04_training_linear_models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 4 – Training Linear Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/ageron/handson-ml2/blob/master/04_training_linear_models.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures. We also check that Python 3.5 or later is installed (although Python 2.x may work, it is deprecated so we strongly recommend you use Python 3 instead), as well as Scikit-Learn ≥0.20."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Python ≥3.5 is required\n",
    "import sys\n",
    "assert sys.version_info >= (3, 5)\n",
    "\n",
    "# Scikit-Learn ≥0.20 is required\n",
    "import sklearn\n",
    "assert sklearn.__version__ >= \"0.20\"\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 as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)\n",
    "\n",
    "# Ignore useless warnings (see SciPy issue #5998)\n",
    "import warnings\n",
    "warnings.filterwarnings(action=\"ignore\", message=\"^internal gelsd\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": {},
   "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_model_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "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",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "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": {},
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1  # learning rate\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "source": [
    "# Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sgd_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
       "             eta0=0.1, fit_intercept=True, l1_ratio=0.15,\n",
       "             learning_rate='invscaling', loss='squared_loss', max_iter=1000,\n",
       "             n_iter_no_change=5, penalty=None, power_t=0.25, random_state=42,\n",
       "             shuffle=True, tol=0.001, validation_fraction=0.1, verbose=0,\n",
       "             warm_start=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-3, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.24365286]), array([2.8250878]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "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 = 200, 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/minibatch_size * 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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.25214635],\n",
       "       [2.7896408 ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "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": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_paths_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "source": [
