\frac{y_{i}-1}{1-f(\\mathbf{x}_{i} \\mathbf{\\beta})} \\right] f(\\mathbf{x}_{i} \\mathbf{\\beta})(1-f(\\mathbf{x}_{i} \\mathbf{\\beta}))\\mathbf{x}_{i}\\\\\n",
    "&=& [-y_{i}(1-f(\\mathbf{x}_{i} \\mathbf{\\beta} )) - (y_{i}-1)f(\\mathbf{x}_{i} \\mathbf{\\beta} )]\\mathbf{x}_{i}\\\\\n",
    "&=& [f(\\mathbf{x}_{i} \\mathbf{\\beta} ) - y_{i}]\\mathbf{x}_{i}\n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "### compute the gradient (derivative w.r.t. Beta)\n",
    "# features: NxD feature matrix\n",
    "# labels: Numpy array containing the true class labels\n",
    "# f: column vector of predictions (i.e. output of logistic function)\n",
    "def compute_Gradient(features, labels, f):\n",
    "    return np.sum(np.multiply(f-labels,features),0)[np.newaxis].T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_** Putting it all together in a simple example... **_  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training ended after 300 iterations, taking a total of 0.74 seconds.\n",
      "Final Cross-Entropy Error: 58199.60\n",
      "Classification Error on Training Set: 13.75%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c3fe128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set the random number generator for reproducability\n",
    "np.random.seed(49)\n",
    "\n",
    "# Randomly initialize the Beta vector\n",
    "beta = np.random.multivariate_normal([0,0,0], [[1,0,0],[0,1,0],[0,0,1]], 1).T\n",
    "# Initialize the step-size\n",
    "alpha = 0.00001\n",
    "# Initialize the gradient\n",
    "grad = np.infty\n",
    "# Set the tolerance \n",
    "tol = 1e-6\n",
    "# Initialize error\n",
    "old_error = 0\n",
    "error = [np.infty]\n",
    "\n",
    "# Run Gradient Descent\n",
    "start_time = time.time()\n",
    "iter_idx = 1\n",
    "# loop until gradient updates become small\n",
    "while (alpha*np.linalg.norm(grad) > tol) and (iter_idx < 300):\n",
    "    f = logistic(np.dot(features,beta))\n",
    "    old_error = error[-1]\n",
    "    # track the error\n",
    "    error.append(cross_entropy(class_labels, f)) \n",
    "    grad = compute_Gradient(features, class_labels, f)\n",
    "    # update parameters\n",
    "    beta = beta - alpha*grad\n",
    "    iter_idx += 1\n",
    "end_time = time.time()\n",
    "print(\"Training ended after %i iterations, taking a total of %.2f seconds.\" %(iter_idx, end_time-start_time))\n",
    "print(\"Final Cross-Entropy Error: %.2f\" %(error[-1]))\n",
    "\n",
    "# compute error on training data\n",
    "predictions = logistic(np.dot(features, beta))\n",
    "print(\"Classification Error on Training Set: %.2f%%\" %(calc_classification_error(predictions, class_labels) * 100))\n",
    "\n",
    "# generate the plot\n",
    "plot_classification_data(class1_features, class2_features, beta, logistic_flag=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.  Logistic Regression with SciKit-Learn \n",
    "\n",
    "[Here is the documentation for SciKit-Learn's implementation of Logistic Regression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html)\n",
    "\n",
    "It's quite easy to use.  Let's jump right in and repeat the above experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training ended after 0.00 seconds.\n",
      "Classification Error on Training Set: 9.75%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c42a400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# set the random number generator for reproducability\n",
    "np.random.seed(75)\n",
    "\n",
    "#Initialize the model\n",
    "skl_LogReg = LogisticRegression()\n",
    "\n",
    "#Train it\n",
    "start_time = time.time()\n",
    "skl_LogReg.fit(features, np.ravel(class_labels))\n",
    "end_time = time.time()\n",
    "print(\"Training ended after %.2f seconds.\" %(end_time-start_time))\n",
    "\n",
    "# compute the classification error on training data\n",
    "predictions = skl_LogReg.predict(features)\n",
    "print(\"Classification Error on Training Set: %.2f%%\" %(calc_classification_error(predictions, class_labels) * 100))\n",
    "\n",
    "# generate the plot\n",
    "plot_classification_data(class1_features, class2_features, skl_LogReg.coef_.T, logistic_flag=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiments\n",
    "\n",
    "## 4.  Dataset #1: NBA Shot Outcomes\n",
    "\n",
    "The first real dataset we'll tackle is one describing the location and outcome of shots taken in professional basketball games.  Let's use Pandas to load and examine the data.    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_Coordinate</th>\n",
       "      <th>y_Coordinate</th>\n",
       "      <th>shot_outcome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>26.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>25.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>40.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x_Coordinate  y_Coordinate  shot_outcome\n",
