{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Chapter 4 – Training Linear Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Linear regression using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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vA3cBtwG3AB+tc4Ndv+qeZtoVdhOfczIgvvrVp59w6w6RLp9IZ/kbtXVB5XyHKtFSzMVX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\n+v+inylMfLGNvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4100d0d5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.21509616],\n",
       "       [ 2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.21509616],\n",
       "       [ 9.75532293]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ca9euwlrqW7YEvfNsT33N0BKWX9URy+NmohDXMZ8ccaldE2uNqBch4RgbZl/5SvEyvGV5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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f6182f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The figure in the book actually corresponds to the following code, with a legend and axis labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_model_predictions\n"
     ]
    },
    {
     "data": {
      "image/png": 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W+gzKz2adZFea0LN/7B6f5I4c8VZiiM+O3norsYyZ98bx2dG4cT3OjsJ0Qs52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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f6171e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"linear_model_predictions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.21509616]), array([[ 2.77011339]]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.21509616],\n",
       "       [ 9.75532293]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Linear regression using batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "theta = np.random.randn(2,1)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.21509616],\n",
       "       [ 2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.21509616],\n",
       "       [ 9.75532293]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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EVaoQXbrk/P9WK1H//kRxcUSpqa7P5Zo1fJ527HB/ztVqFYcOuW8nmJdAaHTt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ecad9358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_path_bgd = []\n",
    "\n",
    "def plot_gradient_descent(theta, eta, theta_path=None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        if iteration < 10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(X_new, y_predict, style)\n",
    "        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "        theta = theta - eta * gradients\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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EVaoQXbrk/P9WK1H//kRxcUSpqa7P5Zo1fJ527HB/ztVqFYcOuW8nmJdAaHTt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f69174e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sgd_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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wykpWFn/sMfbTiZeLQ7W2MtPOVQk/+2zGjZYupetv1KjYnKOuxEe/o+SntZWW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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec1f1b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch == 0 and i < 20:                    # not shown in the book\n",
    "            y_predict = X_new_b.dot(theta)           # not shown\n",
    "            style = \"b-\" if i > 0 else \"r--\"         # not shown\n",
    "            plt.plot(X_new, y_predict, style)        # not shown\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)                 # not shown\n",
    "\n",
    "plt.plot(X, y, \"b.\")                                 # not shown\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)                     # not shown\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)           # not shown\n",
    "plt.axis([0, 2, 0, 15])                              # not shown\n",
    "save_fig(\"sgd_plot\")                                 # not shown\n",
    "plt.show()                                           # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.21076011],\n",
       "       [ 2.74856079]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.1,\n",
       "       fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',\n",
       "       loss='squared_loss', n_iter=50, penalty=None, power_t=0.25,\n",
       "       random_state=42, shuffle=True, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "sgd_reg = SGDRegressor(n_iter=50, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.16782089]), array([ 2.72603052]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50\n",
    "minibatch_size = 20\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "t0, t1 = 10, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi = y_shuffled[i:i+minibatch_size]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.25214635],\n",
       "       [ 2.7896408 ]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_paths_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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h8ODBOfuwFQqFIhd4e3vj7e1tej9lyqPpS6ELeBqssTwHfhJoWVBGBIQE5NvIOy36AD0A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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec1475c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\", fontsize=16)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Polynomial regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f69b7358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.78134581]), array([[ 0.93366893,  0.56456263]]))"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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1LFzosm+ffBJuvTXi9Zsk/iRtgIIiZ3bNQmS89rSbGikvz42deucdOPHEcu1b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\nBJIClIiIBNL/B33SzBmQ3QdiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f69fedd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure high_degree_polynomials_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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dIbswG+8rHYiLh/R0iI+HxocSIDJO7LRhg8jOWLNGzE7av7/ceRIjFfoOug+v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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f615e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train_predict, y_train[:m]))\n",
    "        val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)   # not shown in the book\n",
    "    plt.xlabel(\"Training set size\", fontsize=14) # not shown\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)              # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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sjFXxpVLcKr5XXoFDD7VOYMvL0x6Xc865HKriSysvQTnnXM7K7wTl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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec293f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])                         # not shown in the book\n",
    "save_fig(\"underfitting_learning_curves_plot\")   # not shown\n",