    "# Polynomial regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "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": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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UwReL7WIOoInHXHV4qE9zH31q66Ka2rYhP0can+qKxUbE44DXAdcClwEfAF6Vmb/f1mN2NQfQxBHkqsNDfTqK7VNbF9XEto1xLkuCspUk9gEfBb4B+BLgKPCmiHhKWw/Y57PVp8NDe/deGB6yEkVZ2z3fXbwGXb6Pfc+pS8V6UJl5Fji26UdviYgPAs8CPtTGY/Z5DmDr/BJ4FF3Sdr0W6OY16Op9bM9NXetskUREXAE8Dbhzm9sOA4cBDhw4sPRj9H1F0ebhoRMnxrcirEuzei1dvAZdvY/HuApRdekkoCLiMcCvAW/IzLu23p6ZJ4GTMFkkscpj9WF+Y54J8D73Bvto1vPd1WvQxfvY95y6VnwVX0TsAd4IXAq8IDMf2en+Q7/k+yLDKK7kmij1PGz3OF2+Bn1dkSptVd0qPoCICOBm4Argut3CaQwWGUapsTdYegdWcl5kVuWPLl6DPq9IlZZVeojv9cDTgWsz88HCj12lPg+jdLHTHOu8yFi3W+NWbJl5RDwZ+D7gauDjEfHAxr8bSrWhRtMJ8OPH+7dKqovlz9stvx+DVbbbpeLqq5LLzD8MRKnHK22Voa6+DqN00fvbaUXbkOdLll3J51Jx9Zm1+Bow1p3AvDvNpoNju0Afw2uwzIGMQ4PqMwOqAWPeCWzdaW4No1LBMebXYCd9nuOUDKhd9OUcpRqGt7YLo1LBUcNrUKO+n6yucTOgdjDv0X/XO4Fahre2C6NSwdH1a1Czvs5xSgbUDvpyjlItw1vbhVHJ4HBHLA2LAbWDvgwb1dLOWWFkcEhaxuAvWLiqGuZ25tGXdkrSvKWODCgtrKYwLNGWrra3pudZalKVtfjUf7UsyCjVlq62t4bn2YBU10peUVcDUNNViku0pavt7fp5ngbk0aOTr5ZJUhcMKC2kplp4JdrS9mPMqpPX9fPcdUBK4BCfFlTT+UYl2tLmY+w0jNf181zLylCNm4skpI6cODEZQjt/ftJTOn4cjhzpulUXOAeltrhIQqpc7b0Uz19T1wwoqSNdD+NJtTOgpA7ZS5FmcxWfJKlKBpRa5yXHZ/O5kWZziE+t6roiQs0r0bp+bnZT83OncTCg1KouLwVSewDM+9x0ERS1P3caB4f41KouKyLUXg1hnuemq5JDtT93Ggd7UGpVl0up+3Ce0W7PTVc90NqfO42DlSQ0aH2fR+lyqK3vz53q5fWgKjXmD/2Yt30VPm8aGksdVaito+E+7MCcdF+eJ/NqrFwkUVAbE899uW6Pk+6SFmVAFdTGira+7Pi7vr6RpP5xiK+gNla09WW11dALo/ZhmFXqGxdJDMBQdo593Q7n16TFuEhiRIYwiT7vTr7GEOuyWoY0ZAaUqjDPTr7WnkpfhlmlvjGgVIV5dvK19lSGPr8mdcWAUhXm2cnX3FMZwjCrVBsDSo1aZY5ot528PRVpXIoGVERcBtwMPBe4FziSmW8s2Qa1p8QckT0VaTxKn6j7i8DDwBXADcDrI+IZhduglvTlpGFJ/VAsoCJiP3AIOJqZD2TmHwO/A/zrUm1Qu6wWIalJJYf4ngacz8y7N/3sPcA3bL1jRBwGDm98ey4i3legfbV5PJNh0J65ZD9cesmDD953/9d+7f1nl/wjPd32lbnd4zPWbb9ynjuVDKiLgc9u+dlngUu23jEzTwInASLizDxnHA/NWLcbxrvtbvf4jHXbI2Ku8kAl56AeAC7d8rNLgfsLtkGS1BMlA+puYF9EfMWmn/0z4M6CbZAk9USxgMrMs8CtwE0RsT8ingO8APhvu/zqydYbV6exbjeMd9vd7vEZ67bPtd1Fq5lvnAf1y8A3AZ8EXul5UJKk7VR/uQ1J0jh5RV1JUpUMKElSlXoTUBHx3yPinoi4LyLujojv6bpNbYuIx0XEzRHx4Yi4PyLeHRHP77pdJUTEyyLiTESci4hf7bo9bYqIyyLizRFxduO1/q6u21TCmF7jzUb+uV5oP96nauYngBdn5rmIuAo4FRHvzsw7um5Yi/YBH2VSbeMjwHXAmyLin2bmh7psWAF/A/wY8DzgizpuS9s216i8GnhrRLwnM4d+CsaYXuPNxvy5Xmg/3pseVGbemZnnpt9u/Htqh01qXWaezcxjmfmhzHw0M98CfBB4Vtdta1tm3pqZtzFZ7TlYY65ROZbXeKuRf64X2o/3JqAAIuJ1EfE54C7gHuD3Om5SURFxBZOahkM/sh6TWTUqrfI/EmP7XC+yH+9VQGXmS5nU7vs6Jif9ntv5N4YjIh4D/Brwhsy8q+v2qDFz16jU8Izxc73IfryKgIqIUxGRM/798eb7Zub5jWGQJwIv6abFzZh3uyNiD5OKGw8DL+uswQ1Z5PUeAWtUjtTQPteLmHc/XsUiicw8uMSv7aPnc1DzbHdEBJOrEF8BXJeZj7TdrrYt+XoP1d/XqMzM/7fxM2tUDtwQP9dL2nE/XkUPajcR8YSIuD4iLo6IvRHxPOA7gf/RddsKeD3wdOBfZeaDXTemlIjYFxEXAXuBvRFxUURUcUDVpBVqVPbeWF7jGUb3uV5qP56Z1f8DLgfeAXwGuA94L/C9XberwHY/mckql4eYDAVN/93QddsKbPsxLqzymf471nW7WtrWy4DbgLNMlh1/V9dt8jVudbtH+bleZj9uLT5JUpV6McQnSRofA0qSVCUDSpJUJQNKklQlA0qSVCUDSpJUJQNKklQlA0qSVCUDSpJUJQNKKiQivigiPhYRH4mIx2257Zci4nxEXN9V+6TaGFBSITkpCvpq4EnAS6c/j4gTwIuBH8zM3+ioeVJ1rMUnFRQRe5lcMfcJwD8Bvgd4DfDqzLypy7ZJtTGgpMIi4luA3wVuB74R+IXM/KFuWyXVxyE+qbDMfAvwf4FrgN8EXr71PhHxAxHxpxHxUEScKtxEqQpjuTiYVI2I+A7g6o1v78/thzHuAX4C+BpgvVTbpJoYUFJBEfFcJlfLfTPwCPDvIuI1mfmXm++Xmbdu3P9A+VZKdXCITyokIp7N5PLu/wu4AbgReBQ40WW7pFoZUFIBEfF04K3A3cC3Zua5zPwr4GbgBRHxnE4bKFXIgJJatjFM9zbgs8DzM/O+TTffBDwI/FQXbZNq5hyU1LLM/AiTk3O3u+0e4IvLtkjqBwNKqlBE7GPy+dwH7ImIi4BHM/PhblsmlWNASXW6kUlZpKkHgXcABztpjdQBK0lIkqrkIglJUpUMKElSlQwoSVKVDChJUpUMKElSlQwoSVKVDChJUpX+DmXzq/e6ZjY5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 30,
     "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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 32,
     "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": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure high_degree_polynomials_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 35,
   "metadata": {},
   "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[:m], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\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": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": {},
   "source": [
    "# Regularized models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 39,
     "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": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5507201]])"
      ]
     },
     "execution_count": 40,
     "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": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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//DKXXXYZEyZMYPPmzUyaNIl77rlHY/goSi2nNsqVqKgoevbsybXXXlu4uywpKYlVq1YRGRnJjTfeWOG+S6O8cuzyyy/n9NNP59RTT8XlcjFz5kxmzpzJyy+/rP499QERqVNH7969pTTi4+NLfa8uMXPmTGnXrp34+vpKr169ZPPmzTJt2jQJDAyUZ555xvH+tmzZIkCJx5YtWwrrxcXFyXnnnSd+fn5ywgknyEMPPSS5ubmOjaO+/H6KJ0Cs1ALZUdpxLJkiUn+uy9ooV3bs2CHXXnuttGrVSvz8/KR9+/Zy3XXXyYYNGxwfTwHlkWMPPPCAnHzyyeLv7y9+fn7Sq1cv+fDDD8tsu75cK7WFuxfcLVOXTZUjOUc8yisrU4xUwu+jJujTp4/ExsaW+N769evp2rVrNY9IcQr9/eonxpg1ItKnpsdRGseSKaDXpVJ+9FpxjgOHDxD2bBiBvoGkP5COl3Fb2iorUxy32RljPjbG7DHGpBtj/jLGlOqJZowZa4zZa4xJM8a8b4xp7PR4FEWp26hMUZSGR1xSHACR4ZEeSo8TVMVi5VNAOxEJBoYDTxhjinmuGWMGA/cDA4F2QAfgsSoYj6IodRuVKYrSwFiXuA6AqBZR7sJbb4VHH610244rPiISJyJZBS/zj44lVL0ReC+/fgowGbjJ6fEoilK3UZmiKA2PuERr8ekW3s0WJCXB++/D009Xuu0qcU83xrxujDkMJAB7gPklVIsC1hZ5vRZoaYwpto3AGDPKGBNrjIlNSkqqiiErilKLUZmiKA2LgqWuQotP06Ywbx48+2yl264SxUdE/g00Ac4BZgNZJVQLAtKKvC543qSE9t4WkT4i0ic8PNzp4SqKUstRmaIoDQcRcS91hecrPo0awZAhcOedlW6/ygISiIhLRJYBJwK3lVDlEFA0AEzB84NVNSZFUeouKlMUpWFwJPcIvVv3pktYF04MPtHx9qsjEpMPJa/HxwE9irzuAewTkQPVMCZFUeouKlMUpR7j7+vPd9d/x/rb19sUIT/8YC09q1Y50r6jio8xpoUx5mpjTJAxxjt/l8U1wJISqn8IjDDGRBpjQoCHgGlOjkdRlLqNyhRFUfjkE3jlFfjuO0eac9riI1gT9E4gBXgOuFtE5hhjIowxh4wxEQAi8i0wFfgB2JZ/VH6fmqIo9QmVKYrSwNiRtoOM7Ax3wR13wIQJ8M9/OtK+o7m6RCQJKDHTm4hsxzofFi17AXjByTEoilJ/UJmiKA2Pa2dfyy/bf2HpTUs5t+250LOnPRxCs60piqIoilIrEBHiEuMQhE6hnaqkD1V8FDZu3Mjo0aPp0aMH3t7eREdHl1gvPj6egQMHEhAQQOvWrXnkkUdwuVwVrqcoSv2lvHJFUYqy99BeUo6k0MyvGa0ah8HNN8OsWZCX51gfji51KXWTuLg45s+fz5lnnkl2dnaJdVJSUhg0aBCRkZHMmTOHTZs2MW7cOPLy8njiiSeOu56iKPWb8sgVRTmawsCF4VGYpUth2jT49Ve4/HLH+lDFR2HYsGFcfPHFAFxxxRXs37+/WJ0333yTzMxMZs+eTXBwMDExMaSnpzNp0iTGjx9PcHDwcdVTFKV+Ux65oihH88e+PwDo1qIbdO9uIzWHhoIxjvWhS121lOTkZEaPHk1YWBihoaFMmDABgP79+/PKK6842peXV9mXwYIFCxg8eLCH4nL11VeTmZnJjz/+eNz1FEWpfmqbXFGUo/ltz28A9GrVC1q1gnvvhVtucbQPtfjUQlJTUznrrLMICgri/fffZ926dUycOJF27dqxadMmRo4c6VFfRMrlQ+PjU/GfOyEhgfPPP9+jLCIigoCAABISEhg2bNhx1VMUpXqpjXJFUY5mzZ41QL7iU0U0DJXcmOJmsmHDbNnXX7vL3n7blo0a5S7bvduWtW7teX7v3rZ8zRp32aRJtmzSpEoNd8qUKezdu5dvv/2W4cOH8+CDDxIWFsYDDzzAvffei5+fn0f96dOn4+vrW+ZRGVJSUmjWrFmx8pCQEFJSUo67nqLUeVSuVFquKMrRfHf9d3x51Zf0fPMreOstOOh8xhlV1WsZIsL06dMZOXIkYWFhheVNmzYlLS2NMWPGFDtn2LBhrF69usrHZkpYYxWRYuXlrafUfVasgKVLIToa+vWr6dEopVGb5YqigN20lZQEES0j2PVrCM8+uYZo13T6/eMf0KRYnuFK0TAUH5HiZUVnZAWMGuU5KwM7Iyvp/KIzsgImTar0rGzDhg0kJSURExPjUe5yubjrrrsIDAwsdk5oaChNmzatVL9lERISQmpqarHytLQ0DwtPeespdZ8VK2DgQMjOtomTFy9uYMqPyhVFcYwZM+D666FFC9i/PwjyHqORz8Ms3tGIfg7nKW0YS111iC1btgDQtm3bwrLly5ezdetWepYSubI6TNJdunQhISHBo2zHjh1kZGTQpUuX466n1H2WLrVKj8tlH5curekRKaVRW+WKohTw3//CJf+ZRPNzZuFygUu8yJZGVSJXGobFpw7h7e0N2N0XYE3U48ePL3xeEtVhkh4yZAjPPvssBw8epEm+2XHmzJn4+/szYMCA466n1H2io62lp8Dio/Hpai+1Va4oCkByMvz8M0QM/ZL4pt/h5XMp5HlXmVxRxaeW0bt3b/z8/Bg/fjwTJ05k5syZJCcn07lzZ2bMmEH37t1p166dxznNmzenefPmFe7z8OHDzJ8/H4Bdu3aRnp7OrFmzABg6dCgBAQGMGTOGl19+mcsuu4wJEyawefNmJk2axD333OOxdb289ZS6ydE+PYsXq49PXaC2yhVFWbHChuo5rU8Wy/bH8e+9efTo+y4fHb6GqW8EV41cEZE6dfTu3VtKIz4+vtT36hIzZ86Udu3aia+vr/Tq1Us2b94s06ZNk8DAQHnmmWcc72/Lli2CzYJd7NiyZUthvbi4ODnvvPPEz89PTjjhBHnooYckNze3WHvlrXc09eX3q68sXy7i7y/i7W0fly8v33lArNQC2VHacSyZIlJ/rsvaKlfqE/XlWqkuCmQKiPg2yhVz85myK8RXBOTfJy8s9bzKyhS1+NRCrrzySq688kqPsvbt23PjjTdWSX/t2rUr1dxdlMjISJYsWeJYPaVuUZJPj1p56g61Va4oDZcCmQLgyjXItmg+ujOIsbtOZvon5/NSLlRFmCh1blYUpVwU+PR4e6tPj6IolSc6Gry88kNi+eRC+6U0vvAfNHrnNU5o7cVff1VNv2rxURSlXKhPj6IoTtKvH5x2GnTuDKvajOTvgJX0avUMAD17wtq1EBnpfL+q+CiKUm769VOFR1EUZ8jLgw0bYO5cYc2TSeSsaUPfK2zsqB49rOJzzTXO9+voUpcxprEx5j1jzDZjzEFjzP+MMUNKqXuTMcZljDlU5Ih2cjyKotRtVKYoSv0lIQHCwqBluDD0mw1cvHgX/lt3Atbi8/vvVdOv0xYfH2AHMADYDgwFPjPGdBeRrSXUXyEi/Z0cgNSS1AiHDtkUI02aQFBQTY+m9qNOkEop1LhMAZUrStmoDDt+Vq6EM8/EOvp8/TV89BFceCHgtvhUBY5afEQkQ0QmichWEckTkW+ALUBvJ/spDV9fXzIzM6ujq2Ny6BD89Rfs2mUfDx2q6RHVfjIzMzUKrFKMmpYpoHJFKR8qw46fFSus4jN7/WxWN80gd8pku3sCOOkkOHIE9u1zvt8q3dVljGkJnAzElVLlNGPMfmPMX8aYh40xlbJAtWjRgl27dnH48OEa1b4PHrRrl2AfqyC5bL1BRDh8+DC7du2iRYsWNT0cpZZT3TIFVK4ox0ZlWMVZuRJOPyOXm766idPfPZ3EjMTC94xxOzg7TZU5NxtjfIFPgOkiklBClZ+AbsA2IAqYCeQCT5XQ1ihgFEBERESpfRZEBt69ezc5OTmV+wCVICsLDhywOQiNsXEISsjbqeTj6+tLy5YtNbKzckxqQqaAyhWlbFSGHT9pabBlC7R75VqmrT7I65e0pnWT1h51Cpa7LrjA2b6rRPExxngBHwHZwB0l1RGRzUVe/mmMeRy4jxKElIi8DbwN0KdPn2NOuYKDg2vFxVc0tH8pOQAVRSknNSlTQOWKojjN6tVweo8sgufM47J0WNGqV7E6ERGwY4fzfTuu+BjrAfge0BIYKiLlnSIJUPPegw6h234VxRlUprhRuaLUF1auhD5nN+aeWwaTNfdLevcrvlkzLKxqdnZVhY/PG0BXYJiIlOoRaIwZkr9ejzGmC/AwMKcKxqMoSt1GZYqi1DMKHJvnH/yN93vB2SedXaxO8+awf7/zfTsdx6ctMBroCewtEkvjOmNMRP7zggX1gcAfxpgMYD4wG3jSyfEoilK3UZmiKPUPEdi4PJG23XexLW0bwY2D6daiW7F6zZtbvzancXSpS0S2cWzTclCRuvcC9zrZv6Io9QuVKYpS/9i8IYclB/sQdE1TugwJoX2nM/H28i5WLyysDig+iqIoiqIox2LT1/H08zpEk8NBxE1KJCUrrcR6dWKpS1EURVEU5Vj8kNyDV+/bDp9/jpe3D80DmpdYr2lTyMiA3Fxn+1fFR1EURVGUamPNGuhwuov0Ticds56XF4SEQHKys/2r4qMoiqIoStWTnY3M+oL/rckjrvG7hD4TyhM/PXHMU6piuUsVH0VRFEVRqp7338f88wrez7iKVfsX4hIX7Zu1P+YpVbGzSxUfRVEURVGqntBQDodH8EfUJfy47UcABnUYdMxTqmJnV7kUH2PMm8YYMca0LuG9U4wx2caYl5wdmqIoiqIo9YYrr2TqiL9IGNqCI7lH6NGyBy2DWh7zlJpc6lqR/3h6Ce+9CKQDk5wYkKIoiqIo9ZPVfzTm4AnfAxDTIabM+jW51LUy/9FD8THG/AMYAjwiIilODqyusGIFPPWUfWyo6HegKM6h/yf9DuodDzwAr70GOTms+U34PetLAC46+aIyT62Kpa5yBTAUkQ3GmGSKKD7GGF/gBWAd8Jazw6obrFgBAwdCdjY0agSLFze8BIL6HSiKc+j/Sb+DesemTTB1Knh5kdgjhqwALxIPbiY8IJz+Ef3LPL15c0hIcHZIx+PcvBLok58pGeAu4GTgbhFxOTususHSpfbP6XLZx6VLa3pE1Y9+B4riHPp/0u+g3tGhA8yaBZMmsSr1ZPp27MTucbv5/J+fl5im4miqYqnreFJWrASGAqfkW38eBr4SkcXODqnuEB1tZyQFM5Po6JoeUfWj34GiOIf+n/Q7qHcYA5deCpdeym+PQ69ecELQCZwQdEK5Tq+xpa58ijo4nws0BsY5O5y6Rb9+1gy7dKn9czZEc6x+B5YVK/Q7UCqP/p/0OyhKnZYrKSlw5Ai0alVYtDI2i1tuaMSx8w57UhW7uo5H8fkVyANGAP2BZ0Vks7PDqXv061cHL0iHaejfgfokFGffPli0CJYtq+mR1D0a+v8J9DuAeiBX7rsPPv8cpk+HSy5BBH7OfYE/tr5J9p9PcW33a8vVTI0GMBSRg0A81tqTCExxdiiKUjdRnwSbSHDBAhg3Dk49Fbp0gS++gO7da3pkilI3qdNyJTfXaitHjsAppwCwezccaf8FuzK2E+gbWO6mQkMhNRXy8pwb3vFYfABWAd2AB/IVIUVp8DREnwSXyyYaXLjQWnZiY+3afUwMvP029OkDPvnS5fbba3asilIXqdNyxccHZs+227G6dgXgy2Xx5LZYQ5NGTbig4wXH1VRQkFV+QkMdGl55K+ZvX48GYoHpznSvKHWfhuCTIGJ3pS5aZJWdH36A1q2tonPffXDuuVY4KYriDHVerhhTqPQAfBz/HnjBNd2uwd/X/7iaKljuqnbFB7gXaA9cJyLiTPeKUj+ojz4JBw5YwVtg1cnOhkGD7AaNV1/18FlUFKUKqHNy5auvrE/PG2/ACe5dW9mubH5zfQheMKLXiONuNizMOjh37uzMMI/p42OMCTXGXGOMeQqYDLwgIiuPUb+xMeY9Y8w2Y8xBY8z/jDFDjlF/rDFmrzEmzRjzvjGmccU/iqIolSEz0yo5EyZA7942/MZHH0G3bjBvHuzcaWXa9ddXn9KjMkVR6ggulzX/fvWVdWouwpyEueT47kEh7KUAACAASURBVKdraHf6tu573E077eBclsVnMPBfrDPzi8D95WhvBzAA2I6N+/OZMaa7iGwtWtEYMzi/vfOB3cCXwGPl6ENRFAfIy4Pff3dbdFautM7IMTHw0ktwxhng61vTo1SZoih1Am9vWLIE3noL7rjD460Z//sagNF9R+COgVx+nI7lc0zFR0Q+BT4tb2MikoFnstJvjDFbgN7A1qOq3wi8JyJxAMaYycAnqJBSlCpj61a3n87ixXYmFRNj5dSsWdC0aU2P0BOVKYpSNps2wZtvwpw5kJNjdZDoaLjzTrvLsto46SR44olixVc1/oDdf1/Pv8b3rlCzTsfyOd5dXceFMaYlNq1FXAlvRwFzirxeC7Q0xjQXEQ/dzhgzChgFEBERUUWjVZT6R0qKdUQusOqkp1s/nQsvhOees3KqLqEyRVHcHDlilZsvv4SbbrIrTE2aQFaW3VQ1ZIjdYfnhh1U4qZk9266TX3ddqVXWxHox9JQYQo/Pp7mQ6l7qqjD5u8A+AaaLSEkpxoKAtCKvC543ATw+ooi8DbwN0KdPH3WsVpRSyMqygc8KrDrx8XD22daqM2aMXcryOp4MfbUIlSmK4mbHDrj8cmjXDrZsKb6rcuJE63Jzzz3WQfqbb6zfnqPs3Ak33GADeZ14IgwY4PF26pFUUjJTiI1tz733VrybsDDYvr2SYy1ClSg+xhgv4CMgG7ijlGqHgOAirwuea3wgRSknIrBunduis2yZDR4YEwNPPw1nnQWN64F7r8oURXGzdSv072+tPffdZ3eOl0SjRnYH5muv2QnQ0qWF8QSdoU0bePZZWL3axrQ4ild+fYXHfnwMH3maz06vuOZT65e68rO3vwe0BIaKSE4pVeOAHsBn+a97APuONkkriuLJrl1ui86iRXamN2gQjBgBH3/sXKyL2oLKFEVxk5ICQ4daheeuu8p3zu23g58fDBsGv/4KISEODcYYuO02exxFRnYGL/36Ei5xcWJeb5o3r3g3Ti91VYXR+w