       "0          26.0          32.0           0.0\n",
       "1          25.0          24.0           0.0\n",
       "2          25.0           6.0           1.0\n",
       "3          40.0           7.0           1.0\n",
       "4          12.0          13.0           1.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nba_shot_data = pd.read_csv('./data/nba_experiment/NBA_xy_features.csv')\n",
    "nba_shot_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_Coordinate</th>\n",
       "      <th>y_Coordinate</th>\n",
       "      <th>shot_outcome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>562538.000000</td>\n",
       "      <td>562538.000000</td>\n",
       "      <td>562538.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>25.178772</td>\n",
       "      <td>13.496301</td>\n",
       "      <td>0.458145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>11.212500</td>\n",
       "      <td>8.651198</td>\n",
       "      <td>0.498246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>19.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>31.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>51.000000</td>\n",
       "      <td>94.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        x_Coordinate   y_Coordinate   shot_outcome\n",
       "count  562538.000000  562538.000000  562538.000000\n",
       "mean       25.178772      13.496301       0.458145\n",
       "std        11.212500       8.651198       0.498246\n",
       "min        -3.000000       1.000000       0.000000\n",
       "25%        19.000000       6.000000       0.000000\n",
       "50%        25.000000      10.000000       0.000000\n",
       "75%        31.000000      21.000000       1.000000\n",
       "max        51.000000      94.000000       1.000000"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nba_shot_data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple enough.  Now let's train a Logistic Regression model on it, leaving out a test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enalisnick/anaconda/envs/cs175/lib/python3.5/site-packages/ipykernel_launcher.py:3: DeprecationWarning: \n",
      ".ix is deprecated. Please use\n",
      ".loc for label based indexing or\n",
      ".iloc for positional indexing\n",
      "\n",
      "See the documentation here:\n",
      "http://pandas.pydata.org/pandas-docs/stable/indexing.html#ix-indexer-is-deprecated\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training ended after 0.54 seconds.\n",
      "Classification Error on the Test Set: 41.87%\n",
      "Baseline Error: 45.79%\n"
     ]
    },
    {
     "data": {
      "image/png": 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KEAwGeebZZxHD4Otff5n19fVTzThWC4UiFYvFeP2111hdW+PO3Tv09vVmXRxaOBofLR6XHLNnqPk91Briube+FbfbzddffpknC/Ok05XPFFYLhSUNc5vpHH35pZfZ2tri6aefZmBgQAtGk6HF4wogtk5WLS0tvPX552mPtHPv9Xu88cYbHMYOs2HrKSDF4komU8zPzfHS114kmUjw3HNvpbevL084tIg0B3pg3BXE5/PxzLPPMjM9zeTUFJvrG1y7fp2u7m6cTkdepq9XRlZKsbOzw+TEBKtra3R3dXPz9i0C/kC2ZKRFo7nQ4nGFyEzyA+B0ORm/fo229ggTDx/x6quv0B5pZ2R0lEh7xJo+0F56yM0alpsYzD4zWPESSzqtiO7tMT83x5MnT3C5nNy9e5e+/v7sOTK2aZoLLR5NRN7iRqeep8P83t7eTujtb2dpcZGZmWlefuklQqEQff39dHR04Pf7MRyZ2q2y/S0wyEZaKeJHR2xvbbO4+IS1tXUchsHg0BDDw8NmU6zWiqZHi8cVJTdrl7keytDwED09PayurrIwP8+bDx5gGAahUAttkXZaW1vx+X243R6czvwOXOl0mkQ8Qewwxt7eHlubm2xvbxOPJ/D7fYyOjdLX10cgENC+jUuEFo+Gx1ZdyJu+r3jGK1V9KJ1Rc9USt8fDwOAgvX197O3tsb62xvr6GvPzc0xPJhARHE6n2fvTFl86nSaZTKDS5qxjfr+f3p5eOro6CYfDuF3uPHO1aFwOtHg0Gbl8l5v7ohLynaCZbcXDOhwOwuEw4XCYsfEx4kdx9qNRYgcHxJNJDmMxktbCUoYIHq8Xj9uDz+/D5/Ph9XpxOpxF9U0Lx+WhYvEQEQfwIvBEKfV+ERkF/gCIAC8DP6CUip+NmVeZWptOiy2RYO2pIkrDcOD1+fBmRrjWYJMWjMtJNf08fhR4YPv9y8DHlFLXgS3gQ/U0TFMZZr48vhh1/mQ9qsinMI6qzkpmgp7SM4ud3WRBmsagIvEQkQHgO4DfsH4L8B7gj6wgnwS++ywM1FRO3mrxedulyCc/rP13LVMKarG4elRa8vhV4KeAtPW7HdhWSiWt3wtAf7EDReTDIvKiiLy4ubt7KmM1xTmrTFtMUGoVF83l40TxEJH3A6tKqZfsm4sELVoRVkp9Qin1NqXU2yKhUI1majSaRqMSh+m7gO8SkfcBXiCEWRIJi4jTKn0MAItnZ6ZGo2k0Tix5KKV+Rik1oJQaAf4O8EWl1PcDXwK+xwr2QeAzZ2alRqNpOE4zqvangR8XkceYPpDfrI9JGo2mGaiqk5hS6gXgBev7FPCO+puk0WiaAT2fh0ajqQktHhqNpia0eGg0mprQ4qHRaGpCi4dGo6kJLR4ajaYmtHhoNJqa0OKh0WhqQouHRqOpCS0eGo2mJrR4aDSamtDiodFoakKLh0ajqQktHhqNpia0eGg0mprQ4qHRaGpCi4dGo6kJLR4ajaYmtHhoNJqa0OKh0WhqQouHRqOpCS0eGo2mJrR4aDSamtDiodFoakKLh0ajqQktHhqNpia0eGg0mprQ4qHRaGpCi4dGo6kJLR4ajaYmtHhoNJqa0OKh0WhqQouHRqOpCS0eGo2mJrR4aDSamtDiodFoakKLh0ajqYkTxUNEvCLyVRF5VUTui8g/t7aPishXRGRCRD4tIu6zN1ej0TQKlZQ8joD3KKWeBd4CvFdE3gn8MvAxpdR1YAv40NmZqdFoGo0TxUOZRK2fLuujgPcAf2Rt/yTw3WdioUajaUgq8nmIiENEXgFWgc8Dk8C2UippBVkA+ksc+2EReVFEXtzc3a2HzRqNpgGoSDyUUiml1FuAAeAdwO1iwUoc+wml1NuUUm+LhEK1W6rRaBqKqlpblFLbwAvAO4GwiDitXQPAYn1N02g0jUwlrS2dIhK2vvuAbwEeAF8CvscK9kHgM2dlpEajaTycJwehF/ikiDgwxeYPlVKfE5E3gD8QkV8Evg785hnaqdFoGowTxUMp9RrwXJHtU5j+D41GcwXRPUw1Gk1NVFJt0VxxlMo1pInIyeHzGt7E9ldzmdDicUXJCEIxMbCLRfF9hceUDg8KSghOtaKkaSy0eFwxCoWhtFAIWVFQdnlQgCKdzogPiBjWdsluKzhJWXnRXCzlXhbl0OJxySgvBsdJK0U6mSKZTJJIJKz/cZLJJPGjI9JpRTweJ5VMmvIgglKKZCKBAhwOBw6nwzyvAsMw8Hg8GA4Dl9OFy+3C6XThcrlwupw4nebHMAzsApVfoil+Dbp00lhciHhUq3Q60VRG2cqDSpNMpojHjzg6PCIWO+Dg4IDDWIxkIkkqnQalEBFEBIfTgcPhNDO904nX58PpcCBGpnQhmYiz500lkyStTzyeYi+xSzqVJpVOZ5+5YQgOhxOP14PfH8Dn8+H1enF7PLhcGVHRnJZaSxPVcAHiUa0QqLL186tMuQSSSqWJx4+IHcSIRqNE93Y5PDwknUojIjidTjxeL62trXi9PivzmqUDw3DgMAzEMGq85wqlTPtUOk0qlSKVTpFIJIjH46Z4HRyws73N+toa6XQKEcHtchMIBgi2hPAH/Hg9XhxOJzmd0j6Sk8iV4Kq5P81QbVGqBkVUOqFYlLt36bQifnTE/n6U3d1d9nZ3iR/FAXC73QRagrR3dODz+fF4PbicLvMtX/bWHt8pAoVmHN8mli9EwDBLMQA+ny/fZqVIJVPE43EOYzH29/eJ7u2xtTVHOp3G6XQSCARoDbcSDLbg9XlxOBzWvYBMotfpI59a8lgt+nGu4pFMJrn/+utVHaOA/oF+IpHI2RjVBJRKDKlUithBjN3dHba3tjg4iAEKr9dHW1uElpYWvD4fbrcbw5GpDtgcoUV8DJmMaJ7TfIsVZs3ieVUVhMnEU+qqBEMEw2XgcrkIBAK0d3SglCKRSHB0eMj+/j67OzssLjwhmUrhcbtpDYdpDYcJBIO4nE6wfDCF572qJFMpph5PEj86quq4WCxW9bnOVTwMwyDc1lb1cR6P5wysaQ4KhSOVShM7OGB7e4vNjU3ih4c4XS5Cra109/YSCARMscg6JLMx2b5LgQAUK2FUlwlLhc8Xo+Nhj5diBLfbjdvtoiXUQndPD8lkwiaS26ytruJwOGgNh2lrjxAMBnG5XGXPc1UwRAi1hkgmkicHtuFwVi8F5yseDgcDg4NA6dJy8RfV1Wvos2cCpRSHh4dsbW6xsb7OYSyGy+UiHInQNjJCIBDA6XQWuanF+mSU7HZxphTPyMpmy7HyDUqZ+10uF65WUyD7+gc4jMXY3d1lY2OdzYlHOJ0uwm0RIu0RgoFgtpRVKLxXQUwMw0FPTy+Fz77clSvA7XZVfa4LaW0p+wxtddmr1C8xl85zCT6ZTLK3u8va6hq7OzsYDgdtkTaGhocIBII4XYWPTyhWBcntay6koEoCZunVHwjgD/jp6u7mMBZje3ubjfUN1lZW8Pn9dHR20hZpw+325KU1pa6S/6ywdFmG5unnUfxtmL8/99182JfngR/zNhT0b1AK4kdHbG5ssLq6Sjx+RDDYwsjYGKHWEG6X26a+hW9We8zNwMm2FhOQzLGGIVkh6e7pYT8aZWN9ncWFBZ4sLBBpj9DZ2YU/GMA4ofp0WTjPS2q4TmKX8YGWIpeQTdGIHRywtrrK+vo6ItDe0UF7Rwd+f8DyYeTCZ5HjDs3LRrk0Yd5CweFwEGptJRQK0TcwwPbWJqsrK6yvrREKheju6SUUCuU5jlXpnvNXilrzXMOJx5XA1jKmlGI/us/K8hKbm5u4XG76+vqIdHTg8bjJq7fa3sJXSWTLkd8HREAEj8dDd08PHZ2d7O7ssLK8wsTDh/gDfnp6+wi3tVlNvipbYtf3s3q0eJwTuVJGpvicZn9/n+XFJbY2N/H6vAyPjNIWabNaDsq3XmjyyW/BMe+1w+GgLRKhNRwmGo2ysrzE1ORj/D4/vf39tIZbdb+RU6DF4xzIq7MrRewwxvLSEuura3i8XkbHxwm3hc0Wk1zAK1ElOQsKm4cNwyAUCtHS0sJ+dJ/lpUUmJyYIBIP09fcTam3FMDK+NXXFHKu1o8XjDCl09MXjcVaWl1lZXsbpdDI0PEx7RwdOV2YpnBw68Z6eQhERMQi2tDAWvE50b4/lxUUmHj6kNRymb2CAQCBgqwZpf8hJaPGoM8V8EqlUis2NDZ4sLJBOpejr76OzsxtXXtu6+dbTolF/CjulGWIQCrUSDAbZ3dllYWGeN+/fp7O7m57enmynxJw/5CKsbny0eNSRjOff/G4646J7eyzMzxPd26Ojq5Pevj68Xq91hNUvQzLdwHUqPWvsJQuzx3OYlpYWNjbWebKwwObGBgODA7S3d2Dk+UO0iBSixeNMMMdnLC8usby0hD8Q4Obt27SEQra3YKZ3pU6RF4F9MJ/D6aSru4fWcJilxSVmpmfY2NhkaGgIf8CfOeLCbG1UtHjUgcKu5DvbO8zNzpBMJBgcHqKjs7PAGap9Go1AYXXG4/EyPDJMJBJhfm6WB/fv09ffT1dPNw6HA6VKzJR2RdHicUrswpFIJFh68oTl5WXC4TCDN2/i8/pyLy3J+9cUXLWJm8QaWHbz9m1Wl5d5srDA9vY2Q8PDBAIBaxRvJuzF2nrRaPE4BZmMpZRib3eP2Zlpjg4PGRoepqurK1tnztBMPo2TRCM/AxVOJ5ihivEVF4x9gJ5SCqfTSW//AKHWMHMzM7z5xhsMDA3S2dllG3jX/GJ5GrR4VIm9MxFAOpVmZWWZhbl5AsEgt+7eJRgI5koZTZK4Ss8Zkubo6JBYLEbsIMZhLGbOChZPkE6ncXvcGGLgtaYT9Pl9+Ly+7CjfYwP+mqbviil8wZYgN27dYnlpibnZWfZ29xgcHrJaZK52F3ctHlVQmL+ODo+Ym51he2ub3r4+evr6bL6N5mh2LSYayWSSvb09NtbX2dzY4OAgRjqdzk5q7HA6MMScojAWi5FOp0gkkqRSKQDcHjdt4TbaOzsJh8NWN/vsCbMTKTcq+b4Qwely0j84QLClhZmZad584wEjY6OEQq1Zx2sjX89ZocWjQuyjX5WCvd1dZqamSCvFjVs3CbW2WksQmDRDYioUjqOjI1ZXVlh8ssj+/j4ul4vWcCt9/f0EgkG8Xh8up/NYdUwpRTKZ5OjokIP9A3Z2ttnY2GR5eRmX20V3dze9fX0Eg8GiM4w1/q0yJ4UOt4W57b/D3MwME2++ycDQEF3d3RiGcelH6xZDi0eVpNNp1tdWmZuZoSUUYnh01NZvI7eWSSO7RYv1fF1aXGJ+fo5EPE4kEmFkbNQsNbg9tkspfU0OhwOPx00oFKKntydbelldWWF5aZnFJ0/o6ellYGiQQCDYNPNs2Gc/UJiz2o1fu87y8hLzc3McHBwwODSUnckMGvt66okWjxOwZ7RkMsniwgLLy8v09PbQ19+f1wTbbAkmrRSb6xtMTk6yH43S3dPNwOAgLS0ttiUQcs7QwlnMj19vbtSv0+mkra2NcLiNoeERlpeWWJifZ2V1hZGREfr7B4p2y29YxHR4K6UwHAa9ff34fH6mp6Y4jB0yOj6WN8HzVRAQLR5lsL+g4/E4s9PT7OzsMDo2SntHpzWYyqRZEkomcycSCWamp5mfmycUCvGW554j3NZmGyBmUqwUVe5aC/tOiIDP52VkdJTu7m5mZ2eYfDzJ5sYm12/eIBgMZu1qlntoVmMUbW1teG7fZmpykocP3mRsfNzqCGiGuezoFXZKYBeO2EGMiYcP2Y9GuXHzJh2dXXkTDDdLos9c08HBAfdee52F+QVGRkd5y3PPEWmPZMXQXDbh9L4I8/hcKcUfCHDz1m2efvppDg4OeOXlr7O+tpa16zwWKjotIoLYWo78gQA3bt0iEPAz8fAhm5sbtuu5ODvPAy0eRbA3L0b39nj45gPS6TQ3bt22HKPm3uzaJA2Oyq6Xo9jd3eW1V15lf3+fp595htGx0by5UOt9PZkV6DLRGobQ2d3Fc8+/lUAwwOuv32NpcZG0rc9Mw1NwTW63i7Hxa3R0djL9+DGrK8solQawFr+6QFvPEF1tKcAuHDvbO0w+nsDn8zM2Po7Hm1sCogk0A8jPjLs7u7z++ms4DAeR18t9AAAgAElEQVTPvOVZQqFQdt95iKDZrGn6UPx+P3effprHDx/x8IEpzn0D/RgiTVWFyVyTw+lkcHgIl9vF3OwsyWSS3r6+At/R5UKLh0X++BTY2txkanKS1tZWRsZG87zpzZKw7USjUe7fu4fL6eLu00+ZXa0tzvN67APS3C4XN27dxHAYTDx6iMPpoKenJzvdYrPdZ8Mw6Ontw+FwMjc7QzqVpn9gAMNhlHEyNy9aPApQCjY31pmenCTS3s7QyEjTtqhkMunR0REP7r8BwoUKR+E5lTJbZa5dv0E6lebhmw9xu920t7efu02nwRREsx+QYUBXtzmQbmZ6ilQ6xeDQUHa6w8uE9nlgH6MCG+trTE1O0tHZyfDoaFY4MnX3ZiEjHKlUismJCWKxGLfv3Llw4cjHzHBOp5NrN24Qamnh4YM3OTg4MPc2kbMg5wMx00l7Rwdj49dYX1tnbnY22/u2ma7pJK60eOQ5sxRsrq8zMzVFZ1c3g8PD2bfFxWeyGlGKpcUlVpZXuH7jBq2t4eyuRrimQqfjzVu3SKs0kxOPs5mt2bA70yORCOPXxtlc32B+do5UKuNErWXB98bjRPEQkUER+ZKIPBCR+yLyo9b2iIh8XkQmrP/VL0LbQGxubjI9NUVnd/clKWYq9vf3mZ6aoru3l+6e7gZ38gqBYIDr12+wvrbG8tIS0KwZLdOUC21tEcaujbO+vs6ThXnS6XQuVNNdVz6VlDySwE8opW4D7wR+WETuAB8BvqCUug58wfrdNORWgVfsbG8zNfmYjs4OBgaHcGQWBmqSpthClDK70c/MTGM4DEbHxmxe/8a7Jnufks6uTrp7epiZnq5p5faGQyDcFmF0bIzVlRUW5hfyBKSZOVE8lFJLSqmXre97wAOgH/gA8Ekr2CeB7z4rI+uNXfH39vZ4PDFBa6iVgaGccJidgRork1VC5tK2t7ZZXVlldHQUn88ce9MMfhvDMBgeHSGVTrMwP583Z0qzkOvbkut0F2lvZ2R0jJWlJZaXlpvyugqpyuchIiPAc8BXgG6l1BKYAgN0lTjmwyLyooi8uLm7ezpr64D9UR3sH/D40SMCgQAj42PHpgq8OOTYJ+OfKZfW7E7SudlZgi1Burq6z97cOpHJbH5/gIGBQZYWl7LO02bFLiDtHe0MDQ+zuLDQdD1ri1GxeIhIEPhj4MeUUhWrgFLqE0qptyml3haxdUq6MGzNl5OPJ3C53IyOjzdQP47Tn3t3d5etrS0Gh4ayvUcbvcRhRwR6+3oRQ7K+j2YmJyBCZ083PX29zM7MsL21dcGWnY6KxENEXJjC8btKqT+xNq+ISK+1vxdYPRsT64P51jZ9HMlkkpmpKVKpFOPXrmXX6YBGyGTF30KF3bxLHq0US4uL+P2+pusvAbn77/X66O3pZXlpmaOjONC8b2jIXZchQl9/v9mVfWqS6F4UaE7HcCWtLQL8JvBAKfUrtl2fBT5off8g8Jn6m1d/0uk089Z0cmPj1/D5fScf1DQoDg9jbKyv0dPXly1NXbwgVo8IdPV0k0gk2GryN3SGzAvAMAwGBgcJBAJMTT7m8PAwG6aZBKSSkse7gB8A3iMir1if9wEfBb5VRCaAb7V+NyT2UY6ryyusra4xMjpmje3IH4Le+BS3N5Potre3SadVU5Y6MmTELhgMEgqFWFtZuXSDy5xOJyOjY4gIc9MzJJPJizapak70ECqlvkzp3PXN9TWn/uQPdNtifm6Ovv5+2js7bJMUQ3MJSHGUgvW1NVpaWvD7/Scf0OAYhkFHZyezMzMcHR3htQ1MbGYyY3c8Xg+jY+M8evNNniwsMDg8jCHN02+zeSytGdPPcXBwwPTkFG2RNnr7+/J6AjYWlRp0PFwiEWdnZ4f2jva8+UaamXBbmHQ6RTS6BzSnb6A0QjAYZHhslLWVVTbW1oHmub4rIB6QTCSZmZrG4XQyNDzSxL1HVcEnn4ODA1LJJKHWVpptoqJCcs22ftxuN7s7OxdsUX0R29srEmmnp6+XudnZpnKgXlrxyNx8pRSLT56wH40yOjaK2+Mm4zdo1oxVioP9fQzDyDqBL8PlOZ1OgsEWdnd2Gz4zVYt9xrbeXnN2+ZnpaeLx+EWbVhGXUjzsyyRsbW6yvLTI0PAwLS0hcm/ki7OvPOVLF0WPsDJVNLqP1+vF7XKfcERz0RIKETs4IJU0B8tdNtEHweF0MDwyQjKZ4MlCrgt7IwvmpRQPE8Vh7JDZmRnaOzro7O6ydEM1sHCUxixFle5hqhQcHOzj8/nzxrE0MxmR8Pl8JJNJEsnEBVt0NmTSo9fnZXhkhI21dTY3Ni/WqAq4HKnMRkapU6k0c7OzOAwHA0ND2QzVfG8thSpTAsmNkUhzdHRk67fSuG+sanF73Circ99lcAIXx6xKh9sidPX0MD83mx0Y2Kilj0YZzFFfrCbL7e0tbty8ldeDtBE5cfW0grRzbP1XTLFMJVPHFh+6DJhjjoRE3Cx55F9W6R65zYR92cq+vj72dneYn53j2vXr2YW1G41LKR4HsQMW5ufo6u6mNdya3d5sCcrOScO4U6kkqbQpHul02kqNmb3NKiK5Lt1gXmPx+5DxcSlEjKaslkJOQJwus1Xw0Ztvsr6+Rld3d0MuqH2pxEMpRTqdZmFuDpfLRV9/f96gpIul9PnzTTue0Q9jMSYfPyaVSpYMlkqniB3EmJ2ZZXV1NXfGZtWNDALJZIrDwxjTU1MsPVksGQ6gvaOD/oGBppxA2U5LSws9vb0szC/QEgrh8/mtElfjXNelEA97MXZjfZ2d7R2u37yJ2222Olz8za7k/KVzeTKV5GB/n/aOduuajseXVmk2NzcJBAK0tWWmG7zo664PqXSaePyI1nArAX+goFSVQbG+ttb0EwhlejsrFN29PWxvb7EwN8/49et5KxQ2ApdCPEwUR4eHLMzPW9WV8MmHnBsqK3B2HSt0SZTTOMNhTuvvt01gbCedTjE1NU1bJMLA4ACFwtFYya40xSQ0mUyyvbVFV1c3bZFSY3YUsdhhiX3NidPpZHBomEcP32Rzc4OOjg4a6Uk2vXhYbQ2krc5ghhj09vWZpQ1ppFt99hiGkEgcb868+JJXFRRz8iqzpaWaGlhTXXMRMuNfWkItdHZ18WR+nlCoFbfb3TBVssZ041aDldj2dnZZW1ujf3DA6kXaWMJRj7Vfc5FZcdk/QKglRCDgzwuTWy+2ST4F1wRwGD9idW0t31laJFzzO3gKMXtB9/b2ohQsLy01VAtaU4tHtk9HMsWCpcxtkcgFW1U59u7J1QiL2P7b84/DYWAYjrwwzUaeJloXETuIkUwm8kacFgt32cj4P9weD/0DA6yurLC/nxv7ctE0tXhk2NhYJ3ZwwMDgoDXo7eQZtzTNgmJ/P4qRbYJtzh7Cp0OItLcTDAZYXHhilcDkwgfPNb14xONxFp8s0tndRSAYvGhzLh5p/vp+IZubm2ZHqct1WVXhcBj09Q+wu7vDToOMMG5K8bAr7urKKihFT29vA8/RkeF8DLOPKG5mlFIkkym2NrdwZ6dUvGCjzhl7lbYl1EIk0s7iwgLJ1MXPPNaU4pHhMHbI6vIy3b292S7ol+2tWy3JRILoXvTSTNsXjx9hGIYuVWKm7Z7eXg4PD9lqgIFzTScemeH2SsHKyjIOp4OOzkz7dzMIx9nauLu7x0svv0Qi3vwzjgN4vV6ef/55vB7vRZtyoWRHGPv9dHZ2sbS4SCJhlj4u6hk3nXiYKA5jMdZX1+jt7bXNEn7BZjUAwWCQZDLJ5tbFv5lOS2amcX8wgDRY78qLQkTo6u4mmUywtbGR3X4RAtKU4pEpdbjcbiLtHYAWjgxut4vu7m4W5udJN3mpI4N+tCaZ1iav10tXVxfLy0tFOwWeF00lHhl1jcVibKyv09vXl10RTWMhwsDAABubm+xZy3s2W9XF7vC96j6sfCT7r7Orm1QydaG+j6YSDwAUrK2s4HK5aGtrQ7+XjhMKheho72BmeqYphaPc7yuP1bXY4/HQ0dnJ8vLyha350nTicXh4yPqaOceBWerQb6dCDMNgfHwcOHkekEYknU4zMzNDNBq9aFMaFLMbf0dXJ8lE4sLWvG0a8ci8gTbW1zEMc7p6TWnC4TBPP/N0Uy0zkXnGm5tbTExMXJrm5npif016vT4i7RFWlpZJpdLnXkprGvEASCQSrK2u0tnVlZ2rQ3OczIjiZpy3NZlI8ujRQ0ZHRgjqvh1FsS963tnVzeHRIXt75+/fairx2N7cIplK0d7ZmR1u30wZoxpO20s0l8DkWHyN6EfIzA4/PTONSqcZGhnRLWgV4A/4aQmFWF1Zqbl1rdb00PDikUns6VSa1dVVIpEIXq81Q7hOXSdSSiwaSUAytqytrTI7M8Odu3et7uiXb2Gu+iLZfh97u7vEDg6A83u2DS8emVpeNBolFjugs6vT6u9/VRJVfa5zc3OTqakp0qnGdKAqBVubW1y/cYNwuLpWtFLimFuWQmVLNoWfQhtK7Su2/6RPqess3G/+ztlY/Jjj+zND9ltaWvB4PGysZzqNScGx5a+n1jTWBOJhXuD62hp+v//KjXE42N9nZ3v71G8Th8PJ9NQUjycm8lYja5QSiAhcv36dwaGh2gc4ijneaWtri1SeSNY2dCGX8Wq7Tycdkr8/Z2PxDF/6GhwOB51dXWxurBOP5zqNFRPHSm2rhIYWD/OBKeJHR2xvbdHZ1XVpVkOrlLW1VZ7ML6DSp3vara0hnnvrW5mdm2Pi0QSpVKpOFtZGMf+L4TCyyyzUUrAUhOjeLrPT0yQSxdd7tfuCpGA6tuP7cjHbM251pd4iU74VWl30nPbjy8Vp/g6H21BplV0QvLQ4lLCjhuTVFDlxe2cLULS2tp4Y9rLR3z/A+PVrNYumPUFGIhGef9vzzM/P8frrr5/7gsrlHLbZzHOK+RqVUoTbIty6cydvoa9ctKevAtqX8qjkU+z4avdnWlaKTytp4vZ4aA2HWV9fO9a3p9ixp7zVQBOIRzqVZmNtnXBbBJe7sVd+OwucLicer/dUrg97QoxEIrzjG76Bvd1d1tfWOc85RjIkk0mmp6ZYXl4+buspLXK6nHi93hJCUd18qvnTRNbivK3j3K4lyFXxhPaODg6i+xzGYtljKja5hpve8OKRTCWJx+O0RdqyDqLmdZaWTwh2yhdlT0coFOIbvvEb6e7pzllW0JRbT19IznEJe7t7vPi1r/Ho0cSZVkHrf+/ql+HPBkUgGMDhcLC9vW2zubJja6HhR5WJCA6HI9tTsml1owHITOcPVDQzVz0GpmXOd3h4yOzMLFOTk7RF2njXN72rbp3A7Nd1NTGv3XA4cLqceSsLnuXgwsYXD5tTqHlLHBdDqQxVKrPF43GmJidpb++gLdKG0+nMC2e//5Vk1kz4dDrNvXv32Nvb45m3PEt3d7e1eHV5W/Xzrg4p+H/WNLR4XL7EI5x7cVaBytR/rW65pd5GIgbJVIqXv/4yHo+Hvr5+Ojs7CAZbcNmmPigpHArSSh1bFlHE4NatW3g8nuzETeb2XO/Xwngv37NvXGq91yeKh4j8FvB+YFUp9ZS1LQJ8GhgBZoD/USl1MUP7NEXJZMTd3R3mZmcBGBgcItxWehlOl8vJ3btPMT4+zvLyMktLS0xPT9Hf38/du0+BbQRzWim2t7aIH8WJx+McxGLs7e2ilOKZZ5/FW9DaYa+iFEusyWSSqceTxI+O8AeDjI6NagGpA2d5Dyspefw28HHgU7ZtHwG+oJT6qIh8xPr90/U3T3NaHE5ndn3bwqpCMUTA5/MxOjrKyMgIh4dHKJU+5htJp1JMTU6yu7eH0+nE6XTSGmqlra0t7zyVJl4Rwef343I58fqu9nylzcKJqUkp9f+JyEjB5g8A77a+fxJ4AS0eDYXp14BAIMjY+DXs1aVS/QsyZEotIoKvREZ2Op0899a3muEM49SDFB0OB4NDgzUfr6mdWp3Ntfo8upVSS9aJl0Skq8Z4NOdCdb6EUkJi36+UKjtXiK5yXH7O3GEqIh8GPgzQ19Fx1qdrYM4/M4nYBz7V1mRX6ph6ioMWmuak1l46KyLSC2D9Xy0VUCn1CaXU25RSb/P2hGo8naZW6tk1W9NsnO0zr7Xk8Vngg8BHrf+fqfTAl56vrqNXIg4PfLA+Aq2lGwryeP6lyuNvVK52p6fTU9gcXaz6VY9zYC2qbkZfunRX6vz27ZlHbg9i35b/3R5fqS4ACqVy+0pf+9k11f4+pnO0Q0QWgH+GKRp/KCIfAuaA763p7GfES8+f/TnOW6B0uaE0pYQ2IyC5/bkMasfMVLku9Oa2YvEdO7Jge378mTjsc2YUm4+jeNylh9AXj6/ciFy7iBYJVvL48lTS2vJ9JXZ9c9Vnu0SctUApZQrUwf4BO9vbl2YBp7PmMHbI9tYWoVArhsNeKz8pc2T2q4Lfdqp9BoVxFsR2Ykau/plLkW/5e+uXjhq6h+lV56XnYX5unWXPMnQrYk+DP1D8rZhKwX039PVDR2fl57gMVbwMIrAf3WNudo4bt27hdWQ6quWGtlePvaXq2BlrMbMo9hLSWVZZqx1iUA4tHg1OX/8ALS0hJh9PnEn851HFg/MRKaWgLRJh7No1HI5SSVvlhc9g9ymY+8qJxvG4ipMvWoWZNf+clWRkexh703kunmKx5Oyvryhp8Tg3TOdatTiskZLNzmlEKpmAe25YG4Jiy/VkMk7ooTWytKAn7VllnpOpVBCKddorP7AxL4a6XFb1kTR/qryk6KbVyskU+V96HsSAnetnd/9OU4IqZlJ+57vS+8qj8v7b/5aL47S3SIuHRlMFzdCSV/V8Z+fcPV2j0ZwR1QpU1t+h4A0PtLbCypC5rVTpoh4+KC0eZ07h06u9GU6jqRf5AiUc+KuPo+HnMNVoNGeLrrY0GeV6MjYDetYvjRaPM6LZxSFDZvyGbYvtuxQN0+zXrKkMLR6aomQGehVsNZdlSCvS6TRKKWuVNwMxINP92T72QgvJ5UWLxwXRyJmqsKdl/OiQaHSf6O4e+/tREskk6VTKEg8HhsOB3+ejJRSipSWI1+ez1mSRrAjpqk3jcmYTIGuuDvbRp+l0mujeLqsrq+xYiwh5vV4CwSBer9ecRUzMZRXi8QT70ShPFhZIp1L4/H66urvN+Uyt3rG6amNy3r6iUlMT2KnVDC0eZ0Q90sV5DqRVtk6KBwf7PFlYYHtrE78/wODQEK3hVtxuD2IUvzClFMlEkv39fdbX15iZmWZpcZGBwUHa2sLIuS5QfvLNL7y3xebQOBvKD4/PH8ZfIoZjYfKb/1V2m32g3fHh+Tk7dGtLg1J8MFPNUdQZ+8CsdDrN2uoqC3PzuN1uxq9dJ9zWZg1tL98/RURwuV2E3WFaw63EDmIsLT5h8vEE7e0dDAwN4na7qfkeVIWyOayLz+HRzJS8HiWgsC2UVim62tJEnJyaMwlkd3eHjfV1VLr+OcCeCJPJJAtz86ytrtLT20dvX69tQJ7d+Vk6oeVmtzLwBwKMjV8j0r7F7Mwsj958yPi1cXz+TG+kMxARgYNolNXlFdo72nGUWWritGM+yr2ty88WVkp8M2FPPncZq8y7qkq/sErZUMtpdSexhkUBit2dXTbWN85wjgdFKplkdnqajfV1xq9dZ2BwMG8kr4hC5OTzFy4uLYZBWyTCzVu3MQzh0cOHHOwfmGc9g8sRIBaLsbq6QjKZstmVs63SBbBPWuy7XHzHh97nwhQel9tXXQkpMzdt3nmtv3bf1VmixaPB6e/v5/qNGwWzYp0OpXJNselUmvm5OXa2t7l24waR9ojl17DPRZH7XQn5CVvw+b1cu34Dt9vN44kJjg6PsFct6oVSEGlv5/bdp/B4PUVtzoiCmcHKfXLh87cd/11cZM6+rnTMb4OgkGN+KVOgMs9EFR/dW8P5tXg0KJlMK4aBw1l6fZTaMBO/UrC6ssLa6gojY2O0hluzub4eM67bBcTtcTM2fg0RmJmeIpVMUTrjVUdeC4Zh4MgKrT3u4+fKiWj+79ImFR5/XACLlQiKx3NcqHIz3RfOQVIoXiX2ZTW+0IBy97j2+6/F40Kp7o1ebzLNq/0Dg7RFIjmr6miSPS6P18Po2Dj70SirK8vnNEO8OkEQKoihguMrE438+Ar709i35bekWC8SyZUicvuyMVR28ry4T3f/tXhcCCeLhv0B19NZmsmwqVSahfk5AoEA3b29tjp53U6VJVeKEQLBIH0DgywuLhI7iOXZVBeOlQYquaDiz6PYjF2FGd/uszj+qYTKwhU/B/m/swWRYqWUQr9Kfr+bWtDi0bCYKWFleZmZ6SlUKn36GG25amd7m2g0Sv/goLVsZGWOxNMiInR2duL1+VheWqyv30Nge3ubyYlHxOPxiu0pt/0s7snJjttiDtVi8RRusbW22G6s+bPwRuf3+9CtLQ1PqUdkPcAixWMR0+9Rz9pNOpVmeWmJtkiEYDBIKSdavck47BxOB319fWxtbRE7OKjvORBEMv1SjpemymXKSrZX22qToVjrjd15W0tcpYRXmUZXHF+taPFoGIp3wurq7mZkZNQaK3LKM1hF3/39KAcH+3R1dZXsMXp2mDaEWsN4PB421teAOjXdKmhtCzN+/ZrVIY1jcVfW0lL+Y8/0hZ9iYQpbb0oJSbEwxVuHSiFmZcTIL1UUO8fxI6tHi0czIPVp+Ms0z25ubOL1+ggEgnWItToyL0SHw6Cjo5OtzU2SyeS529E4lGpJKU1J56zN9VF5itGtLZcCe/NoLUXjSkglU+zsbBNpj2T7jlR7jvJv3soJtbaSTKVsjtOqDs9SzH57BitsAj39Lc2VAkrFW7itmA3Hw0vJcEX7ZhRt0i0epvRHih5XCVo8rhSKo6MjEvEELS0hqmkVKBQIc16P2py4YvVF8Hq9uFwu9qNRsu/LJhiIUk9hr98L4vyb/PXYlivG4WEMMQSv11yKsdp0m0qmWF5eZnt7G6XS+Px++nr78Pl9VdtiOAwCgSDR/WjVx2oKKdXL9eQHXKt46ZLHuXJxHcIyHB0e4Xa7rVXVqnvLp1IpJqcmicfjjI2NcePGTYLBIBOPJziostUkk179fj9Hh4dWXxY9aVBt5D/H87qDWjyuGEdHR7hcrprm19jc2MRhOBgeGcbn9+H2uOnu7qa/r48nT54A1Vc7XG4XyWSSVDp1cmBNQ6HF44qRSCRwuVw1Hbuzu0NnV+exZuNwW4REIkkiUX2ridPpIjMvqqa50OJxxTjN5DgqrYoKj2ENRlOqegeqGOaUh7rk0Xxo8WgYzufNaxgG6RozqtPlJBaLHdueTCRIJZNWN/fqyPo4dMGj6dDi0RCcX84p7KpdDe3t7SwvLZGIJ7LbVDrN4uIiLS2hmsQjh1aPenFed1I31Z47pQYoNT4tLSHCbW08fPgmkUg7TqeTra0txBDGxsYu2jzNMc42bWnxOFdKtcWfrwnZztAFc12eNL5SBHp7+wgEAnz9pZdJJpOMjI4wNj6e70S1j9Oon+U1kOl4BidlJJHyPVyL789sKD/qtVS8pc550nFFjqhwW36c1Z8nHy0eV4xi6SSZTKLSQAXzlAK4XW7cLheGCB6Ph1QqTSpVuR/F6XDmBm+pvH91pn5v3uIZrJL4y3X/rr1reFGsHuoFY4KLBLK+nfLUWjyuGIFggLStW3k6nebx48fs7OxUHIdSitjhIQrF7Owsi0tLFR9riMH1G9cJh8MAOF0uWsNhnI6LTop1zsjZOHO+peILLpUToOL2lJ6FvXj4YhMy12MYwKmemIi8F/jXgAP4DaXUR09tkeZM6e7usZKYOQjLMAyuXbtm9rOo9EWdTXdWhqvmOCFPKHw+b3Zu07OisrjPYk6Twkxbfn8hpe3JtzV/ysJKzlHs+OovvmbxEBEH8GvAtwILwNdE5LNKqTdqjfNqchZvvPKnK0wmTmt9k0pbX2peOlKpYuM+80aeampFmdXOvFG2YL+/Jx5fJadpqn0H8FgpNaWUigN/AHzgFPFpzpj8+TaP76sunhqGt5ediUs31dbOxdy701Rb+oF52+8F4BsKA4nIh4EPWz+P3m68494pznlRdADrF21EDTSr3dC8tjer3TerPeA04lFRBUsp9QngEwAi8qJS6m2nOOeFoO0+f5rV9ma2u9pjTlNtWQAGbb8HgMVTxKfRaJqI04jH14DrIjIqIm7g7wCfrY9ZGo2m0am52qKUSorIjwB/jtlU+1tKqfsnHPaJWs93wWi7z59mtf3K2C3NMGekRqNpPPSoWo1GUxNaPDQaTU2ci3iIyHtF5KGIPBaRj5zHOWtFRH5LRFZF5J5tW0REPi8iE9b/tou0sRgiMigiXxKRByJyX0R+1Nre0LaLiFdEvioir1p2/3Nr+6iIfMWy+9OWU77hEBGHiHxdRD5n/W4Wu2dE5HUReSXTTFttWjlz8bB1Y/924A7wfSJy56zPewp+G3hvwbaPAF9QSl0HvmD9bjSSwE8opW4D7wR+2LrPjW77EfAepdSzwFuA94rIO4FfBj5m2b0FfOgCbSzHjwIPbL+bxW6Av6mUeoutX0p1aaXc6l/1+ADfCPy57ffPAD9z1uc9pc0jwD3b74dAr/W9F3h40TZWcA2fwRx31DS2A37gZcyeyuuAs1gaapQPZt+mLwDvAT6H2XGy4e22bJsBOgq2VZVWzqPaUqwbe/85nLeedCullgCs/10XbE9ZRGQEeA74Ck1gu1X0fwVYBT4PTALbSqnMdOyNmmZ+FfgpIDPHQTvNYTeYvcH/QkResoaQQJVp5TwmUah0nLCmDohIEPhj4MeUUrvNsIiSUioFvEVEwsB/BG4XC3a+VpVHRN4PrCqlXhKRd2c2FwnaUHbbeJdSalFEuoDPi8ib1UZwHiWPy9CNfUVEegGs/6sXbE9RRMSFKRy/q5T6E2tzU9gOoJTaBl7A9NmERRyJETYAAAEYSURBVCTzcmvENPMu4LtEZAZzRPl7MEsijW43AEqpRev/KqZgv4Mq08p5iMdl6Mb+WeCD1vcPYvoTGgoxixi/CTxQSv2KbVdD2y4inVaJAxHxAd+C6YD8EvA9VrCGs1sp9TNKqQGl1Ahmmv6iUur7aXC7AUQkICItme/A3wLuUW1aOSfnzPuAR5h12Z+9aGfRCbb+PrAEJDBLTR/CrMt+AZiw/kcu2s4idn8TZhH5NeAV6/O+RrcdeAb4umX3PeCfWtvHgK8Cj4H/B/BctK1lruHdwOeaxW7Lxletz/1Mnqw2reju6RqNpiZ0D1ONRlMTWjw0Gk1NaPHQaDQ1ocVDo9HUhBYPjUZTE1o8NBpNTWjx0Gg0NfH/A0zvnAnI7d98AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a17510198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# split data into train and test\n",
    "train_set_size = int(.80*len(nba_shot_data))\n",
    "train_features = nba_shot_data.ix[:train_set_size,['x_Coordinate','y_Coordinate']]\n",
    "test_features = nba_shot_data.ix[train_set_size:,['x_Coordinate','y_Coordinate']]\n",
    "train_class_labels = nba_shot_data.ix[:train_set_size,['shot_outcome']]\n",
    "test_class_labels = nba_shot_data.ix[train_set_size:,['shot_outcome']]\n",
    "\n",
    "#Train it\n",
    "start_time = time.time()\n",
    "skl_LogReg.fit(train_features, np.ravel(train_class_labels))\n",
    "end_time = time.time()\n",
    "print(\"Training ended after %.2f seconds.\" %(end_time-start_time))\n",
    "\n",
    "# compute the classification error on training data\n",
    "predictions = skl_LogReg.predict(test_features)\n",
    "print(\"Classification Error on the Test Set: %.2f%%\" %(calc_classification_error(predictions, np.array(test_class_labels)) * 100))\n",
    "\n",
    "# compute the baseline error since the classes are imbalanced\n",
    "print(\"Baseline Error: %.2f%%\" %(np.sum(test_class_labels)/len(test_class_labels)*100))\n",
    "\n",
    "# visualize the boundary on the basketball court\n",
    "visualize_court(skl_LogReg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad.  We're beating the random baseline of 45% error.  However, visualizing the decision boundary exposes a systemic problem with using a linear model on this dataset: it is not powerful enough to adapt to the geometry of the court.  This is a domain-specific contraint that should be considered when selecting the model and features.  For instance, a Gaussian-based classifier works a bit better, achieving 39.02% error.  Its decision boundary is visualized below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/enalisnick/NBA_shot_analysis/master/results/spatial_features_results/Gaussian_Mixture_Model.png\" alt=\"\" style=\"width: 250px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.  Dataset #2: NBA Shot Outcomes Continued"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we do better by adding more features?  For instance, if we knew the position (Guard vs. Forward vs. Center) of the player taking the shot, would that help?  Let's try.  First, load a new dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_Coordinate</th>\n",
       "      <th>y_Coordinate</th>\n",
       "      <th>layup</th>\n",
       "      <th>dunk</th>\n",
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      ],
      "text/plain": [
       "   x_Coordinate  y_Coordinate  layup  dunk  3pt  hook  jumper  fade_away  \\\n",
       "0          45.0          11.0    1.0   0.0  0.0   0.0     0.0        0.0   \n",
       "1          37.0          27.0    1.0   0.0  0.0   1.0     0.0        0.0   \n",
       "2          24.0          33.0    1.0   1.0  0.0   1.0     0.0        0.0   \n",
       "3          25.0           6.0    0.0   1.0  0.0   0.0     0.0        0.0   \n",
       "4          42.0          18.0    1.0   0.0  0.0   0.0     0.0        0.0   \n",
       "\n",
       "   Guard  Forward  Center  shot_outcome  \n",
       "0    0.0      1.0     0.0           0.0  \n",
       "1    0.0      0.0     0.0           0.0  \n",
       "2    0.0      0.0     0.0           0.0  \n",
       "3    0.0      0.0     1.0           1.0  \n",
       "4    0.0      1.0     0.0           1.0  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first we need to extract the file from the zip\n",
    "import zipfile\n",
    "zip = zipfile.ZipFile('./data/nba_experiment/NBA_all_features.csv.zip')\n",
    "zip.extractall('./data/nba_experiment/')\n",
    "\n",
    "nba_all_features = pd.read_csv('./data/nba_experiment/NBA_all_features.csv')\n",