    "plt.show()                                      # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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fKGcSlIhcDvwMOBx4UlXLnYlXRH4HjAEaAs8Bv1DVg8YE8ATlwmD/fmtuWbjQ\nEtbChbYsWBCMZqNzz7UpTmrzOpKruei1qfjrVNu2xTp/RDuAgHXF79rVepS2b2/Jb/dua7rbtcu2\n4+87iw4V1qePDS+W6s3ouZSgzgRKgZOBRuUlKBE5GXgUOAFYC7wAvKOqNyQp6wnKhdrGjTBzJrz1\nli2zZ6enthWVl2dfVD172nWwwsJYJ4AmTaxrfHRqE+eqKmcS1NcvLHIL0KmCBDUZWKqqN0W2hwOT\nVbVDkrKeoFydFz1jji4lJdbLavny2LJnj531HnJIbBSM6Bm0j3rhakt1E1QNpourdQOwWlPUHKCt\niLRU1c1Zism5wIr23IrKz7emmD59sheTczUR5D42TYCtcdtbAQGaZicc55xzmRTkGtQOoFncdjNA\nge3JCo8bN+7r9aKiIoqKimoxNOecc+UpLi6muLi4xscJ+jWoJar6+8j2cOAJVT1osBS/BuWcc8FV\n3WtQGW/iE5E8EWkI5AH5ItJARJLNxjIJuFhE+olIS+BGIKWp551zzuW+bFyDugnYBVwL/CSyfqOI\ndBGR7SLSGUBVpwJ3AG8ASyPLuCzE65xzLgt8JAnnnHO1Kmea+JxzzrlUeIJyzjkXSJ6gnHPOBZIn\nKOecc4HkCco559It2U2qiftSKVPHeYJyztVdtZEQ9u2DZ56xaZM//hg++shmfXzmGRuxd+NGm50w\nXUksxInOE5Rzru5KZ0LYvRvuvRd69YL77oMjj7RphQcPhm9+0/Z17w6tW0PDhvCHP9gskkOGwFln\nwS9/CW+8AX/+M0yeDP/+t/1csADWrbOh6NMdczrK1KIgj8XnnAub4mIIwjiZK1bAnXfCm2/aXOqN\nG9skWDNnwqxZsaHhRSxprFoFzZrZ8uSTNmlW48Y2WRbYTI4ffGDTJEe1bWu1KYAGDeDLL+019u61\nWQAPHLA4VqwoG9tbb5Xdfuih2HqDBjYvyksvxeaPnz8f1q61aXS3b7efK1facaPzy7/1Fnz1lU2J\nXL++LZMmlY3lqafs8TZtbGne/ODfV7LfXy3+Tv1GXedyVSpfHkEzbpwtUal84aWzzLHHwuWXw2OP\npXfGx6hBg+Cmm6x5b/z4so8lvvcbboCLL7bEtXatLc8+a5N1LVxoU9ouXQotW8LOnZbsMvk9l59v\nCbFHD6v1tWkDixfD0KGW4KLJ7j//gddeq/BQYZwPyjlXntJSmDHDvnCjc3LPmFG9L/LqqErS2LoV\nXnjBmqw1OKV9AAAY80lEQVQ+/9zO2jt2tFrIq6/GpvHNz6/4ONu22bWcjz+G11+3L/AuXaBzZ9vu\n29e+7Netgw0b4OWXrSmtQwerRfztb/Dzn1uTGcA551izWbduFldJidU0jjsOtmyxMs2awbvvWtPc\ntm0W4/r1lkR27bIkF50P/bzzrHnvkEPKTsxVnoICe+89e8b2bdxYNonFJzVVi/eGG+y11q2z5emn\n4eyzrTbXtKn9fOgh+1w+/NBqVO+/D4cdZjUsVXvtZcvss9mzx2p2q1fb72XrVtu3f78tn35aNu4P\nPyy7XZszXapqzi/2NpyrA0pLVe+6S7Vx48QJdFVFVHv2VD3lFNUrrlD9859VzzlH9cMPVdevt+eO\nHXvwMd94o+Lt+H2lpapz5qiOGqX6z3+qzpih+vbbqrNnq152meonn9gyZ47qWWepnn66an7+wbEm\nLnl5qp07qw4Zotqrl+oPf6h64YX2Po44QrV/f3t/lR0nleWww1SnT7f3k/h5JPt8qlOmos+wKmXS\nFU91yuzerfq736l+9JHqtGmqkyernnqq6sSJqpdcolpUpDpsmH2mY8fakuw9qWrkO7rK3+1eg3Iu\n21Jt19+7F84802oiUdEz9Xr1rCa1eLEt8WWeftp+NmwIjRrZdZfOna320amTNc+sWWPNOQ0awHPP\n2Vl9x46QF5lo4KWX4L334PHH4bPPbN+zzx78Xu6//+B9IvZeRo2CadOsueiTT+xs/osv7FrOzp12\nnWfVKnvOokXJj3PIIXDooXYW36GD1XRKSuy9Fxba2XyjRvYan31m5bdvj10L+u53rdYZfV+11SSa\n7LiJ+zJZpjoaNrQa5KBBsX0LFsCVV5Ytl9h0mU7VyWpBW/AalMsl0bPMkhKrgfzoR6off6y6fXus\nTOLZ7PPPqx5/vJ2tNmqk+swzB5e58UbVzz5TveUW1e99T3XwYCvfooXVUKpa06hf32pk0eNEl4YN\n7Wfv3qrt2qm2bq3atq3ta95ctbDQfoKdcV91Vew9l3fWvnev6pIlqm+9pfrjH6v+/e+qDz2kevfd\nqiNGqM6aZWf0yT6f0lLV3//+4M85vsz+/cnLJEpXzSdo0vW+kpVJVjtLgNegnMsBe/bAAw/Ao49a\nrSTa6+uZZ+xnu3ZWe9myxa55dOpktYDf/ta2O3eGF1+Eo46CuXPLHjs/HwYMsCUq/ux2xw647jqr\nhU2fbr3Vtm+32kj37rbesKFdi4jWahYvjh2rXz8YONAu7M+cefBZc+KZdLIz6/LO7AsKrGZ06KF2\nLe2cc2KPbd4MRx+d/HlgNat6ldwxk5dXeZny4stUjaU2Bb22Vg5PUM7VpmhT3dq11q35wQctUUS1\nbm3df1u3hk2bYhe+wS7cxzvmGJgyxZq2ILUvj3hNmtjrnHiiLVHlJZZdu6yr8tq1MHUq/Pd/x8rM\nnFnxa5Unm81cQU8iucoTlHM56qWX4Pnn7dpM9DoIwPDh1qvqhz+0JDZunPUEW70aliyBe+6xbr0f\nf2w1m3nzLKk88IB9IUSXeOn+ki4stBgPO8yuW9XGa3mCchXwBOVcbdi/35rT7rnHEg9YV+CbbrIm\nusR7gcCaoLp0seWNNypvLkuF11hcDvOhjly4pDIUS3WGa6nKc6ZOtetAEydacurfHy67DK64omyP\nqKhsX9MIwzUWF0qeoFy4VDZ22O7ddhG+ojKpHKe8Mlu2wK23Wnfcli3hwgutM8N998W+5L024lxK\nvInPhYMqPPGE3WdTr57dUd+0KfzznzZaweef27J0qZV/5hm7ttKvn41lVq+eDenSsaOtv/GG9aaL\njkT9/PM2OkF0BIQOHezYQ4ZYzzew7d/8xu7x6dTJalL/+MfBsVYn2XiCcnWQj8Xncl9xsY0MnVgz\nSkak4vHMCgps6JvVq60XWyrH69IFeve2wUK3boU+fSxRduuWG+PjOVfLfCw+lzvSPSLyli02FhvY\nOGo9elgTW0mJ9YIrKrIecSNG2BhmEybY/Tb//rfVit5802o8X31lozUsXGjHio7jNmSIJavhw21c\ntrlzrWfd0qWW7OJHpO7QAc44wx7r1s2Tk3M1UZ27e4O24CNJ5I7SUtXrrrOf8VIZyyyZ2bNt5AJQ\nve22mo9BtmOHjcbw61+XjbG845SUqC5YoPrKKzY+3Y4dqcXtXB1CNUeS8E4SLrOuucZu+GzY0K7x\nfOc78JOfWA3oqadsmoLdu1PrlPDcc3D66Va7GT3aunVX996bqMaNrQdey5ZlR6Qu7zn161vz3ogR\n9rzGjSt/fedcSryJz2VGcbENNPrww7ZdUmI3pC5ZEivzf/8XW2/RwprTevWKLVOmWGLLy7Pk8etf\n2yCnxx0Hf/1rbFDSeH7fj3M5yztJuMwoKYmNH/ftb9v1n9WrbfTqlStjs4bOm2dD/qT6++zWzUbZ\nbtu29mJ3ztWId5JwwXbHHZacevWCYcOsKaxPH1vAOhVER0ooKYHf/Q5OOcUS2XvvWdJasgRatbKO\nDPXr2yCiI0bAX/6SfOgf51xO8wTlat8XX8Att9j6Aw8kH1U6PrkUFFivu9NPtyUqldGynXOhkfFO\nEiLSUkSmiMgOEVkqIj8up9xYESkRkW0isj3ys3tmo3U1VlpqUyeUlNioCsOH+/Uc51xKslGD+guw\nB2gDHAW8IiIfq+q8JGX/rqoXZDQ6l16PPGI989q0gT/9KfXneRJzrs7LaCcJESkENgP9VXVxZN8k\nYJWq3pBQdizQM5UE5Z0kAmrTptjke5Mn202yzrk6p7qdJDLdxNcH2B9NThFzgAHllD9dRL4SkU9F\n5LLaD8+lTXGxzXW0ZYttf/GFXS+qzkjizrk6KdNNfE2ArQn7tgJNk5R9GngAWAcMAZ4Tkc2q+nSy\nA4+Lu1heVFREkTf/ZNdxx1mXcYDzz4fx47Mbj3MuY4qLiylOw8loppv4jgT+o6pN4vZdCXxHVb9f\nyXOvBb6pqj9M8pg38QXN44/DBRfY6Ao/+IEnKOfqsFy5D2oBkC8iPeOa+Y4A5qbwXAWq/AZdFqjC\n//yPrV95pQ3e6pxzVZTxkSRE5Eks2VwCDAJeBo5L7MUnImcAb6nqFhE5GngeuE5Vn0hyTK9BBUlx\nMZxwgo3usHx5bL4k51ydlCudJAAuBwqB9cBk4DJVnSci3xaRbXHlzgUWRfY9CtyeLDm5ALrrLvt5\n+eWenJxz1eZj8bnUpTJn04IF0LcvNGhgY+y1aZOJyJxzAZZLNSiXq1KZAmPMGPs5erQnJ+dcjfhY\nfC41774L06dDfr5NhRFdXnzRbsZt395mmX3lFSv/299mN17nXM7zJj5Xsddesy7iM2dWXrZpU0tS\np5wCr75a+7E553JCdZv4PEHVValcT3rkEfjzn+Hjj20E8kGD4OSTbdqMxYthzx5YtMg6QuzZE3ve\nz35m8zT5FBjOOXLnPigXFIkJKn577Vq70faGG+DAATj0UJg0yZr4Eqe3iE55ceAArF8Pd94JEydm\n4A0458LOE1SuS6UmFG/2bLjxRpg/H776yiYM7NsXnnzSJgf8979t9PGoiy+2m26bNoX9+8s/bl4e\ndOhg5ZxzLg08QeW6GTMOTlDJakdDh8Jll8HDD9scTQD33pv8mPn5VmtauBA6d7YaUXnNdT4FhnOu\nlvg1qFx28cWWcDp3hn79bDnsMOtxd+ut0LGjXTv6zW/ggw/g7bfteZdfblNhtGgBs2bBxo024sOQ\nITYl++jRcNJJPmOtcy4t/BpUXVJcDE89ZckJYNUqW157LVZm0iQoLLSEM28e7NtnTXCPPGIdHXz6\ndOdcwPmNurmoqAhWr7b1Y46x0Rv+8Ac48UQ44gjb36AB7NoFn3xiyal/f6sZNWgQO0Yqr+Occ1ni\nTXy56J13bL6lxo3hF784eCr1aG1oyxa7jvTQQ3D//SAV1LCr2tnCOedS5EMd1SU332w/f/MbGDmy\n/HItWsC3vmVNexUlJ/Dk5JwLHL8GlWuKi+1+pObN4eqroWXLg8t4zzrnXAh4E18uUYVhw+A//4EJ\nE+D3v892RM45Vykf6igE76NSU6faOHetWsGSJdCsWbYjcs65Svk1qLArLY3VmMaM8eTknAs9T1BB\nVlxswws9+aR1H3//feu5d/nl2Y7MOedqnTfxBVVJCYwaBZ9/biOHQ2w6i7FjbdtHC3fO5QAfSSJM\nVq2CM86wgV0BevSA666DCy6A22/3ER+cc3WCJ6iguf9+6z6+c6dtn3UWfOMb0Lt3bBQI55yrAzxB\nBcnYsXDHHTb5X1GR3WR7xx1ly3iTnnOujvBOEkGgamPpTZhgyenii61LeWHhwWU9QTnn6ghPUEHw\nj3/EupDfeSf89a9QUODJyDlXp3kvvmx7/XU45xyb3Ra8h55zLnS8F1+u2rTJklOXLvDTn3oPPeec\ni/AmvmwqLYVbbrH166+HvLzsxuOccwHiNahsevFFm1CwUye46CKb58k55xyQhRqUiLQUkSkiskNE\nlorIjyso+0cR+UpENojIHzMZZ61TtV57YDfhNmjg15yccy5ONpr4/gLsAdoA5wP3iUi/xEIi8nPg\nDOBwYCBwmohcmslAa1Px7bfDxx/bZIL/9V/ZDiclxcXF2Q6hynIxZsjNuD3mzMjFmKsrowlKRAqB\ns4GbVHW3qs4EXgJGJyl+ATBRVdeq6lpgIvCzlF8s8ZeY7JearTKqFE+caOtjxkDDhgeXD6Bc/MfI\nxZghN+P2mDMjF2Ourkxfg+oD7FfVxXH75gDDkpQdEHksvtyAco/84Ydlt5980gZXLW87m2Vmz7be\ne+3awaWhqRQ651xaZTpBNQG2JuzbCjRNoezWyL7kvvnNg/f99a8Vb2e7zDXXJB8twjnnXGZv1BWR\nI4H/qGqTuH1XAt9R1e8nlN0CnKiqH0S2jwLeUNXmSY6bo3fpOudc3ZALN+ouAPJFpGdcM98RwNwk\nZedGHvsgsn1kOeWq9cadc84FW0Y7SajqLuB5YIKIFIrI8VhPvceTFJ8EXCkiHUWkI3Al8EjmonXO\nOZdN2ehmfjlQCKwHJgOXqeo8Efm2iGyLFlLVB4B/Ap8CnwD/VNUkF3acc86FUSgGi3XOORc+Phaf\nc865QMrpBFWVYZOyRUQuF5H3RWSPiDyc8Nh3RWReJP4ZItI1W3HGE5ECEXlIRJaJyFYR+VBETol7\nPKhxPy4iayIxzxeRi+MeC2TMUSLSW0R2i8ikuH3nRX4H20XkeRFpkc0Yo0SkOBLrtkhs8+IeC2TM\nACJyroh8HvkbWBi5Bh7Iv43I57ct7jPeLyL3xD0euJgBRKSbiLwiIpsi/4v/KyL1Io8dKSIfiMjO\nyHfiEZUeUFVzdgGeiiyNgOOBLUC/bMeVEOOZWEeQe4GH4/a3isR7NlAA3AG8k+14I7EVAjcDXSLb\nI4FtQNeAx90PqB9Z7wOsBQYFOea42KcCbwKTItsDIp/58ZHfx2TgqWzHGYntDeDCJPuDHPP3gKXA\ntyLbHSJLLvxtFEY/18h2YGMGXgEeBuoDbbH+A7+KbC8Dfh1ZvyKynV/h8bL9hmr4S9sL9IzbNwm4\nLduxlRPvLQkJ6hLsnrD497ML6JPtWMuJfw5wVq7EDfQF1gCjgh4zcC7w98hJQTRB3Qo8EVemR+Tv\nvXEA4n0DuCjJ/iDHPLOcpBrov41ITD8FFuVCzMDnwClx23cA90VOEFYmlF0OnFTR8XK5ia+8YZPK\nHw4pWMoM5aTWBX8xAYxfRNoBvbH70AIdt4jcKyI7gXlYgvoXAY5ZRJoB44GrgPj7+RJjXgKUYH/3\nQXC7iKwXkf8Tke9E9gUy5kgT0zeBtpGmvRUi8mcRaUiA/zbiXICdfEcFOea7gR+LSCMR6QScCvwb\ni+2ThLKfUEnMuZygqjJsUhDlRPwikg88ATyqqgsIeNyqejkW47exe+5KCHbME4C/qurqhP1BjnkM\nVjvqBPwVeElEehDcmNthzUo/wJofjwSOAm4iuDEDELm2NAx4LG53kGN+i1hT7wrgfVV9kWrGnMsJ\nagfQLGFfM2B7FmKpjsDHLyKCJae9WJsx5EDcat4GugC/IKAxR4b+OhE760wUyJgBVPV9Vd2pqvtU\ndRLWfDaC4Ma8O/Lzz6q6XlU3AXdhMW8nmDFHXYA15