2gKzBMRDKPUe9DYIQxJtIYEwI8BEyrgvEoSp0mPR3mzrWzu8hI66w4b56dYC1fDhs3WsfGyy+vf0pPPipTFAW7lH3JJdZHr7xKTwEjRliF6aqrbEaJCpObC/ffbxPyHYN3fnuHA5kHaOt9BhecEl2JDqt5V9fxYoxpC4wGsoC9RbatjQZ+xub6ihSR7SLyrTFmKvAD4A98ATzq5HgUpS6SkwOrVlmLzsKFsHat3VoeE2Pj6vTsaXdt1CayXdlsTN5IXGIc8UnxxCXZx9v7Vi5fhcoURXFz//3WWvPccxU7/7nn4B//gEcegSefrOAgJk2CZ56x20JXrSpxnS31SCpTfrbpPFtveoBzBx7/FvaihIbWYsVHRLZx7HzzHu5XIvIC8IKTY1CUuoaITWlTsHz144/WCTEmBh591K7lBwSUfO6KFdUb0j4rN4u/k/8m25VNr1a9ANiwfwPd3uhGbl7xaeTafWsr1Z/KFEWxLFxoQ06sXVvxDQo+PnaH16mnwmWX2R1fR1OmTLnrLiukpk4t1blo0tJJ7D+8n3MizmHDG8PpX8npR2AgHD5cuTaKUqXb2RVFKZm9ez3TQXh7W0Xn2mvhvfcgPLzsNlasgIED3UkMFy92VvnZmLyR2N2x1oqzP564xDg2Jm/EJS7Oa3ceS25cAkDbZm0B6BDSgcjwSKLCowofu4R14S3ecm5QitIAOXAAbr4Zpk2r/HJ2y5bwwgu2vdhYz80PpcoUEbeSEx4OP/1UqtITnxTPq6texct4MS7qZe7wNbRtW7kxBwbajWNOoYqPolQDGRlWVhQoOjt22BlVTIzddtqpU+k7M0pj6VIroFwu+7h06fErPkdyj5CwP4H4pHjik+IZ2WtkoSLz/PLneXPNmx71DYZOoZ1o16xdYZmfjx8HHziIn4/f8XWuKEq5uOMO+Oc/7SYGJ7j2Wpg5E6ZMgccfd5eXKFP65sItt0CPHjBunK14DGEV3DiYKyKvINQ/lOS4nvTvf/yy7WgKIsjn5DgTTV4VH0WpAlwuWLPG7acTG2vzX8XEwDvv2Oc+lfz3RUfbWVnB7Cw6uuxz0rPSeXrZ04V+OJtTNpMneYXv92jZo1Dx6R/Rn70Zez0sOCc3P7nEzMqq9JSf7duta8SmTXa2feONDu6yUeodCxfadDJxJYXsrCDG2A0Rp55qc++dfLItL1Gm/PSTdS788kurMZWRqO/E4BOZccUMXHkuRt4K55zjzJgLrD7NmlW+LVPXEq336dNHYmNja3oYiuKBiL2RFfjp/PCDDXExaJBVds49t3iAMSc4ej0+Izuj0IJT4GAc3DiYjy/7GLA+OoFPBuISFwDexptOoZ2IahFFZFgkV0ZdSfeW3R0dozFmjYiU4E1QO6hOmfLpp3Z3Xv/+0LGj3Rgzb56NATdlihXuilLAkSM26OiLL8JFFznf/rPPWnedb75xl5Xo4/POO3YgZ55ZalvbUrfRMqilxySoc2f44gtn0ma0bm0nkK1bV16mqMVHUSrI/v02J1/B8lVWllVyLrnEBg2rygzmh7IP4W286dfPn3794PXVr3PdS8+xNXUrgudkJiwgrPB5Y5/GPH/B85wQdAJRLaLoHNqZxj71IMJhLScvD8aOtUrOokV21aCAXbtg/Hi7RXnePAgOLr0dpWExdSp061Y1Sg9YP+V33oEFC2x6C7DKTr8m68DfH+hoC0eOPGY7GdkZXPjJhfj5+PH1NV9zYvCJ7N1rZWS3bs6MNSDAOT8fVXwUpZxkZtrIyAVWnU2brBk3Jsbe1Lp2rfxa9tEczDrI+v3rrQUnMa7QirMtbRszLp/BVd2uAiBP8tiSugVfL19Obn4ykeGRhctTUS2iEJHCrMh3nXmcAUCUSvPyyzZw3OrVxZe12rSxKwn/93/WsfTbb6lUsDelfrB1K7z0Evzvf1XXR6NG1pp099322mvUCPjlF7jgApuCYsWKMr2pc1w5XP3F1STsTyAqPIpQf1t/0SJr6XYqRY6TO7tU8VGUUsjLg99/d/vprFxpTbYxMfZGdsYZzjjagfW9iU+KZ//h/Vx0sp3e5ebl0nxqc3Lyigcq9vXyJTEjsfD1lVFXMrD9QDqFdsLX26FBKY6QkGATVq9cWbovj5eXtRKOHWsDzH3/fd3NqaY4wwMP2GXRqs6hO3SovfZef90qQPTsaeNpnHaaDfd8DFx5Lv715b/45q9vCPUP5fN/fk6Ar4298fXXMHy4c+NUi4+iVBFbt7otOosX252bgwZZAfTFF85kON6UvIkftv5QuE08Pimenek7AQjxC+HA+AMYY/Dx8qF7y+7k5uVaC05YpPXFCY+kU2gnfLzcf98WgS1oEdii8oNTHCU31zovT55sd+4dC2NsgLnzz7e+FxMmVM8YldrHihXw88/w7rtV35cx8NJtCUSP6MiNN/oSEhJoO2/a9Jgm7KzcLEZ+PZKZcTNp0qgJ313/HV3DuwLWOfr77+0E0SnU4qMoDpGSYh2RC/x00tOtojNkiL0JnXRSBdvNTClclopPiufiUy7mvPbnAfD9pu/59/x/e9Rv7N2YruFd6RrWlSxXVqGDYOzIWIzT62dKtfHKK9ZnZ8yY8tX38bH51vr2tc6lZ5xRpcNTaiEiNqN6tTm7v/suJ99+O29HTeDJJx/n2Wcpc+vUkdwjRE+L5tddv+Lv48+8a+fRp7Xb1/inn2yy5JYtnRumWnwUpYJkZdnZVIFVZ/16m7V40CCbZ69794r76dz3/X38b+//iE+KZ8+hPR7vNWnUpFDxOePEM7j+1OsLLThdw7rSIaQD3l7F81Co0lN3yc62yvO8ecd3TUVEwBtvwHXXwZ9/5vuYKg2Gzz6z186//lVNHZ5yCuTkcN6p+7nxPeH22w3t2h37FD8fP85ocwZ7Du3hy6u+LIziXsDcuTYhqpM4afHR7exKvUYE1q1z++n88oudicTEWGXnrLM8I5eWxv7D+4vlodp9cDfrb19fqJx0f6M76xLXARDgG0BkeCRdw7oSFR7F+e3Pp2+bvlX5UWstDXU7+7Rp8N//WpN/RbjsMutm8fDDjg6rzpGaCr/9Zm962dn2Pt21a/30gcrOtp/trbfziDx9LzvSdrD/8H4OZB7gcM5hsnKzOK/9eZza0u4P35KyhT8T/yTEL4SWQS1pGdiS4MbBx54w7d1rd2lccYW77K+/4OSTeewxOxmcMcPzlDzJY+Gmhfh4+TCww0DAOjWnZ6XTPMDTE18E2re3W+Sd2tEFNsnqWWfZR93OrihHsXOntegUHIGBVtG59Vb45JPSNymICEmHkwAK/WXmbpjLrXNvLSw/mr2H9tKqid23PuX8KXgbbyLDI2nbrC1eph5KZqVc5OVZP52XXqp4Gy+8YANd3nhj1Tu41jZcLpg+3e52i421CmBwsE3tEhdnUzhceCHcdx/06lV2e7WZg1kH2X1wN6eEncJbb0G7yCT+seJEspdll1j//eHvFyo+CzYu4Pb5nomAgxoFcWLwibRt2pavr/m6cLPDhv0baHo4j5bdz8RkZtqYCp0725PyIxjee6+dGP7yC/Tsm8GKnSv4YcsPfPLnJ2xL20ZE0wgSbk/A39cfX2/fYkoP2ImmlxdERTn1DVmcTFuhio9S50lPtwG3Cvx0EhPt1syYGOtU2r598XP2HdpHXFJcoRWnIBfVgcwDPNj/QaYMtJmFQ/xCSDqcRFCjII8t4gWPLYPci9jDT3FwC4NSp1mwwG4NHjiw4m20a2e3uN97r13+aCh89539zKGh9nHgwOJJehMTrS/U8OF2efrVV21AyLpAnuTx685fWbBxAd9t+o7Y3bFEhUex7Lo/mDIFvv02jEHfN8Hby5uIphGEB4QT6h9KUKMgGns39ggwemLwifyj8z9IzkwmMSORPYf2cCj7EAn7E0jKSLJKT2Ym+Ptz0acXsTF5Ix92MLTMacwrn19GTkQbAnwDuLrb1VwZdSWBgXD5Q19y/ty7yV280yOqe/tm7bm1160eZSUxd679XZxepQ8IUOdmpQGTk2NjohT46axda51AY2KsMDztNDvjEBH2HNrDos3xbNi/gX/3/XehCfiCjy/gj31/FGs7uHGwx/bxvm36su3ubZwUfJL62yjl5rnnbFDCyl4y48dDZKR1Fj33XGfGVlvJzYX777e7J//zn2PfPFu0sA7At99ulZ4zz7QhA0aNcv6G6xRxiXG8GfsmsxNms/vg7sJyHy8fAnwDeOa5HC64wJeePQ27u++mkXejMtscfspwjwmXiJB6JJUd6TtIPZIKTz8NU6ciixcTFhBG6pFUbhm2n1zvI5CzDjbZpfmiPjoXnOfHS3u3Y8SL3q16M6DtAIZ0HsL57c8v04rtcsH771vLutOoxUdpUIjYWCgFfjo//WRnd4MGwaRJ1jk5IAB2pO3gi/Vf8NY8tx9O6pHUwnYu6XIJbYLbANDvxH7WihOWb8VpEUVUeBStm7T2UHD8fPyIaNrA1hlKIi/Pxs/39XUHL9q3z0ZxDA93m8zT06322bixXYxvgGzbZp2Si7pQVJSAAGu1fPBBu8O4tt7UK0tKClx5pX0eG1v+AI6NG9u8mUOHWmfgH3+EDz4on99edVA0cGh8Ujyvrn4VgIimEVx8ysUM7jiYAe0GcPBAEN26WV8moFxKT0kYIKRxU0Ja5geMSpoDKSmYOXNYMWkFAJk5mezL2EdiRiIHDlvfoYJt6ADntjuHL87dyO3/OolF6xodV26suXOtUnqMzBYVJiDA+ns5gojUqaN3796i1H/27BH5+GORG28UadNGJCJC5JYRefLqR9tlRuy38sLyF2TEnBHy5uo3C89Ztm2ZMAmPI+TpEDn7vbNl1NxRsi11W819oKogL08kM1MkPd2zfPVqkSVLRLKy3GWLF4u88ILI2rXusjVrRG64QeS559xlOTkip54q0rWrZ5uDB4uAyIIF7rJXX7Vlt93mLtu+3Za1aVNYBMRKLZAdpR1Oy5SnnxYZNcq59nJzRSIjRebPd67N2kRKikjv3iJ33GEvv4py+LDIFVeInHuuyIEDzo2vIvy2+zf51+x/ye3zbi8sy8zJlAkLJ8iqnaskLy/Po/6YMSL33FPJTqdPFznlFJG5c91lO3aI/PJLhZobM0bklluO75xzzhGZObNC3ZXJG2+IjB5tn1dWpqjFR6kVZGRYS87ChbBwkbBjB5x/nmHQIGg6/HF+TZ7P50nxvL/pIGxyn5eYkcjoPqMBiGoRxejeo90+OC2iaBnYkpUrDUuXwq4wiOhXcv+OIWLX4g4ftvuQC6ae+/ZZs1VYmNvrLyPDRijz9oY77nC3MWmS3Vrx5JNux4U33rCesmPG5IdXxaZ/79vXeneuWeM+f/hw2LPHenm3sRYuPvsM3nrLhmctyBi4dy98+KH1Eh03zpYVeI+6XHbtoSCFfECAjeKaUySK9Ikn2qld27busmbN7BjD3PnBGhqffmqXapzC2xsefxweesj+VPXJ6pOebj/T2Wfb76wyn83fH2bOtMuD55xj43O1qKKYniUl8hQRlmxZwlPLnmLxlsUABPoG8sygZwhsFIifjx9PD3q6WFsbNsCsWVY8HBe7d9v1n4KoqomJtrHPP3fvJT/xRHtUgKlTrf/Ut9/a36gsYmOttfOyyyrUXZk46ePj6MwJuAOIBbKAaceodxPgAg4VOaLL04dafOoHOTkiy1e4ZNzkLdLt0nniGz1VWo6+UdpM6isBk4Nk0363debaL64ttOCETw2Xcz84