    "nba_all_features.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One thing to notice is that this data is noisy.  Look at row 2 above; it says a player made a dunk from 33 feet above the baseline--that's beyond the three point line. \n",
    "\n",
    "Now let's train SciKit-Learn's Logistic Regression model on the *train_features* and *train_class_labels* and then compute the test classification error--which should be around 38%-39%. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/enalisnick/anaconda/envs/cs175/lib/python3.5/site-packages/ipykernel_launcher.py:2: DeprecationWarning: \n",
      ".ix is deprecated. Please use\n",
      ".loc for label based indexing or\n",
      ".iloc for positional indexing\n",
      "\n",
      "See the documentation here:\n",
      "http://pandas.pydata.org/pandas-docs/stable/indexing.html#ix-indexer-is-deprecated\n",
      "  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training ended after 1.74 seconds.\n",
      "Classification Error on the Test Set: 38.95%\n",
      "Baseline Error: 45.91%\n"
     ]
    }
   ],
   "source": [
    "# split data into train and test\n",
    "train_features = nba_all_features.ix[:train_set_size,:'Center']\n",
    "test_features = nba_all_features.ix[train_set_size:,:'Center']\n",
    "train_class_labels = nba_all_features.ix[:train_set_size,['shot_outcome']]\n",
    "test_class_labels = nba_all_features.ix[train_set_size:,['shot_outcome']]\n",
    "\n",
    "#Train it\n",
    "start_time = time.time()\n",
    "skl_LogReg.fit(train_features, np.ravel(train_class_labels))\n",
    "end_time = time.time()\n",
    "print(\"Training ended after %.2f seconds.\" %(end_time-start_time))\n",
    "\n",
    "# compute the classification error on training data\n",
    "predictions = skl_LogReg.predict(test_features)\n",
    "print(\"Classification Error on the Test Set: %.2f%%\" %(calc_classification_error(predictions, np.array(test_class_labels)) * 100))\n",
    "\n",
    "# compute the baseline error since the classes are imbalanced\n",
    "print(\"Baseline Error: %.2f%%\" %(np.sum(test_class_labels)/len(test_class_labels)*100))\n",
    "\n",
    "# we can't visualize since D>2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great!  We've improved by a few percentage points.  Let's look at which features the model weighted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_Coordinate: -0.00\n",
      "y_Coordinate: -0.01\n",
      "layup: -0.00\n",
      "dunk: -0.04\n",
      "3pt: -0.05\n",
      "hook: 0.27\n",
      "jumper: 0.86\n",
      "fade_away: 0.76\n",
      "Guard: 0.90\n",
      "Forward: 0.28\n",
      "Center: 3.08\n"
     ]
    }
   ],
   "source": [
    "for idx, feature in enumerate(nba_all_features):\n",
    "    if idx<11:\n",
    "        print(\"%s: %.2f\" %(feature, skl_LogReg.coef_[0][idx]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interestingly, the classifier exploited the location features very little.  The position of the player was much more important, especially if he was a center. \n",
    "\n",
    "## 6.  Dataset #3: 20 News Groups\n",
    "\n",
    "For the second experiment, we'll work with the very popular '20 News Groups' dataset consisting of, well, 20 different categories of articles.  SciKit-Learn already has it ready for import."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The training data size is (1079, 1000)\n",
      "The test data size is (717, 1000)\n",
      "Example text:\n",
      "Library of Congress to Host Dead Sea Scroll Symposium April 21-22\n",
      " To: National and Assignment desks, Daybook Editor\n",
      " Contact: John Sullivan, 202-707-9216, or Lucy Suddreth, 202-707-9191\n",
      "          both of the Library of Congress\n",
      "\n",
      "   WASHINGTON, April 19  -- A symposium on the Dead Sea \n",
      "Scrolls will be held at the Library of Congress on Wednesday,\n",
      "April 21, and Thursday, April 22.  The two-day program, cosponsored\n",
      "by the library and Baltimore Hebrew University, with additional\n",
      "support from the Pr\n",
      "\n",
      "Example count vector:\n",
      "[[ 0  0  1  0  1  0  0  0  0  0  1  0  5  3  0  0  0  0  3  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  3  0  0  1  0  0  0  0  0  0  0  0  0  0  9  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  3  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  2  3  0  0\n",
      "   0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0\n",
      "   0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  3  0  0  0  2  0  7  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  1  0  1  0  0  0\n",
      "   0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  1  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  6  0  3  0  0  0\n",