y2P2xfIzznyfTEVeBZrdmwNHBKZy69aMedy\ngvp62KS4feUNmxREc7EzOQBEpDHQk2DF/zfsj+xsVT0Q2ZcLcUflY2f6nxHMmL8DdANWiMha4Grg\nByLyAQfH3AO7IL4gG4GmKJAxq+oWYFWyhwj+3/No4NGEfUGN+RCgM3Bv5ORlMzb6z6nY30Zir72B\nVBZzti+q1fCC3JNYT6FCrOq+meD14ssDGgK3Ye3IDSL7WkfiPSuy74/A29mONy7u+4G3gcKE/YGM\nG5sA8xygMXbidTJ2dnZagGNuiPV0ii5/Ap6J/KP3x3pqHR95T48DkwMQc3PgpLi/459EPufeQY05\nEvd4YFbk76Ql1hQ1Lqh/G5GYj4t8to0T9gc55kVYE3Ae0AJrZp+ENbEuxVpiCrCefUsJay++yIfR\nEpiCVR+XAedkO6YkMY4FSoEDccvNkceGYxfzdwKvA12zHW8krq6RmHdF/kG2Y23KPw5q3JF/2mJg\nU+RLcg5xPc2CGHM5fyuT4rbPxXo6bY/8o7cIQIytgfew6websJOY4UGOORJXPnarx2as88z/AAVB\n/tvAThIfLeexoMY8EOvluQkbzu5poHXksejg3zsjPwdWdjwf6sg551wg5fI1KOeccyHmCco551wg\neYJyzjkXSJ6gnHPOBZInKOecc4HkCco551wgeYJyzjkXSJ6gnIsjIk+JyDNVfM47InJHbcUUJCLS\nV0RKRaR/tmNx4ec36rqcIiKl2BhqkuRhBR5T1YtqcPym2P/Ftio8pwWwT1V3Vvd1M0FEngLyVPVH\nNTiGYMMFfaWqpWkLzrkk8rMdgHNV1D5u/XTgwci+aMLafdAzsGlDVHV/ZQdX1SqPCK02GGmdoHZG\nuz7bcbi6wZv4XE5Rmy5hvaqux8bcQ1U3xO3fHtcMNUpEikVkF3CBiLQVkb+LyCoR2Skin4rIefHH\nT2ziizTf3SUid4jIRhFZKyK3JjynTBNfpMwYEfmbiGyLTJB3RcJz+onITBHZLSKficiJIrJPRMqt\n3YjIkSLyRuSY20TkQxE5Lu7xw0XkVRHZLiJfisjjItI68tjt2GC6P4h8NgdE5Oiqvk5iE1/kvZfG\nHTO6fnTk8QYiMjHyme+IlD+hot+xc1GeoFyY3Y7N+9MPm1m3EfAONvz/AOAvwKPxX/LluBBLhkdj\nM99eKyLfr+Q5V2GjZx8J3APcE5n/CRHJA16KHPObwKXYaPfJmi3jPYPNnHpU5Lh/wObqQkQ6A29G\nXnMQNuJ4K2zAViJlXwRexibw6wB8WNXXiYi/LnAqVoNtHznmI9jUFosijz8ZeY8/BA7HBg/9l4j0\nreS9OudNfC7UJqrqSwn77olbv09ETsJG4H67guN8pKq3RdYXi8hlwHexL/zy/FNVH4zGISK/wUag\n/hibAqQLMERVNwKIyLXAjEreTxdgqqpGv/yXxD12BTBTVcdFd4jIRcAaEfmGqn4mInuwa1AbavA6\nZcQ3b4rIBcCPgG+r6qZILev7QIe417xbRE4GLsHmv3KuXJ6gXJiVqSFEai43YVN/d8LmpSkAXq3k\nOJ8kbK/B5m+qyKcVPKcvsCyanCJmVXI8sCkiJovIJdgUC8/GJZHBwFARSbyGpthkdp+lcPxUXicp\nETkWmx7iPFWdE9l9FNZKszjSuSKqANhThXhcHeVNfC6sFJt3Jt5N2BTwtwJF2Pw0r2JfmBXZl+TY\nlf3vVPQcoWwzWUpU9QasafIVYBgwV0R+HHm4HjY32kDsfUWX3sBraXydg4hIV6wpcYKqvhD3UD2g\nBGsmjI+pH3BZVWJydZMnKFeXHA9MUdWnVfVTbEbPPlmIYx7QXURaxe07JpUnqupCVb1HVUdgs0lf\nHHnoIyypLFPVJQnLrkiZEmym05q8ThkiUog1dU5T1f9OePgjbCbVNkliWpdKHK5u8wTlwipZh4MF\nwMkiMkRE+gEPAB0zGxZgNZOVwKRIz7vjsQ4d0Xu8DiIizUTkHhEZJiJdIx07jgXmRorcg3VSeEpE\nvikih4rISSLykIhEm/KXAUeISC8RaRVp8qzq60DZz/YRLOndJCLt4pZ8Vf0Mq1lNFpEzRaR7JLYx\nIjKyWp+cq1M8QbmwSvZFPxa7njQNu7ayDvhHNY5TWZlkz/l6n6oeAM4AmmPTpz8IjMe++Mu7NrMP\nu4Y1CfgC6w03A7gucsyVwHFYc+U07BrY3djU6wcix7gPqzXOxu5lGlzV10ny/oYRqblh19nWRn4e\nFXn8PKwn30RgPlbbOgZYUc77dO5rPpKEcwEgIsdgPQm/oarzsh2Pc0HgCcq5LBCRUcBm7H6hXljP\nuR2qWtk9Wc7VGd7N3LnsaI5dd+oEbASm4/cFOVeG16Ccc84FkneScM45F0ieoJxzzgWSJyjnnHOB\n5AnKOedcIHmCcs45F0j/Hx5xJuIT7n4tAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec2093c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ])\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0, 80, 0, 3])           # not shown\n",
    "save_fig(\"learning_curves_plot\")  # not shown\n",
    "plt.show()                        # not shown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Regularized models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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l6mKExkNZh54AjgOv5pyntU4GXswx/l4p9RdwFUZA5WQoMFtrvTfrGpOBeYgg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\nAkdERERy5/8B9BC3etHWP98AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec293978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.55071465]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.13500145])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.5507201]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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3NaEh7psWuWqV6Q6vKqXMWlt//glRUa7Xx7IERynVCrgPyAGOFi4UpIH7MVs6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\nJEmqjgNHkiRVx4EjSZKq48CRJEnV+QUpU5s1twT9NwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec2f0c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.53788174])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.54333232])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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3rlxqKtxxh00NH0ni4+NRVY5l68WSnJxMjx49qFSpEnFxcbRt25affvopS54F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\nIlmAMsYYE5EsQBljjIlI/x/O4IJF+mxZxQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec274b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n",
    "\n",
    "poly_scaler = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "    ])\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(n_iter=1,\n",
    "                       penalty=None,\n",
    "                       eta0=0.0005,\n",
    "                       warm_start=True,\n",
    "                       learning_rate=\"constant\",\n",
    "                       random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train_predict, y_train))\n",
    "    val_errors.append(mean_squared_error(y_val_predict, y_val))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.base import clone\n",
    "sgd_reg = SGDRegressor(n_iter=1, warm_start=True, penalty=None,\n",
    "                       learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # continues where it left off\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    val_error = mean_squared_error(y_val_predict, y_val)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(sgd_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239, SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.0005,\n",
       "        fit_intercept=True, l1_ratio=0.15, learning_rate='constant',\n",
       "        loss='squared_loss', n_iter=1, penalty=None, power_t=0.25,\n",
       "        random_state=42, shuffle=True, verbose=0, warm_start=True))"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "# ignoring bias term\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[-1, 1], [-0.3, -1], [1, 0.1]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_vs_ridge_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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YLLB21ltlYSd8OloAM9RdSaAO5ZOGdIOQbZ1e67x3rwMq+4DdDXlblGva2GSguApHVr9K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\n8qDj5UBXIUR+uAu2kcUgKsg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jFHq3ZY933xEA4YPOT0D2C1BxHzQdrjyezNRAKeP/8Our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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f6161f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.1, n_iterations = 50):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + 2 * l2 * theta\n",
    "\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 0.5, 0, \"Lasso\"), (1, N2, 0,  0.1, \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * N2**2\n",
    "    \n",
    "    tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
    "    levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
    "    levelsN=np.linspace(0, np.max(N), 10)\n",
    "    \n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(t_init, Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    plt.subplot(221 + i * 2)\n",
    "    plt.grid(True)\n",
    "    plt.axhline(y=0, color='k')\n",
    "    plt.axvline(x=0, color='k')\n",
    "    plt.contourf(t1, t2, J, levels=levelsJ, alpha=0.9)\n",
    "    plt.contour(t1, t2, N, levels=levelsN)\n",
    "    plt.plot(path_J[:, 0], path_J[:, 1], \"w-o\")\n",
    "    plt.plot(path_N[:, 0], path_N[:, 1], \"y-^\")\n",
    "    plt.plot(t1_min, t2_min, \"rs\")\n",
    "    plt.title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    plt.axis([t1a, t1b, t2a, t2b])\n",
    "\n",
    "    plt.subplot(222 + i * 2)\n",
    "    plt.grid(True)\n",
    "    plt.axhline(y=0, color='k')\n",
    "    plt.axvline(x=0, color='k')\n",
    "    plt.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    plt.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    plt.plot(t1r_min, t2r_min, \"rs\")\n",
    "    plt.title(title, fontsize=16)\n",
    "    plt.axis([t1a, t1b, t2a, t2b])\n",
    "\n",
    "for subplot in (221, 223):\n",
    "    plt.subplot(subplot)\n",
    "    plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0)\n",
    "\n",
    "for subplot in (223, 224):\n",
    "    plt.subplot(subplot)\n",
    "    plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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qb+X2zTf+cO8rr8B77yn8iYjEM40AikiNLVjgR/z+/ne/fthhcN99cO21/tCv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\nP99kAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec001eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data', 'target', 'feature_names', 'DESCR', 'target_names']"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris Plants Database\n",
      "====================\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20  0.76     0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "This is a copy of UCI ML iris datasets.\n",
      "http://archive.ics.uci.edu/ml/datasets/Iris\n",
      "\n",
      "The famous Iris database, first used by Sir R.A Fisher\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      "References\n",
      "----------\n",
      "   - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris-Virginica, else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=42, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f40ec186e80>]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p3MdH2z7izU1volB80f4LhtcfbnYk8QAypi+cWqlSsG0blC8Pu3dD27aQkPDAXxO54M6C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\nQV1QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec1867b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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g4CCrV68un3nmGRkeHp6P37jxldX3ZklKTJTy44+lrFJFSm0WHSkDA00dVf7F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\nFjZf8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec0d2278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
    "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.61561562])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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8t3Tnk4PvkJmu4/tmfzC733bCd92moD+AGFuWx3FCfxqcWYVy4dd440T/uUe4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f6117e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris-Virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='multinomial',\n",
       "          n_jobs=1, penalty='l2', random_state=42, solver='lbfgs',\n",
       "          tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n",
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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RwRSPCsEY7qF6StMphZylFk68b8HQRuB/lxaviQ3f2tpqhbhNgWx6M4qsRHeuvTORQbcm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kDaDBOVafZrin1al3LHoh28dPBLWsUWsHRkP57vP4jd3wZhqd2AQ+ESUl+CHAT8evqBLMt/AyYg\noDkXpaCgcHGQJBmTqfaKSEmJBr3eNp2w3RILIeySWchqfYM0yM3RKASszUIUL2SFqxVHgzsD981i\nwepD9E68nx/iFvDUqAh+iXyLKnVZncf6MBk/ZuLJHaeekTFTiFWx7FY97hhT8OFB1Ljb5Qgjq3Tk\nh99N4q27OdpjKe7pa+mwOoQWO59GXZFbPe4c9wshKLs+iKPrhpL280jUuRWEx6wgcOLP6Pbn1zKT\nFaeOEmEfaojdpUXlAPuuM3BglJGSP+z3U3ZyNzJkVgIvHfyS6+9L5uvnOjAnZjg/v9OOKhs95xUu\nDvUlyCoubBBiwo7NfQoKCpcvXboUodNZGD8+jj//9CAlxYmDB53ZutWL2bOj+OUXb8aPP2pTLKsP\nsn1vFkKnRrZxo15jNMjNkSArFWSFfwMqi4ZrUsfy2Nq/uWvr+yS13Mjc20NYd81cihxtc7kRqFHj\ni4R185+BDDJ4FJlKAlh4akwD9goJwcnA/hwa/D0Hb9qCtjyD6M/CCd52H/rCxOph59vEGdp5cOLN\n60lOvAtDiCshQ9YRfPPXOG88CnUkvLpAQfBCq5+y2/USh/5rJL6nkbzPzMgm+659ao3MtWMOM//P\n77nn3T/YvzGAh8NG8uW8ThRlOth/LhSanPoSXQGsEEKc/S6gB/4nhKi+NyHL8i3NsTgFBYXmJTLy\nJO+8s4d58yIYPvxaystVCAEODma6dCliwYIkevXKR5ahvr2uar2wq1EIWGUWlioTttRNZEmLsBhB\ntoCw3YapIY1CbHETUBJk210XbHGDaEpnjaaKdbHdPi72fPYgEIRl9SIsqxc5rof4OWYJz4yKIubI\nUAbunUXLgtg6j3fnVtIYTim/YaYIMNGaz5HQnbs5r4FUekRwpNd7ZHR5Dp+kt2n3fT/KvTqR1WEW\nJwP6n6NTPr2hz+ztQO6ca8ib2Qm3Ncn4z/4NgLxpHSkeE46sr0Wn7CxoMVmF/0SJgm8tZC616pT9\nH1DhN0GF2s321yIEtOuZQ7ueOWSluLDxjUjmdhxGx5uPMWhqIq1iCxt1XhQaTn0J8kc1PLeiORai\noKBwaQgOruCjj3YBYDQKzGZR3XYasCk5hlM+yPZ2pbKjgowQyJIGYTYgq21PGBpSQbbFTUBtURJk\nW10XbHGDaEpnjaaKdbHdPi72fA3FtySUsb+/wS07FvBbxHu8PmQI/kXtGbBvJlFHb0Sq4ea0KwOJ\nIZNc3kFPBA50OOVkYV9yXN94k4MPmXHzyOowG8/UlbT6YxqypCY7ZiYFbccgq3QXbOiT9WqKxkVS\ndHcEzpuO4fXabvzm/UnB/TEUTIzB7FNzRVeoBF7DVXgNV3HyHwuZS8zsetGAz90qWkxRoQ+2L+n3\nDzvJXa/9xYj5u/llWTiLhg0gMKKIG6YmEjMoA8k+e2aFRlJngizL8j0XayEKCgqXFlkGjUZGo5GR\nZetjSbItOQbQNERiYWezEFmlQ7JUYca+BLmpG4WAUkFWUHAyeDBo76P0j5/BP23X8M01T/DltQ/T\nP34G3ZLvQms+N7FU4Yo/s895zp7kuIIk0hiOL9PxYhwSjrWOldV68ttNID/8HlyP/4Rf/CICdzxO\nbuQUciImYdZ7AZxbVRaC0oGtKB3YCl1CPl5L9xAe9QnFt4WSN7Ujhvaetc7n0kXCZYVE1VGZzLfM\n7OtmwK2fRMB0FS5d7ctsnT0N3Dx7P4OnJ/LXmhC+nNeJNY92YdD0RLqPTUPrYLt/vELDUT6PKCgo\nAOcmwkJgd7XCWkG2c06tVWJhKw3RITffJj0lQVZQAFBbtFybchdzvtzF2N/eYl/wN8y9PYRvusyj\nxCG7yebR055W/I8S1rOfYDKYi5F6mvkKQUnQIFKGbCDlxg3oSlKJWRNKq98moys6WD3sfJ1yVZQX\nJ97tT3L8nZj8HGkz4CtaDf8Wpy3H6tYptxKEvKAmLlmLSzdB8p1G4vsYyF9rRjbbqVPWWrjurjSe\n/vs77lzyF7u+CeLhsJGsfTqW4uxLL7u52lESZAUFhSZBrbPPBxlA0qmQDfZ207NPT9ycNm+Ki4WC\nwhkEgnYnrmfK+u+Y9c02SvW5PDW6PZ/0vpcMj/1NEt+F3rTla8L5AzNFJBJFOuMpZ1+9x1d4xpDe\nZzn7/5OESe9N+297EbrhFlxObKlOek8nyqeTZbOfIznzr+VgynhODm1Ni2lbaXvNatw/SULUce1S\nuwoCpqmJS9TS4iEVGYvM7IoykPmmGXOpnXfaBET2y2LGus08tmk9xdkOPB4znPcn9iAj0a3+AAoN\n4qInyEKIKUKIHUKISiHE8nrGzhBCZAohCoUQy4QQmou1TgUFBfuw+iA3wMXCDomFRaU7x+/UFqyb\ngJrJB1mtNApRUKgJ/+J23P7b2zyzOgWvkyG8dtNAlg4ZRELLDXZZutWGnjBa8SZRpKCnHancSAoD\nKeZHZOo2FjY5+nOiywLix6ZT1OpmWv02mYh1XfA89CnCfMa46+yKsuygpvC/0RzacwfZz3bH/dMD\nhId/hPeL/6AqqP06INQC79tUdPhVS/iHGoq3WdgZZiD9cRNVx+0/DwHtSxj/1nZeTFyLd6tSXhp8\nA6/cNID9m1rUVdhWaACXwq4tA1gADAJq9TIRQgwCZgPXA5nAOqyd/eZchDUqKPyrSE93ICCgEq22\n4VdYjV5QVmC/Btli6yY9QFbpkSz2VW0Fers1yLa4CWjMekz/8gqyra4Ll7M7g0Lz4lzpzZDdTzBw\n7yPsCFvJV9c+wpdYdcpdD92Oxty43wE1XvjzOL7MopDVnOBxMngYX2bgyR1ItacZWNSO5EVMJK/9\nvbgd/QG/+EW0/PtRciIfIjdiImadxwXOF0iC0sEhlA4OQb83F6/X9hAW8THFY8LJf6gjhlD3Wudz\nuVai/RqJysMymW+Y2dvZgPsgq07ZOc6+eqWLdxXDntjHkEf2s311G1bO6oqksjBoWhLXjklDo1O6\njzQWYa/JdZNNLMQCIFCW5Qm1/PxT4LAsy0+cetwP+FSW5RY1jJUNhnXNul4FhauZyMj+fP31dsLC\n6m4AUBdb3y4nK9HE6NddbT7m8C2r8JrUBdchYQAsXz6szvERa7twpOfblPtcY/McFeznMGOIpPG3\neM9mZc8HCCiIpm/iA42ONX/+GIqLL0wU3Nwqefrp1Rc9Dthu4dZU2DLfxV6TQtMjI5MUuImfOyzm\nmPcu+iRMoXfiJFwqfZos/kk2k8NiytmBN5PxYTIa/Gw63iFvN/7xi3A7+h35oXeSEzOdKte254yp\nTpZPoc4sw/PtfXgu20959xbkTe9Eec+Aenc4m4pkspebyXzDjL61IGCaCo+bJYRkv+WdLEPCpgDW\nL4nkWLwH/e4/SL/7D+Li/e/+EF8T47XjkWW53pN8OTf8iMJaNT7NXsBXCOEhy7JiDKig0IRotRYq\nKxunuGqQi4X23E56EyZ8XWeSbNUg21tBbkaJRRNt0isu1lNZ+WENPxl/SeKA7RZuTYUt813sNSk0\nPQJBZMZAIjMGcsIjgZ9jFjN/TDidU0fRP34G/kXtGx3flf640p8KkshlCYm0x52R+DIDB6LqPL7C\nuxOHr/8ETVkGvglv0P7rayn160l2h1mU+l1Xo5+yqYUTOc90J/fRLnisOEDg/Zsxu2nJn9aJ4pFt\nQVOz07vaXRA4U02Lh1QUfGXh2PNm0h8z02KqCt+7JVSO9vkpRw88QfTAE2QkuLNhaQSPRo6g623p\nDJqWSIt2JTbHUrByOW/ScwaKz3pcjLVxiculWY6CwtWLTmfBYGhcm1O1tqGNQmyXWFgkXQNcLJrH\n5k1xsVBQaBwBhVHctW0ZT60+iGt5C14d2oc3Bt/EgYDNTaJTdiCCVrxLJMloCSaF/hziRkrYWG98\no1MgGV2fJ35MOiUtBxKy9R4ivu6GR+pqsFg/1J/vfCE7aSi4P4aU/XeSO7crHu/vJ7z9x3i/ugup\nqPZrhaQReI9W0eEPDaHvqSneZNUpH3nShOGE/echMKqICe/+yfPx63Dzq2Bhv8EsGdGPxC3+ik7Z\nDi7nCnIpcPa9WldABk7WNPiZZ1ZVf9+nTzR9+sQ06+IUFK4mdDoLVVWN+7ys1jfAxUKvts/FQq1v\nYAW5GXyQLTqMKmWTnoJCY3Gt9GXozqcYtOdR/gpbweqeD6I2axmwbyZdUsegtmgbFV+DDy14Ej8e\noYCVHGcmIPBjJh6MRUJX67EWjRO5kQ+Q2/5+3I9+i1/8YqtOOWoqee3vxax1u6DxCJLg5M2tOXlz\na/S7cvB+bQ/h7T6i6M725D8Yi7F1zc4TQghcewpce0pUpFjIfMPM7o4GPG+WCJimwinWvmu0m18l\nI+bvZcgj+/lzZRs+mdoNrYOZQdMS6fqfdNTaf4dOOWlrEge2HrD7uMs5QU4AYoEvTj3uCGTXJq+Y\nN2/sxVqXgsJVh05nbnyC3BCJhb0uFpIOYafNW0NaTduC2qyjUlPj53UFBYUGoDU70OvAfVx34L8k\nBm1gU4dXWdvtcfokPEDvxEk4V3k1Kr6EHm8m4MU9nGQjOSziBHOqdcpqvOs4WEVRyHCKQobjmPsP\nfvGvErP6OfLDxpEdPQ2DSwjABfKLyjhfjn90A+rjpXi9uZe2PT6jrHcgedM7UdH9gi1V1TiESbR5\nTSJovkz2/8wkDTPi0F7QYqoKj8H26ZR1jmb63ptC7wkp7FsfyE9LI/lsbmcGPJBE33uTcfY01B/k\nCiaiTwQRfSKqH3/97Nc2HXcpbN5UQgg9oALUQgidEKKme7sfA/8VQkQIITyAucAHF3OtCgr/Fpqi\ngqzRC0x2XmeF7lwNcn00XIOsdNJTULhSkJCIPnYj07/fxEM//Eiu2yHmjQljVc8pZLumNDq+Vad8\nA6GsJ5SNGDhCAuEcZRKVHKz3+HKfLhzut4qEW/ciS2oi1nahzaZROGVvrx5zvp+yqaUz2c9fR3LK\nOMp6BRJ0z0+06fU5rl+kgKn2Sq7GU9DyUWvjEZ87VRybb2ZPrJHs982YK+y8YydBxyEZzF6/kRnr\nNpF5wI1HI27lk+ldyUlV1KvncykqyE8A86FaAHQH8LQQ4gMgEYiQZfm4LMsbhBAvAVsAPdZK8lOX\nYL0KClc9Op2FyspGapAb0ChE6OyzebOodAi7bd50yMKALMt2tbWtj6ZMkN3cKqlpI531+YsfBy6+\nNZst8yl2cf8+WhZ0YNwvH1DsmMmWqDd4eXgP2mZdR//4GYRl9m7037QDUQSzjACeJZe3SaYXjnTD\nj5k407fO+EbnII53e5kTnebhnbycNpvHYnQKICtmJkXBw0GyXlPPripbnLUUPBhLweQYXL9Jw+u1\nPfg//jv5D8ZSeE8UFtea5SSSVuB7pwqfOyRKfpE58ZqZo/NN+N2nwn+SCq2ffechuGMh9y3/ncIT\nDmx6M4IFvYYQ2j2HG2cmENYjpz4Djn8Fl8zmrSlRbN4UFBrH7bd34ZZbMhkzJqPBMdL/NvL59BIe\n+cP226BZ87cgNCr8nuhd/VxdLhbBv95PuVcnciMn2bW23WiJpQSJpkukfm3/Pw77befure83WUwF\nBYW6qVKXsT38YzbHLEFvcKV//Aw6p/0HlaVp+ohZqKCAT8hmMRKO+DIdD0YjYYMO2mLCI30dfvGL\n0FRkkR09jbzwCVi051Znz7eJc/g7C+8lu3HafJyicRHkT4nF2Kr+im7FQQsnlprJ+9yC13CJFlNV\nOEU37E5gVbmK3z4O5aelkTi6GRg0LZEuI9NRa678HPF8bLV5u5xdLBQUFC4SVheLRmqQtTTAxUKN\nxd5OenZqkMHaLKSpZRYas16RWCgoXGR0Jif6JE5m/pokhux6kt/bL+OJsW34KfZlyrVFjY4v4YA3\nE4kkgQAWUMBHJNCaLF7AREE9B6spbHMbB4b9Qdr1n+Kc9TsdVofQ8q/ZaEqPVQ873/2ioqs/x1be\nSOpfo0GWadt1NS3vWI/Djqw6p3NoJ9H2TQ1xiVp0IYLEIUYSbzJQtNGCvcVPnbkqs14AACAASURB\nVKOZ/pMO8vz+tQx9fB9b/hfO7Pa38sOrUZQX/zubGCsJsoKCAnp9E2zS0wu7N+nZ7WKhst/FAppn\no57GrFdcLBQULhESErFHbmHGd5uZvOFrjnvt5Ymxbfisx3RyXdIaHV8g4cYQwthEW76nkkQSCOUY\nD1LJoXqPL/PrTtqAz0gc/g9YTER9FUvrzbfjmLuzesz5OmVjsCtZL/UiOXkcFV39CLp9Pa37foHL\nulQw16FT9hYEzVHTOUWL1ygVhx8xsTfOSPaHZiz2XpMliLvlGI//vIGpn2/h6F5PHgkfyaezriH3\nsLNdsa50lARZQUHh1Ca9JtAg2+1iYd8mvYZokKF5Nuopm/QUFC4PWuXFMWHzCp78Yh8ak54XRnTl\n3YG3ker3R5P4KTvSkRA+JoL9SLiRTHdSGUEpv9Yb3+DamuPdFxE/5jDl3nG03XQr7b7tg3v61yCf\nSXrPrihbXK1NRpKT7ib/wVh8XtlJeNQneL65F6m09p3Qkk7gN05Fx90aQl5Sk/+FmZ1hBo49Z8KY\nZ/95CIkrYNLHv/LMP9+g0Zp5usdNvDGmD4e2N03Xw8sdJUFWUFBoGh9kXcMkFrIdm/QaXkFu+mYh\nSgVZQeHywqOsJSP+foHnVqYTltmbD66/ixeHX8vONp9jEbZfZ2pDSwCBPEcU6bgygCP8l4N0pYDV\nyNT9Qd+sdSO7w8PEj04lN2ISLfY8R/Rn7fBJeBPJWAZcWFFGLVFyWxhpv/6H48sH4rQ1g/Cwj/Cb\n8zvq46W1ziWEwH2gROR3WiJ/0FB1VGZXpIHUB4yUH7Df+9grqJxRz+/i5eQvadcrm3fH92JBrxv5\n+4tgzKardzefkiArKCig05kb3WparWuAxEKnukgaZKWCrKDwb0Fvcqbf/qk8syaZQXseY3P0azwx\nti2bYhZRoWl8y2UVTvgwhUgO4M+T5PEW+2lDNq9gPqcBcA1IagpCx5I07C/S+3yAa8YmYlYFE7hj\nDpqyE9XDzkmWhaC8RwDHPhtC6u+jEJVmQjuvpOW4n9DvzqlzOqdoidB3NXSK16LxEyQMMJI03Ejx\nFvt1yg4uJgZOOcCLCWu5cWYCG9+I4LGoEWxYGkFFydWnU1YSZAUFhabxQW5ooxB7fJAl+32Qofk2\n6SkVZAWFyxdJVtEpfQSPfPMb9238jMN+f/HE7a354tpZFDgfbXR8gYQ7txDONtqylnJ2sZ/WHGM6\nVaTXc7Cg1L8nqTes5cCw7UiGk0R9EUXIlrtxyN97ztCz5RfGNm5kLepN8sFxVMZ4ETzye0IGfoXL\nd4fBUvv1V+snaDVfTVyKFs+hEmnTTOzraiRnhRmLwc7Chkqmy4ijzP1lPfd/vI3U7T48HH4rqx/r\nTP5RJ7tiXc4oCbKCgkKTuFhoHASD59i3icOqQbbTB/kykVgoFWQFhSuH1rlduW/TGuZ8uQsQPDuy\nI8v6j+Gwz99NEt+RzrRmJRHsRaDlAJ1J4zZK+bPeY6vcQjl23evEj06l0iOSsA03Ef59f9yOfl+t\nUz5ffmFx15H3cGcOHrybwglR+C74i7CYFXi8F48oN9Y6l8pB4PdfFR33aGj1jIrcFWZ2hRs4/qIJ\nY4H9OuXQbnk8sHIbT23/DtksmHfNUN66ozdp/zSu6+HlgJIgKygoNMkmPUkluGG2fdUDSa/GYlcn\nPX2DEmSrxKLpXSxMkpIgKyhcSXiVBnPb9ld4bmU6rXOu5X8DR/HKLb3Y3fqrJtIpB9GSl4gmHWd6\nk84dHKQHhXxev05Z70lWx8eIH51GXvg9BPzzJFGfR+Kd9C6Sqbx63DnJskZF8dh2pG4fTcbb/XBZ\nf4R2YR/hO+9P1Jlltc4lJIHHjSqi1muJ+FpDxUGZ3REG0qYZqThkf6LsE1LG2Jf/4ZWUL2lzTR5v\nju3LwusHs/PrICzmK1OnrCTICgoK6PWN1yA3BKFTI9upQZYaoEG2VpCbNkFWm3UY1YrEQkHhSsTB\n6Er/+OksWHWIvvsf4qfYl5g3OpwtUa9Tqa59A5ytqHDBl6lEkYwvD5PDayQQRg5LMFO3DlpWaSkI\nu5OkETs52vMd3I9+T8yqEHwS37pgbLX8QgjKewdy9KubSfvlNlRFVYTFfkrgvZvQxefVOZ9TrETY\ncg0d92hRuQriexs4MNJIyW8N0Cm7Ghk8PZGXkr6i/+QDfP9SDI9GjWDTW+2pKrsUzZsbjpIgKygo\nNEmr6YZgr8RCbmCC3Hyb9JQEWUHhSkYlq+mSNopH123nni2fkBywlSdub83aro9R6HS80fEFajy4\nlXb8RmtWUcqf7Kc1x3kEA/XooIXgZEBfDg36hgNDf6XSPaLGYWdrlAEMYe5kLu1LctJdGELdCBn6\nDSE3rsP5hzTUeUVoj9e8sU/bQhC8QE3nQ1rcb5A4NNHEvh5GclebsRjtS5RVapluo9J58rcfmLj8\nVxI3t2BW6Eg+mxNHYYajXbEuFVdWOq+goNAsNMUmvYYg7JRYWBossdA3i82bokFWULh6aJvdg7Yb\ne5DrksaWmKU8e1ss0UeH0H/fTFrld2p0fCeupQ1rqCKdXJaSRCdcGYQvM3GiS53HVrm3o8q9Xa0/\nPztJPt3K2uzlQO5j15A3Mw73TxNp+fR7CLkKnKso7RrB8WcmIWsvdJ9QOQr871fhd59E4fcWTrxm\n5shcEy0eUOH3XxVqd9slE0JAWI9cwnpsISfVhZ/eiOCJuFvocONxBk9LJLhTPd0JLyFKBVlBQeGS\nJciStgEV5AY0CpEUFwsFBQUb8TnZhlF/LGHBqlQCCmJ4e9AwXh3al33B32LBfh/h89ERQksWEU0a\njnTmMCM5SC+KWIdM43XQF/gpY8F17waqOruRPelWypwH4rIhjaAHV6LKKa81jpAEnkNVRG/S0v5z\nDWV7ZXa1N3B4lonKw/brlH3bnuTOxX/z0sEvCYop5LWR/XjxhhvY/V1LLI0/rU2OkiArKCg0Savp\nhiD09tm8WSvIDZNYNIcG2aSqapJOXQoKCpcfjgZ3Bu2dzbOrU+mdeD/fdX6ap0dHsC3iHQzq2hNL\nW1Hhhh+ziCIVHx4ki4Uk0p5c3sRM7Rvs7KHy/bvx+O5X9ClHOfLydAom9OLoNyM4OagdumOHCY9e\nQcCkn9El1l3JdY6TCP9YQ+w/WiQd7Oth4OAYIyV/2p/ZOrkbGTIrgZcOfknve1JYt6Ajc2OHseV/\n4VSVX3ypX20oCbKCgsKlk1jo1Fjs1iA3zOatqSvIkqxCWFRYJNsTfAUFhSsPlUXDNaljefyrHdy5\n7X/sb/Ujc24PZt01cyl2zGx0fIEaT0bTjr8I5kNOspkEQsjgcQycqD9AXWs3FOP57u+ciHie8jWT\nrPNVVmHydKBodGeSE+7C2NKFkEFrCR76NU6bjkIdG/N0LQXBC9V0Ttbi2ksi5R4j+3oZyPvCjGyy\nr1ig1sh0H3uYp7Z/x92v/8W+HwN5OGwkX87vSFGWvlGvuylQEmQFBYUmsXkDMBtlik6YSdpUxe4v\nK9m7rpJju42UZNecBEs6lX0VZKlhPsjNsUkPQGPRKTILBYV/CQJBWGZvHtjwNY+s+4MKXRFPj4rk\nw77jOO65r0niO3MdbfiSdmzHQilJRJPOXZSzu0ExPQ+tQFiM5EY+AFjlF6pFUah2OmNyd8Hs40Du\nE11JThlH8a2htHj4V9p2WYX7x0mIOooXKhdBiykq4hK0BM5UkfmGmV2RBk4sNWEqsbNhlICIvllM\n+2oLc7espzRfz5wOw3n/vh4c2+fRoNfdFCgJsoKCQpNILMoLLXw0rpinI/L44M5ivnmylDXTTrL0\nhkI+vKuY43svNK+3SizsqyA3NEFu6k16oDQLUVD4t+JXEsbY395kwapU/IsieH3IjSy5aSD7g35s\nEtmVjrYE8TpRpKInhlSGkkw/ivke2Q4dtFPeTopCbq1+rCnPxPX4BoS5kuyspdYnTWZkvZqie6I4\n9kVvKm6R8F2+hnbRS/B5fgeq/Ipa4wuVwGuEiphftISv0HDyL5ld4QbSHzNRddT+8+AfXsK4N7bz\nUtJafNue5NWhA3h5yEDifwqoq7DdLCgJsoKCAlqtpdE+yCsnlSCpBfP2e/NSli/zE71ZeMSHhcd8\nCOmm5dP7SzCe14pa6NRY7PJB1jdwk17zVJC7H7wHyaKYASko/FtxqvJk8J7HeG7lYa5Nvou13R7j\nmf9E82v7/2FQ1Z5Y2ooaD/yZTRRpePNfTjCPRCLJ5V0s1B+/1O86NGUZ1Y+9kj/GKXcHee0nYtG6\nULXsdio/nkDl8nH4/m8tgS9+hKCEojtjEUEpuP+6nvDIj2jx4Ba0yYV1zuXSVaLdpxo6/KVFNsPe\nrgYO3mHk5D/265SdvaoY+lg8Lyd/ybVj0vjs8c7M7TiMrR+EYrhInv3CXhPoyxEhhGwwrLvUy1C4\nCkhPz+K991ZSVVWATufJxIm3ExLif6mX1eykpDgxdGh3DhzY1OAYD3vnMD/RGxffmi9eM92zeTbd\nB0f3Mz+XZZl4/bPElM9FqKzPL18+rNY51BW5RH0ewd676za+P58sXsJELi152a7jFBQUFOxBRuZg\nwBY2dXiVoz476ZU4iT6Jk3Gt8Guy+KVsJYfFlLEdbybiwxQ01Pw+5ZC/l9CfhlPlEoJF7YS27DjZ\n0VPJbzfBOsBiAkmNd9J7eKWupDhoCFmxs9FP+AhRacB79XpKY6Jx+TYHz2X7Kb/Gn/zpHSnrHWjV\nRtSBqUQmZ7mZzDfNaFsKAqar8LxZQqjs76wny5C0xZ/1S6JI3+1Fv4kH6TfpAK4+9hc+xmvHI8ty\nvYtQKsgKCqdIT8/i2Wefol+/bdx663769dvGs88+RXp61qVd2EWgKSQWHi0lDm4xYKiQMRutX4YK\nmfJCC7s+r8Q3XH3B9VQIYe2mZ6PMojGd9JqjgqygoKBwNgJB+xP9eHD998z4dgsljpk8NSqCFb0n\ncsI9sUniu9CXtnxNONswkU8ikRxhAhXEXzC+wiuW+LGHKQ4aQkHbMRwauLY6ORZmA0hq1OVZ+O97\nGafsP3HM3UH0Z+1wekwg67UUDL+eis5tyHnqWg6mjKesrzcBU7bQttsa3D49AMbar91qV0HAdDVx\nSVpaTFaR8ZKZXVEGMt80Yy61X6cc2S+Lmd/8zGM/baAgw5HHokawfFJ3TiS52XcSbZ1TqSArKFiZ\nM2cR/fptw8HhzHMVFbB5c28WLpx56RZ2EcjN1dKhQz8yM9c3OEbyLwY+Gl9My45qgjpq0DkJqkpl\nctPMpGw1MOo1FzqOuHBncoLvy7Q7+CBqD+uJr6uCLMwGOn3gxK57L9Qz10Uu71LOToJ5z74XpaCg\noNBITupz2Rb5Nluj3iIorxMD9s2ifUZ/BPZXUmvCRD65vEMeb6InGl9m4sqgWuP7JL6F0TGQohDr\ntbbF7udwT19Lfthd5ERPw/3wV/jHv8qhgeswOfgA4BdwP66/7kaXfgKjtztFPQbh8X4qupRC8id3\noOC+aCwedTtPyLLMye0yJxaZKfnNgt89KvynqNAFNuw8lOTq2PJuO35+pz0hcfkMmpZIZL/M+grb\nSgVZQcFeqqoKzkmOARwcoKqqbt3V1UBTuFiE99Xy6F+etO+nJT/dTNqfRvLTzbSIVDH7T88ak2M4\n1W7aRh2yLGkQshlk+zRtSgVZQUHhUuFS6cNNu+bx3Mp04tL+w+c9pvPsbbH8Ef4hRqnx1yU1XrRg\nLlEcxpM7OMGjJBFNHu/X6P9udGiBujK3+rFkKqPSPYKcyCkAlAQNRpircMzbBRYTrsfWE/DcCira\nBXP0uSmYfD1xSfiD9PXDOLJ2KLqkAsLbf0yL6VvRphbXuk4hBK7dJdp/rqHDb1rMFbA3zkDKeCOl\nu+3XKbv6VDHsiX28cugLOo84wqczuzLvmqH89nFbjE1gW6rsLlFQOIVO50lFBRdUkHW6S2czc7Fo\nCh/klG0GWnXWcP1UJ7uOs0digRDVThay2qH+8acPUxJkBQWFS4zGrOe6gxPocfAeElv+xM8dFrGu\n6+P0TZhC78TJOFd5NSq+hA4vxuHJ3ZzkZ3JYxAnm4sNkvHkADdZqcFHrEeceZziJWe0EkvrU4xIc\n8/dQ6d4Ofckh/OIXkxsxieOmV2EzVDmNot2Orqjziqjs6EPGBzegzijF6619tOn1GWXXBZA/vRPl\nPVrUqlPWtxW0Waym1TwV2e+bOTDSiL6tIGCaCo8hEkKyvaqs1Vvoc88heo07xP6NAWx4LYovnoyj\n36QD9JuYjLNXw679F72CLITwEEKsFUKUCiEOCyHG1jJuvhDCIIQoEUKcPPX/kIu7WoV/ExMn3s7q\n1f5UnNoYXFEBq1f7M3Hi7Zd2YRcBrdaCySQa1e5zxb3F5KVZK8EWi4wsn/mqC6FVYbGrm579OuTm\nsnlTUFBQsBeBIOr4IKb+sIHp328iz/Uw88aEsbLnZLLdkpskvisDCOUHwtiCgeMkEs4RJlJB0gXj\nS1regNvxH/FIXYN7+jrCf7yBgrZjMLiE4JG6BslSxYkuC6rHO2X/iUEOo/S7GdZ21hYLKmMJ+TMi\nrTrl/kEE3reJNtd9htuaZDDV/sai9hAEPqwm7qAWvwkqji0ws6eDkaz3zJjL7ZMASxJ0GHSCR37Y\nyKzvNpKb5sLsiBF8/FA3spJd7YoFl0CDLIRYderbCUAc8D3QXZblpPPGzQfayrJ8tw0xFQ2yQpNw\nxsWiEJ3O41/jYgHg4nIzOTk/4ODQiCy5ASTHvUvQB8NwiLWe57o0yACxK/xIuHUvJkfb/12K+YFc\nXieUHxu1VgUFBYXmoMQhm1+i3uTXyHcIyenGgL2zCM/s02Q6ZSM55PE2ubyFI53xZSYunNFBux/+\nihZ7X6DKpTUmvQ9HeywFWSZmTSgnOs8nP3w8AKqqIgL+eRKBhaPXvYlz5lZ8E95Ar9+J7mgWBcP7\nkv3gaDBbcPnuMN5L96A5cpL8KR0onBCFxU1X5zplWaZkm8yJ18yc/MuC/70q/Cer0Po37DwUZTrw\n8zvt2Pp+OG275jJoeiIvDLjRJg3yRU2QhRCOQCEQKcty6qnnPgaOy7I857yxSoKscNlyNdrB+fgM\nISXlJ9zdG9Y62WKRkS2gUl943bFYZAxlMlongXTerbOU7ssIXHojjtcEAvUnyDErW3Fw6K8YXIJt\nXlsJP5PFc4Sz2eZjFBQUFC42BlUFf4V/wqaYRWhNjvSPn0GX1NGoLdomiW+hkgJWkMNiBGp8mYEH\nY5GwJq7CVFEtX3M78i0hv97H3juzrD5rQuB5aBWeqSvJjZhMpVs4IVvHU+EVS3b0DMxaV8J/HET2\nvAGUdY2unlO/Mxvvxbtx3niUorsjyJ8SizGk/opuRbKFE6+byVtjwfMWiYCpKpw6NEz4UFWu4vcV\nbflpaSRZye6X5Sa9cMB0Ojk+xV4gqpbxQ4UQeUKIeCHEpOZfnoJC/VytdnA6nZnKyoZv1Pvh6TJ+\neKaMiuIzFWizyfoBvKpUZtMr5eQfvlBrbG+zkIZ005PQN4sG2SxMFDmeIClwEztbf8GekHUc9dpN\niUN2k8+loKBw9aM1O9AraSLzP0vklh3Psj38I54c25YNsS9SpitodHwJPd7cSwT7CeBFClhJAm3I\n5DlM5COrzmymrnRvT4V7JKrKAhACx9x/cE//kirXUIpbDSFo+wwqPSLJ6jCbKrdQTHpvDE5BiM9D\nqVw+jsr3rfXNys5+HF8xmNR/xiKrBG2vXUPQmB9x+Kvu90yHcIm2r2uIS9LiECpIHGok4UYDhRss\n9Ur3zkfnaKbfxGQW7rO9mHqxE2Rn4PwtjsWASw1j1wARgA8wEZgnhBjdvMtTUKif995byZgxWdWb\n+RwcYMwYa0X5Skavb1w3veRfDLSMVePgJmExWy9eO1ZWkpNiwsFVIvGnKgqOXJggS3a2m7ao9A3U\nINvvn1wXZdpCPuh3J0+OCWXZgNGs6/Y4q3o+wOKh1/N+/7Ec99zXpPMpKCj8e5CQiDk2hOnfb2Ly\n+m844ZnAk2NCWX3dQ+S4Hmp0fIHAjcGE8RNt+ZEqDpFAKEfFFCqx6qCNDn4gJNr90B/f+CWErb8R\no2MAmbGP4nb0e7SlR8iNmHTmbp6QkIwnURtOpXlCWDXKpzAGuZD9Qk+SU8ZRfl0Lgu7aQJven+P6\n1SEw1y7t03gJWj6mpnOKFp+xKo7MMbGno5Hs5WYslfbrlG3lYrtYlALn19VdgZPnD5Rl+cBZD/8U\nQrwG3IY1cb6AZ55ZVf19nz7R9OkT0+jFKijUxNVqB6fVNs7qzWSQUWms38sWQAWbl5Sjc3LCN8x6\nqamqwRzeHps3ALkBCbLV5q1pE+QVfe5Dbdbx9JqDeJYFVT9vVFXyfdwCPu47gUfW/Y7GUrfmTkFB\nQaEuWuV34p4tH1PkeIJfot/gpeHdCc3qRf99MwjN6tlonbIjHQjhA4w8Ty5vkExPnOiOr3YmB2/a\nSIvdz6MtzyCjy3PkRUwE2YJ7+jqKWt1ClWvb6jguGZtwzv6D1IFrz4l/OknWT/gIAIuLlvyHOpL/\nQAdc16XhvWQ3/o//Tv6DsRSOj8TiUrOcRNIKfO9W4XOXRPEWmRNLzBydb8LvPhX+k1RofWs+D0lb\nkziw9UCNP6uLi50gJwNqIUTbs2QWsUCCDcfKUPtvwbx5NZphKCg0OVerHZxeb25UBdmjpYrsZDMW\ni4ykBkO5TFWZTF6aGZNBRqMXqHUX/gkLndpuFwt7JRaiGSQWSYEbeWZ1Cq6Vvuc8rzHrGb7jOTbH\nLMGorkBjUBJkBQWFxuNeHsDwvxdy4665/Bn+EZ/0+S8OBncG7ptFp8O3orJoGhVfgz8BPIs/c8jn\nY45yPxJOFHaahQePIDhTAVFXFWB09MesPdPFLvj3KeREPYhZ516tWT6b8xNlVBIlI0MpGRmKw19Z\neC/Zjc9zOygcH0HBlFiMQTWJC6x+yu79BO79JMqTLGQuNbM72oDXrVadsmPkue9jEX0iiOgTUf34\n62e/tul8XFSJhSzL5cBXwDNCCEchxHXALcAn548VQtwihHA/9X1XYCqg7MRTuORcrXZwOp0Fg6Hh\nl4Sud+rZsbKSrx4+yY5PK/ljeQXerVXs/KySxdcXENhBTUDMhZ/JJZ3KLomFrNIhLPZrkJtaYuFZ\nFsTBwM0YVBWYJSNmyYhBVUGZtpB/2nyGX1G7JtuBrqCgoHAancmJvokP8NSaA9y4ew5bI9/iiTFt\n+anDK1Roa2/UYSsSjvgwiUgSacFT5LGM/bQhi5cwUQSSGqODLxa1MwCasgwC/3oUYa4k45qF1iB1\ntLOrXD6u+us0Fd38ObbqRlK3j0aYZNp2WUXLuzag31n3fg7HCIm2b2uIS9CiCxIkDDKSeIuRop/t\n1ymfz6VoFDIFWA7kAHnAJFmWk4QQPYEfZFk+LcEYAywXQmiB48DzsiyvuATrVbiENKVbxBdfbOXV\nV9/CxcXIyZMaZs16gNtu62P3fCEh/owfP4WFC19HoynFaHRmzpwpDVrX5eSGYdUgN0xiIcsyscP0\nIMO2dys4tsfEsOec6fugI9s/rqA010L3exxw8rwwARc6NbLBTg2yyX4NclNXkEf//jrL+93J32Er\nCMqLQ2d0okpTSo7bIZJb/MLY397CweBWfyAFBQWFBiAh0TF9OB3Th3PEeyebOrzK3LGtuTZ5HP3i\np+FdGtKo+AIJd4bizlDK2U0Oi0igDZ7ciT6kOxEbJ+Oc/RuqqiKEbCKt/+fIKl2N1ePaOL+qbAxx\nJeuVXuQ82RWP5Qm0GvUDxhBX8qZ14uRNIaCquYij8REEzVUTOEtF7moLh2eaEGoImKbCe7SEVMPd\ny3pf/8X2QW4OFJu3q5PTbhGnN8SdrtQ+8cRTdieRX3yxlQ8+WMyMGVTHWrwY7rlnRnWSbOt8TbWu\npnx9TcHgwT14+OEUBgzIrX+wjZiNMirNmQuTLMuI8y6cxx/8AX20L96TugD127y13Xgr+aF3UNR6\npO3roIR4WtKREjtWXz8lDtnsCF3FUe+dVGhL0Btd8C+MoPvB8XiUBzbpXAoKCgr1UeB0jC0xS/mj\n3XLCT1zPwL0P0ybn2iaLbyCDXF4nj2W4G7rTMTEIs8dgKj1jrZv17EiOa6JafnEaoxm3r1Lxem03\nqqIq8h/qSOHdEchOdctJZFmm6CeZzKUmyvbLtJikwm+iCo2XYLx2/OXng9xcKAny1cmcOYvo12/b\nBVrfzZt7s3DhTLtide8+mgULqi6I9eSTOv78c41d8zXVupry9TUFw4d3495707n55sZZlOWlmTi6\ny0RxpgVkGSdPCf9INS0i1Wj0F16TTszagKaVGz7TrBfx+hLk1pvHUtxqKAWhtktaLFSxFxc6YbDv\nxdRBcoutBOd2QWeyr7W2goKCQnNTqTnJH+0+4OeYxbiVt6B//Aw6Hh6BSm4a4YCZUvL5kBwWo8Yb\nX2biwUiEncIEr+SPkEzl5IePw6J2POdn5yTLsozjH5l4L96N4x8nKJwQRf4DHTAFONc7R1m8Vaec\n/7UF71ESC96777L0QVZQsJmmdItwcTHWGMvZ2Wj3fE21rsvNDcPqYtHwS4LFLPPNk6UsjMvnmydK\n2f9DFft/NPDjwjLeGFLIplfLqCqrwcVCa68GWd+ATXpaZGFEpum6BH7Udzx5rmkAWLAgI2M59Z/M\nlV94UFBQuHLRG13ot38qC1YfYsC+Wfwcs4T5Y8L5OWYJlZoLjMPsRoUzvjxIFMn48zh5vEkCoWTz\nKmY77tRVurXD9fgGYlYFE7hjLpryzDM/O0ujjBCUXxfA0S9uIm3bf5BKjYR2WkngPT+h31P3XU+n\nGInQ/2notE+Lxsv26val0CArKNhEU7pFnDypoaLiwgpyaemZ2zS2ztdU67rc3DCsLhYNt3n75Y1y\nDm83MGubJ4Edzr39lRFvZNXkk7i1kOgx4dwqgdCpke1xsZB0DfBBFghZ6KjdTQAAHXlJREFUh4wB\ngb7+A2zguVWHq7+XTtUalE15CgoKlxOSrCLu8EjiDo8kzXc7mzos4oe4BfQ4OIHr9z+EZ2mrRsUX\nqHBnOO4Mp4wd5LCI/SzEi3H4MA0ddXc8LfO7ltQb1qErTsFv/xKiPo+kKHgY2TEzqfDqcE6SfLqi\nbAh1J3NJH7Lnd8NzWQLBI76lKtyDvGkdKR0cAtL/27vv8Cir7IHj3zOTySQhEJIAoQkB6U1EyqoU\naYKoiCsqiii7sgryQwWxYUFEcVUEO4p91+7qKigWiqLgqoAgoRcDSEuAEAglbeb+/phJnDQyk3mT\nCcn5PI+PZubOfc+88gxnbs49t/jP4fD6QpNpYfCYf+9NV5BVpWVlt4g77riF2bMpMNfs2Z7HA72e\nVXFVtm4YwXax2LchlzO6OGjUyVFk93Cjjg4S2thJ3Vr8QSGBnqQXaIIM5XNYiO9KcY49k8NRe0it\ntY30qL2WXkcppYLVPPUv3LToQ+79eBVucfHIFZ15rd+17Ki7wpL5a9CNZrxHW1YDNjbRhd+5muP8\nVOprs2Jasuv8F0i6ejuZMa1o+dVgWi0YSK0/vvQ21i/a/cIdG8HBO89hy+YbOHx9WxIe+pmWnd4m\n9pV1yEn//04pidYgq0rtzy4Ph3E6Yy3pYhEdncOxY6V1sTj19ayKy8r3F6z/+79OtG+fwbhxyaUP\nLsbCmcfZvjybvz5Rk/hmdnKzwLgNxsCuVbksnHmcbiMi6DGqYF3Jgdn/I2dPBg1nXgiUXoPc6Oe7\ncTlj2d/5noDiW0s92rIWB9bc36QmX1AjM57E1O64bbl82v1eVp35Ibn2LOIyErnsl0dpt2egJddS\nSimrnQhP58fWr7Ok47PEZzSl/9pJdNp1CTZT9t8k+nJxlEO8QSpP46Ah9biD2lyGUPr84som9vcP\nqL/2KcSdTUrHiRxqcR0mrODfH4XrlGt8v4f42auJWpFC2j86kDa2I7n1C+4T8XeTnpZYqEpt9+4D\nrFmzKb+d2u7dB4pNIP1p4da1a2v69u2R31Kta9fWReZJTKwf4Aa54L5gBn698hMREVwNcu+xkRzY\n7uKp3mm07B1OzQQbxg1H9rrZ9WsO3a6JoNu1RcsbJCKwEgsTFngNMngOC3Fb2Ortq86P0Xf9BJqn\n/oV550xjb9w6/r74XZoc7MKyNq/yedepxJysT6M0PdVTKVX5RGXXZkDSJPquu5XVzT/mq7Nn8PG5\nk+mfdDvnbh4d9AZkO7Wox23UZTzp/JdUZrKHO6nH7cTzN+yUvMHO2MNJazmKtBbXUXPvtyQkzaLR\nyvs50HYcqe1uITfSc0BTgTZxIhzv05jjfRoTvvkw8c+toWWndzg67EwO3tqZrA7xAcWvCbKqtJYt\nS+KJJx5i0iSXtw3aCZ544iHgIXr2/DPpyGvhNn16Xgu3LGbPng1wyhZujzyypUwt1aycqzIJdpOe\nM9rGtXNq0XdCFBsXZpGR6sZmFxqfFcbwWTWJTyx+1cBzkl4AfZBtTuw5gW8ysRFh6XHTOWGZ4F2E\n2NLwOwavvpeW+3vhxk3/dbex6swPOFgzWRNkpVSlZjdhdN1+Nedsv4pt9ZexuNNs5p8zlV6bbqLP\nuvFBt6wUwojlSmK5kmP8j1SeYh/TqMON1GUC4TQ+xYuFjEb9yGjUj4jDG0lYN5sOH7bmcLMrSOkw\nkcy49kDRfsrZrWPZ93xfUqf9hbi560gc8imZHetw6LbOfsetNciq0pox4zluvdWVv4ktMhJuvdXF\njBnPFRj31FMv5vc3zhs3caLn8Txz576bn9DmjRkxwlPeECgr56pMnE5XUAlynoQ2dnqNjWLwlGgG\nTI6iy5URRNcteV5buD2wFeQyHDUNeTXI1q0gn3GwM8kJntq6+ultSI3ZSnbYCVy2HA5F78Rly8Hh\nsmZDoFJKlTdBaLm/F2O/+YR7Pv2ZTEcG06/syOv9ruOP+DWWXCOac2nOf2jDCtxksZFOJHMtJ1hV\n6mszY9uys9dc1l21hezoJrRe0J+WXw6m1u6Fnv7LUOSEPld8JAfu7caWraM5cnUr6t+z3O9YdQVZ\nVVoOx7Fi26A5HMcLPGZlCzd/VLb2bFZxOt1kZAT3kZC+x8X/3jzJxoXZZKS6MQaiaguNOzvoenUE\nrS4IL/IaiQjDBLBJz22PwBbgUdMANotP0xu6cjqvDLiaZ4cMpvWevnzfbg7rmiygecq5/Jb4GS32\n96Tpga6WXU8ppSpK3aNnMmL5cwxdMZ0f2s7lhcGXkHCkFQPW3kH7XRfld+4pKyfNOIOnacg0DvIq\n2xmGk+bUYxIxXIqcYv7cyLrs6/Ig+zvdRdz29zjjp4kYsZHSYSJpLa7F2J1Ful8Yp53069uSPqoN\nOL/xK0ZdQVaVVk5OdH6HhzwnT0JOTsG6KE8Lt6LjimvhVnhMWVqqWTlXZRJsF4uDyS7eHXeU9V9l\n03tsJKNeq8Xf/h3DJQ9F48o2fHxHBmvnFy1xEKc9oBILY3ciAR41DZ4aZCsT5JgTDbj1i69p/8dg\nfkuchxHDoZrJbGn4HT03jmH4/56iRlacZddTSqmKFpVdm0G/3cUj7/3OeZtuZF7XB5h2VTu+b/sS\n2faTpU9QCjsxJHAHHfidOoxlP4+wgTYc4EXcnDjla01YBIda/431VySxu/uTxG1/n47vJdLg1+mE\nZR7MH1dgVTmAU/40QVaV1pQpE3j2WXuBNmjPPmtnypQJBcZZ2cLNH5WtPZtVnE43WVll3728dWk2\nuZmGyT/E0XVEJM3PDadpVwftBjkZ9VoM3UZGsPy1oh+oNmcYJjuAGmS7s8wryFaWWACEuyLpn3Q7\nd322nOnvb2X6+9uYPO97+q6fgMMVoQeGKKWqhDB3OD22jWTKJ6u49oeXSGr6BfeNbMpn3e7nSOT+\noOcXHMRxDa35haa8xlG+YR1N2cMUsimlbaYIR88YxNYhX7NlyEKcGcl0+KAlTX4YizN9c/6wwuUX\npdESCxWQP9uSeTpBBNOWbNmyJGbMeC6/Q8WUKRMKbL7r2bMjn312IZMnf0lcHKSlwcCBFxYYA56N\neM899ymTJyfnj4uJaVagi0ViYn3s9tZMnryf+Hg4dAh69GhdJPZHH32H//zno/x5hg+/kvvuG1lg\nTGJifUaPHu+N/Tg5OTWYMmV8kG3egr+fwfIkyGX/ziw2cJ8iz808YgiPLPrtXZwB1iDbyl6DbOUm\nvTwHav7OrrqrOFxjN0bc1DxZlwaH29PwcHutQVZKVSmC0HrfBbTedwEpMVtY3PFppl3Vjs47Lqd/\n0u1Bb0oWhGh6EU0vMtnGAZ5hIx2I4VLqMYkozjrl6zPjOrCjz+uEdZtBvQ0v0mZ+L47X60FKx0lk\nNLggoBVkTZCV36zs3uBPh4o5c+axYcOXzJxJ/vVmz/6SOXMaMG7c0Py5Ro6cQXR0Mg884DsumZEj\nZ/DOO1MAuPPOl9m9e2mhuZZy551RPPnkzYAnOf7xx4948knfMR/x6KMUSJJ37NjPm2++wKRJqd5x\nx3nzzRdo3Diw+1DZumEEu0mvaVcHK97L5K3RR+h1cyTRdbxt3va7WfdFFjt+yWHQPUXbBkmAB4W4\nwyKCOCjEuhVkt7iY1+0BlnR4hlon6lMnozkAadE7OR5xiP5rJ9I/aWLQrZKUUqoySjjSimuXvcjQ\nlQ/zfduXeXbIIBqldaT/2km0231h0CeLRtCCM3iOBkzjIHPZzhAiaEs9JlGLwaeuU46qz96uD7Ov\n873Eb3ubJstvwW2PJKWj/21V9aAQ5bcpU2bRr9/3RY5GXrKkd8C9fIcMuSk/wfSda9aseixYMBeA\nc875K48/7i4y5u67baxa9Un+Y507D8tPfH3HTZ4Ma9Z86veYs88elp8c+465805YvfrPP19W3Qcr\n76cVPvqoIR9/3JD3319Z5jnSdrqY/+Ax1n+VRfYJgwg4IoWm3RwMursGLXqFY4xBfL7Fn1y9jz/G\nzKPVqpsLzFXSgSG1/via+kkz2TJkYUCxJXMNMVxKHNaUwizqOJu1Tedx1Y/P0DitU4Hn9sQl8Xbv\nf3D+pjH03DTGkusppVRllmPLYkWL91jcaTYGN/2Tbqf7tpGW/SbNTTaH+YBUZmHIoh63E8cobESW\n/mLjJuaPL0lImkW/+Uv0oBBlLSu7N/jToaJ2bXexY2rXdhd4LD6eYsfFxQU2Ji6u+DGxhfbeWXUf\nKls3jIgIN5mZwZ2gFNfUzg1vxQDgyjG4XeCI+PNzqHByDHkHhQRQgxzUQSHWlVjsjVtH04NdaZzW\nCYMpsFrSKK0jCemtOVBrm2XXU0qpyszhdnLeltGcu+UGNjZaxOJOs/ms+330WT+e3hvGUjOzblDz\n2wgnnlHEcR3H+JYUZrOXB6jDWOpyCw4SSn6x2DjS5GKONLkY5vu3sq2b9JTfrOze4E+HivR0W7Fj\n0tML/rE9dIhix6WlBTYmLa34MYcL5atW3YfK1g3D6XQF1cXClzEGu0NwRAjGGNxuz2+qCifH4D0o\nJIBNemWtQba6zVtCeitSYraQUmsrbnGRFXacTEcGJx1H2dRwCUei9tHgcHvLrqeUUqcDQWi3ZyAT\nvlzA7fOXkBa9i6kjWvF275vYV3ujJfPXpB8tmE8rlpLLfjbQlp3cyEnWW/AOPDRBVn6zsnuDPx0q\nxowZXWx3ijFjRheYq3377sWOa9++e/6YgQMvKnbMwIEX5Y8ZPvzKYscMH35ludyHytYNI9hNer58\nE2ERwWYr+Ru7LcCjpj01yGXdpGddgtxn/XhqnqzHE8PO5dUBI/jkL3fxSY+7eKPfdbzRbxRNDnah\n+7bTu7OJUkoFo2F6O0Z9/woPvb+Z2scbMevSC3h+8MVsarTYki4/EbShCS/Tni2E04ytDGAbgznK\nwqDn1xpkFZA/uy4cxumMLbHrgj/dGf7sYpHXCWJCkQ4Vc+bM49VX36R2bTfp6TbGjBldYINenmHD\nHmTHjrX53ScSEzvx6acPFxgzaNDdpKRszh+TkNCar79+vMCYvC4WsbGelePiulgEch9KY9U8Vvjp\np1gmT+7AsmU/VOh1cw+dYHO7F2ifcmeBx0uqQY44vJEzF17O+qs2BXSdPdyNnVjqc0+ZYy3O3tj1\nbGj8DRmRqdiMndhjZ9D+j8HEH2tq6XWUUup0l2PP5OeWb7Oo0yzsbgcDf7uDrttHEOYueohUWbjJ\n4jDvksIsABKYRCzXYsOZP2bsWPGrBlkTZGW54rozvP9+/XLrzuDP9ebMmcfnn7+efyR13urwJZf8\nvdiEuzpavTqGm27qzIoVSyv0uq5j2WxoPIuO6QUT15IS5PCjv9P6i/4kXZMc0HX28iCCnQZMLXOs\nxXHjxmXLwW3LxS0ujLixux3avUIppUpgMGxo/A0Lz5rJvtgN9Fl/C703jCU6K96y+TNYRAozOcla\n6nILdRlHGHX8TpC1xEJZbu7cd/OTVfAkpCNGeFZKQ3W9V199Mz85zhszcaLnceUR7EEhZWULtA+y\n3YmU4aAQq9u8ARyO2sOXXR7h6Uv688jwzsy4ogvPXHwhH503kc0Nv7X0WkopVVUIQvvdg7j9i4Xc\nuuArDsRs48FrWvBuz1tIqbXVkvlrMZCWfE1LFpHNTtbTkl2M9XsOTZCV5Sq6O4M/1/O3I0Z1Fmwf\n5DybFmdxMNn/TXeE2cCAyfXv/4XbXrY+yFZv0jtYM5m3+4xh/RlfccH68dzw7ZvcuPg9Ll05jVxb\nNh+dO5G1Tedbdj2llKqKGqV15Ibv3mDqhxuIzoznyWHn8eKgoWxpsNSSOuVI2tOUV2nHJsJO1emi\nEG3zpiyX152hcH/f8urO4M/1PB0xivZULtwRozqzapPe8ldOcvYVEdRp5t9qtIjkn6YnYaXXoRl7\nWU/Ss7bN26ZGi3HZcrjrsx+LPNfhj4v4+qwnWNbmFTrtvNSyayqlVFUVc6IBQ1dOZ/Cae/mp5b94\np/dNOHNq0n/tRLr+fhV2tyOo+R0k0JBpwMOljoUQrCCLSKyI/FdEjolIsohcc4qxj4vIQRE5ICKP\nlzROVS4V3Z3Bn+v52xGjOnM6g++DDBAWIeRkBvat3+b0/zQ9Y3cGsYJsXYJsM3ZctpJjznJk4HD5\n0cBeKaVUvvDcKHpvHMvUDzZyyaqp/NjmNe67phnfnPUkJ8LTKyyOUKwgvwhkAnWBLsAXIrLGGFOg\nOZ6I3AwMBfLaGiwSke3GmLkVGq0q1tKlSfTpU/yZ64mJng1yvt0Z7r+//Loz+HO9vI14d99dekeM\nyuxU9z1YERHWrCA7IoTc7MAS5EAOCzHi/dhy54LN/48wzwpy4CvPmzd/R+vWFxR5PDG1O7+0eIc3\n+o6iz/rx1MiMBzEcidrH2qbzSK73M0NW3x/w9VTJ91yVH73noaH3vWQ2bHTaeSmddl7Krjq/sqjT\nLO6/pjk9to6iX9Jt1M1oXq7Xr9AEWUSigL8C7YwxJ4HlIjIPGAVMKTT8euApY8w+72ufAsYAmiBX\nAkuXrjtlopaYWL9Cj0v253rjxg097RLiwkq778GwqgY5zAk5AS7USiC9kEW8dchZuANIkMtag7xl\nS/F/gTU83J7rlr7KZ93v4/mLhpAddgJBcORGknigG8NWzKDlvt5FTtlTpSvpnqvyo/c8NPS++6fJ\nwS78fcnbHK6xm+/aP88/L+9Oq3196L92EmemnFcun7EVvYLcCsg1xmz3eew3oHcxY9t7n/Mdp8dS\nKVVOHA6DyyW4XGAPotIizCnkZgVYYhFu97vEAvLqkDPB4X8rNasPCgGocyyRG5e8A+Bp9SYuHK6I\nP+PU5FgppSwTe7wxl//yT4b8+gA/tn6dt/reQI3MeAaunUzn5MuxG+vS2oquQY4GjhR67AhQ04+x\nR7yPKaXKgQj06HGYnJzgPhbiE+3UiA9sjoizEpAw/19zvE43JMDdzWHUJZzyObzDYLC7HThcERgM\nbjwdOTQ5Vkop6zlza9B3/QSmfbCZwWvuZUmHZ3hi2LmWdL3IU6EHhYhIZ2CZMSba57FJQB9jzGWF\nxqYDA4wxK70/dwG+NcbEFDPv6X/aiVJKKaWUKnf+HBRS0SUWW4AwETnTp8ziLGB9MWPXe59b6f25\ncwnj/HqjSimllFJK+aNCSyyMMSeAT4CHRSRKRM7H06ni38UM/xcwSUQaikhDYBLwRsVFq5RSSiml\nqqNQnJIwHogCUoF3gLHGmI0i0lNEjuYNMsa8DMwHkoC1wHxjzCshiFcppZRSSlUjFVqDrJRSSiml\nVGWn5+wqpZRSSinl47ROkAM5tlpZQ0TGi8gKEckUkddDHU91ICLhIvKqiOwQkSMiskpEBoc6rqpO\nRP4tInu993yTiNwY6piqCxFpKSInReRfoY6lqhOR77z3+qiIZIjIxtJfpawgIiNEZIM3h9nq3Zel\nyoH3z/ZRnz/nuSLyzKleE4qjpq3k17HVylJ7gOnAICAyxLFUF2HALqCXMeYPEbkY+FBEOhhjdoU4\ntqpsBvB3Y0yOiLQClorIr8aY1aEOrBp4Hvgl1EFUEwa4xRijm+ArkIgMBB4DrjLGrBCRBqGOqSoz\nxuSft+E91Xk/8OGpXnPariD7HFt9vzHmpDFmOZB3bLUqJ8aYT40x84C0UMdSXRhjThhjHjbG/OH9\n+QsgGTgntJFVbcaYjcaYHO+PgieRODOEIVULIjICOAwsDnUs1Yi2Sq14DwEPG2NWABhj9hlj9oU2\npGrjSiDVmzeW6LRNkCn52Go9jlpVaSKSALSkhL7gyjoi8oKIHAc2AnuBBSEOqUoTkVrANOAONGmr\nSI+JSKqI/CAifUIdTFUnIjagK1DPW1qxS0SeExFnqGOrJq7H00r4lE7nBDmQY6uVqhJEJAx4G3jT\nGLMl1PFUdcaY8Xg+a3ri6eGeFdqIqryHgVeMMXtCHUg1chfQHGgEvALMF5FmoQ2pyksAHMAVwPl4\nDkI7G7g/lEFVByLSBOgNvFXa2NM5QT4G1Cr0WC0gIwSxKFXuRETwJMdZwIQQh1NtGI8fgTOAcaGO\np6oSkc7AAODpUMdSnRhjVhhjjhtjcowx/wKWA0NCHVcVd9L772eNManGmDRgFnrfK8L1wDJjzM7S\nBp7Om/QCObZaqargNaAOMMQY4wp1MNVQGFqDXJ76AE2BXd4vg9GAXUTaGWO6hja0asWg5S3lyhiT\nLiK7Qx1HNTUKzwbsUp22K8gBHlutLCIidhGJAOx4vqA4RcQe6riqOhF5CWgDDDXGZIc6nqpOROqK\nyNUiUkNEbCIyCBiBbhwrTy/j+QLSGc9ix0vA58CFoQyqKhORGBG5MO9zXERGAr2Ar0MdWzXwBjDB\n+1kTC9yO5/RgVU5E5DygIfAff8afzivI4Dm2+nU8x1YfxHtsdWhDqvLuB6biWWUAGIlnU83DIYuo\nivPWTN2Ep6VhimdxDQPcbIx5L5SxVWEGTznFHDwLCTuB24wxn4c0qirMGJOJ5884ACJyDMj0/vpZ\nlQ8H8AjQGnABm4DLjDFbQxpV9TAdz28Et+ApufgAP1c2VZldD3xsjDnuz2A9aloppZRSSikfp22J\nhVJKKaWUUuVBE2SllFJKKaV8aIKslFJKKaWUD02QlVJKKaWU8qEJslJKKaWUUj40QVZKKaWUUsqH\nJshKKaWUUkr50ARZKaVOIyJyg4hklDImWUQmVVRMpyIiTUXELSJdQh2LUkr5SxNkpZQKkIi84U36\nXCKSLSLbReRJEYkKcI55ZQyhUp7wdIr3VCnjVUqpkpzuR00rpVSoLASuA8KBXsBrQBQwPpRBVVIS\n6gCUUioQuoKslFJlk2WMOWCM2WOMeR94BxiW96SItBORz0XkqIikiMi7IpLgfW4qcANwsc9KdG/v\nc4+JyCYROeEtlXhcRMKDCVREaonIXG8cR0XkWxE5x+f5G0QkQ0T6iUiSiBwTkSUi0rTQPPeKyH7v\nHG+KyIMiklzae/JKFJFvROS4iKwXkQHBvCellCpPmiArpZQ1MgEHgIg0AJYCa4GuQH+gBpBXfjAT\n+BBYBCQADYAfvc8dA0YDbYBxwNXAfUHGtgCoDwwBOgPfA4vzEnYvJ3CP99p/AWoDL+U9KSIjgAeB\ne4EuwCZgEn+WT5zqPQE8AjwNdAJWAO8FUpKilFIVSUsslFIqSCLSHbgGT9kFeBLbNcaYKT5jRgOH\nRKSrMWaliJwEoowxB3znMsY86vPjLhF5DLgDmFrG2PrhSUrrGmOyvA9PFZGhwCg8iS2AHbjFGLPN\n+7qZwOs+U90KvG6MecP78z9FpC/Q0hv38eLek0h+dcUsY8wC72NTgOvxJOu+SbRSSlUKmiArpVTZ\nXOTtJhHm/edTPEkkeFZY+xTTbcIAZwIrS5pURIYDtwEtgGg8iWswv+3rgmf1+qBPsgqeFeMzfX7O\nykuOvfYCDhGpbYxJx7OiPbfQ3D/jTZD9kJT3H8aYvd5Y6vn5WqWUqlCaICulVNksBf4B5AJ7jTEu\nn+dswOd4Vn4Lb1BLKWlCEekBvIdntfhrIB24DHgyiDhtwH6gZzGxHPX579xCz+WVTtiKeawsckqI\nTSmlKh1NkJVSqmxOGGOSS3juV+BKYFehxNlXNp7VYV/nA7uNMTPyHhCRxCDj/BVPTbA5Rbz+2AR0\nB97yeaxHoTHFvSellDrt6Ld3pZSy3gtADPChiHQXkWYiMkBEXhaRGt4xO4AOItJKROJFJAzYAjQS\nkWu9rxkHjAgmEGPMImA58JmIDBaRRBE5V0QeEpHzS3m574rzM8BoEfmbiLQQkbvwJMy+q8rFvSel\nlDrtaIKslFIWM8bsw7Ma7AK+BNYBz+HpdJG3Ue4VYCOeeuRU4DxjzOd4yilmA7/h6X7xQFlCKPTz\nEGAJnhriTcD7QCs8dcZ+zWOM+QCYDjyGZ1W6HZ4uF5k+44u8pxLiKekxpZSqFMQY/YxSSikVOBH5\nBLAbYy4LdSxKKWUl/fWXUkqpUolIJJ72dV/hWRm/AhgK/DWUcSmlVHnQFWSllFKlEpEIYD6e3sWR\nwFbgce8pgkopVaVogqyUUkoppZQP3aSnlFJKKaWUD02QlVJKKaWU8qEJslJKKaWUUj40QVZKKaWU\nUsqHJshKKaWUUkr5+H9UrFG7NTGzDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40ec04aeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap, linewidth=5)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  6.33134077e-07,   5.75276067e-02,   9.42471760e-01]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "(without using Scikit-Learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "And let's set the random seed so the output of this exercise solution is reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(2042)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but the point of this exercise is to try understand the algorithms by implementing them manually. So here is one possible implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "validation_ratio = 0.2\n",
    "total_size = len(X_with_bias)\n",
    "\n",
    "test_size = int(total_size * test_ratio)\n",
    "validation_size = int(total_size * validation_ratio)\n",
    "train_size = total_size - test_size - validation_size\n",
    "\n",
    "rnd_indices = np.random.permutation(total_size)\n",
    "\n",
    "X_train = X_with_bias[rnd_indices[:train_size]]\n",
    "y_train = y[rnd_indices[:train_size]]\n",
    "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n",
    "y_valid = y[rnd_indices[train_size:-test_size]]\n",
    "X_test = X_with_bias[rnd_indices[-test_size:]]\n",
    "y_test = y[rnd_indices[-test_size:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for ay given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    n_classes = y.max() + 1\n",
    "    m = len(y)\n",
    "    Y_one_hot = np.zeros((m, n_classes))\n",
    "    Y_one_hot[np.arange(m), y] = 1\n",
    "    return Y_one_hot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 1.,  0.,  0.]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Y_train_one_hot = to_one_hot(y_train)\n",
    "Y_valid_one_hot = to_one_hot(y_valid)\n",
    "Y_test_one_hot = to_one_hot(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's implement the Softmax function. Recall that it is defined by the following equation:\n",
    "\n",
    "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def softmax(logits):\n",
    "    exps = np.exp(logits)\n",
    "    exp_sums = np.sum(exps, axis=1, keepdims=True)\n",
    "    return exps / exp_sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y_train))   # == 3 (3 iris classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
    "\n",
    "So the equations we will need are the cost function:\n",
    "\n",
    "$J(\\mathbf{\\Theta}) =\n",
    "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n",
    "\n",
    "And the equation for the gradients:\n",
    "\n",
    "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n",
    "\n",
    "Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.44618386482\n",
      "500 0.835100303577\n",
      "1000 0.687696155441\n",
      "1500 0.601029983545\n",
      "2000 0.544278281196\n",
      "2500 0.503726274224\n",
      "3000 0.472835729391\n",
      "3500 0.448187250818\n",
      "4000 0.427834726281\n",
      "4500 0.410589102282\n",
      "5000 0.395680325749\n"
     ]
    }
   ],
   "source": [
    "eta = 0.01\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error)\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.3172417 , -0.6476445 , -2.99855999],\n",
       "       [-1.16505434,  0.11283387,  0.10251113],\n",
       "       [-0.72087779, -0.083875  ,  1.48587045]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96666666666666667"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Well, this model looks pretty good. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6.62957494791\n",
      "500 0.534163155437\n",
      "1000 0.503771274864\n",
      "1500 0.494805645558\n",
      "2000 0.491408194841\n",
      "2500 0.490008507445\n",
      "3000 0.489407428961\n",
      "3500 0.489143102469\n",
      "4000 0.489025165491\n",
      "4500 0.488972058096\n",
      "5000 0.488948000479\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_inputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.70940845273\n",
      "500 0.574099607346\n",
      "1000 0.543638281366\n",
      "1500 0.535638768431\n",
      "2000 0.533256378917\n",
      "2500 0.532654427178\n",
      "2765 0.532605822457\n",
      "2766 0.532605823051 early stopping!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1 \n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "best_loss = np.infty\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_inputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients\n",
    "\n",
    "    logits = X_valid.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_valid_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    if loss < best_loss:\n",
    "        best_loss = loss\n",
    "    else:\n",
    "        print(iteration - 1, best_loss)\n",
    "        print(iteration, loss, \"early stopping!\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Still perfect, but faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's plot the model's predictions on the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1bNiw9Pjs2bN599136d27d6mG2NhYZs2aVeas4OLFi9Hr9SxevLjUHM6bN4/H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\nmpf6f0EDf48dLp+QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40f6ab9748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "X_new_with_bias = np.c_[np.ones([len(X_new), 1]), X_new]\n",
    "\n",
    "logits = X_new_with_bias.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "zz1 = Y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap, linewidth=5)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.93333333333333335"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_test.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_test)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Our perfect model turns out to have slight imperfections. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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