      "   0  0  2  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  3  1\n",
      "   0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  4  0  0  3  4\n",
      "   0  4  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0 13  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  1  0  0  0  0  0  0  0  0  0  0  3  1  0  0  0  0  0  1  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  2\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  2  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0\n",
      "   0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  1  7  1  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0\n",
      "   0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  1  0  0  1\n",
      "   0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0 12  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  1  0  0\n",
      "   0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "   0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "\n",
    "# use SciKit Learn's loading methods\n",
    "categories = ['soc.religion.christian', 'alt.atheism']\n",
    "train_20ng = fetch_20newsgroups(subset='train', remove=('headers', 'footers', 'quotes'), categories=categories)\n",
    "test_20ng = fetch_20newsgroups(subset='test', remove=('headers', 'footers', 'quotes'), categories=categories)\n",
    "\n",
    "# transform the text into word counts\n",
    "vectorizer = CountVectorizer(stop_words='english', max_features=1000)\n",
    "train_vectors = vectorizer.fit_transform(train_20ng.data)\n",
    "test_vectors = vectorizer.transform(test_20ng.data)\n",
    "\n",
    "train_targets = train_20ng.target\n",
    "test_targets = test_20ng.target\n",
    "\n",
    "print(\"The training data size is \"+str(train_vectors.shape))\n",
    "print(\"The test data size is \"+str(test_vectors.shape))\n",
    "# print the first 500 words of an article\n",
    "print(\"Example text:\")\n",
    "print(train_20ng.data[0][:500])\n",
    "print(\"\\nExample count vector:\")\n",
    "print(train_vectors[0].todense())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the vector is super sparse and very high dimensional--much different than the data we've been working with previously.  Let's see how SciKit-Learn's Logistic Regression model handles it.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training ended after 0.02 seconds.\n",
      "Classification Error on the Test Set: 23.99%\n",
      "Baseline Error: 44.49%\n"
     ]
    }
   ],
   "source": [
    "#Train it\n",
    "start_time = time.time()\n",
    "skl_LogReg.fit(train_vectors, train_targets)\n",
    "end_time = time.time()\n",
    "print(\"Training ended after %.2f seconds.\" %(end_time-start_time))\n",
    "\n",
    "# compute the classification error on training data\n",
    "predictions = skl_LogReg.predict(test_vectors)\n",
    "print(\"Classification Error on the Test Set: %.2f%%\" %(calc_classification_error(predictions, test_targets) * 100))\n",
    "\n",
    "# compute the baseline error since the classes are imbalanced\n",
    "print(\"Baseline Error: %.2f%%\" %(100 - sum(test_targets)*100./len(test_targets)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "24% error is respectable, but there's still room for improvement.  In general, working with natural language is one of the hardest application domains in Machine Learning due to the fact that we often have to reduce the abstract, sometimes ambiguous semantic meaning to a superficial token.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:red\">STUDENT ACTIVITY</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Engineering for 20 News Groups\n",
    "Can you beat the baseline error rate on the 20 News Groups dataset?  One way to do this is to have better features--word counts are rather blunt.  Go read about [TFIDF](http://www.tfidf.com/) and then use SciKit-Learn's [TFIDF Vectorizer](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html) to compute a new feature matrix for the 20 News Groups dataset.  You should be able to get an error rate of about 40% if not better.  The code is started for you below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classification Error on the Test Set: 23.99%\n",
      "Baseline Error: 44.49%\n"
     ]
    }
   ],
   "source": [
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "\n",
    "\n",
    "#### YOUR CODE GOES HERE\n",
    "\n",
    "\n",
    "print(\"Classification Error on the Test Set: %.2f%%\" %(calc_classification_error(predictions, test_targets) * 100))\n",
    "\n",
    "# compute the baseline error since the classes are imbalanced\n",
    "print(\"Baseline Error: %.2f%%\" %(100 - sum(test_targets)*100./len(test_targets)))"
   ]
  }
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