V2775jZ55ddXZMWOFcfsZ/lyEX9/EW/vPPH3z5PlC1I9K6xcKfLtt3a6WMCSJXbavmqVu2ztWpFrrhF57DHP87t1E2nbViQ7277OyxO55BJr9fjiC3e999+3ZTfe6C7bv9+WhYZ6tnnWWbZ82TJ32dNP27Lx491lcXEijRqJ9O3ref6ll4oMGCCya5e77LPPRO66S+Tnn91lO3eKfPCB/bxF+f13kYQEEZfLXXbUDPV4oBKzs7omU+LjRVq3tlaayuDKc8nOtJ2yYf8GWbt3rWxO3iI9+2TKrFnOjLM2kJUlEh1tZ/GVuLxK5OGHRbp3F0lKcrZdkaIyxT7+8kueLPh7gfR7t1+hnAqcEih3L7hbNidvLrO9yy6zf+/j4t57rTx44w132Z491tpTGbPZUSxaJHLSSSKpqWXXvfZaT+Ox08yaZb8rkdpn8dkNPAEMBsoKu7VCRPo73L9SC8mTPLakbOWvzVlsXd3V7r768w8yrj6LRpJBk47g0wj25S9rt0iDlG/+C6cOhtNOY1y/cYyOuoles5YRJIFw03h34489BmunWkeIAkvKu+9aa8ktt7DU+yGys8HlMmRn5rD0hvfol3iP+/zrrrN+Kn//7c4p8PXXNnPf889biwrY/bOffgoDBsAjj7jP37oVDh2yOyd8fe2UNTgYmjSxfjEFnHiinYYW+MIABAXZbTtH58F4+GHr9JC/xRSAW26xlpyiU9jISBuR8Whmzy5e9s9/2qMobdrATTcVr1s0dXgBNWdmqFMy5dNPra+Kd/FYlMdERNiXsY8Tgk4A4MDhA5z44lEz9Yvg6tiWXJDVh7vPuIuYjjEOjbpmuPNO+zd5/XXnL6/HHrPGyZgYa/k5Hj+Vsli6lHyZYh8/m7ePlxrZ1ObN/Zsz9syx/LvvvwnxLyUxWxFWrIBVq6xbXKn897/W4/vRR93W2q5drYlr3z53vRNOcDxq4MCBVuxcdx18+WXpuQmXLbPW+tdfd7R7D2rtri4RmQ1gjOkDVMy+ptQ8eXn2xpudDa1auctXrLAKwIABVmKBlQI//wznnQf9+7M9bTsbf/ma1lPfZENwHmPP8mN75npcXpn8/nIwZ2YGEvLSBp5+sS2nTMvgkzl+XPa/I3x4bwyHL72MqPAoeixNIPimUXDl/2DmTLvjoOlheOgCu9wyvoji8/PPNqnWbbe5FZ/Dh2HLFti3j+hr7bbi7GyhkSuH6JCjdnKdfbZNyOdT5K9w/vn2de/e7rKoKLtVoXVrz/NXr7bLWUVjy0+fbg+KmsRj6PfTUTeqxo1LTmZTkl05PNweDYy6JFNEbOC3Y97EjiLHlcMHv3/A08uext/Xn3W3rcMYQ3hgOD1a9iAjJ4PG3o1Jy0pj76G95PrtY/7f87jhVHdY34T9CRzKPkTvVr3rzM7DN96wf90VK6omEKExdu5z+DBccondIu+Uw3N0NPg2yoNsLxo1gqsuOoFDSSM4ufnJ/LvvvwlqFFSudvLybFLaKVOKROdesMB+Kfff797D/8MPdjJz+ulw6qlWpuy4nuh519LvvGMnEXWCF1+ESy+1c6/p04v/Xjt2WGX/ww+dyWVYGk6mrKgSZ0HsDK0ss3QGsB/4C3gY8ClP2w16qevgQbs8UdSZdd8+kXnzRFYUWfLJzRV54gmRRx7xPH/yZJGLLhKJjXWXTZ9uHVHvv99dtnmzNaNGRHie362bCEjub2vkr/1/yVfrv5Jl/xpg606eLIcPiwx67V9y+q2IgPza2u1kHP50K0lt6mfr7t0rIiLJh5NFbr9dpHlzkU8+cffz888iAweKPP64u8zlEhk3ztqwi9rFlyyxNtD8NkXEejb+/bdIcrKIWNP0k0/ax+rkaJN4dfdfW8AB5+a6IFN++02kQ4fyL9t8s+Eb6fxy58L/SJvn28i+Q/tKre/Kc8nrMzZKu4s+lT3p7uv9hi9vECYh3V/vLu+ueVcyczIr+1GqlBUrRFq0sH/Rqsblsg7PV17puXJbUXan75YRc0aIufUsGT1+S8X/05mZsnzMdHm1zRTPcZ12mpWRP/7oLlu2TOSdd0S2basxmZKRIdK/v8iIEZ6O4xkZ1jF96tSqH8Pq1bYvkcrLlJpSfDoA7QEvoDsQDzxwjPqjsOv8sRFH34xrmtxckd27RbYdtWNo2TLr45F/8xURkaVL7Y174UJ32d9/iwwbZhWAovTqJRIW5nlDv/VW+5O99Za7bM4cW3bRRe4b/C95tgw8/+3DhtmyOXPcZW+/bctGjHCX7dsnEhJid/eISEpmikz+cbJ8N7iz/NStiUTd5VsorAf9C5kbfZXcc9oSCQoS6XDlG9JzfLQ8P2aofPXGOPll+y9WwRGxCtWOHZV3gKgjPPmkFVBgH598sqZHVDNUk+JT4zJl8mSRsWPLrnck54jcOf/Owv9Q55c7y4w/Z4grr+w7s8tlfVfmzXOXTVw8UcKmhhW21+LZFvL0z0/LwayDlfg0FqcnDampIu3bi3z5pTPtlYfMTLvbaNy4irdxOPuwTPlpigROCRQmIT6P+8jLK18u/YSi2u+GDXbnYxH/wIyULMnGR/KMETl0yF33xRetH9/69SU2W5MyJSXF3iZCQ0XuvFPk6qtFmjWztyWnfbRKIi5OpEsX+7xOKj4l1L8aWFOeuuWenaWmimzZ4ql47Ntn/3FLl3rWnTRJ5L77PJWEKVNELrhA5Kef3GWffmqnKkWVlH377NcYHu7Z5hln2PKilpjJk23ZAw+4y9autWVRUZ7nt21ryzcXcY67/36RVq2so2wBsbEiF14oy295x3MmcPPb1mJS1NFt+XLr/LZnj7ssLU2yN2+UhE2rZFbcLHls6WNy1edXeWzDTD+SXmybuP/EE8X35sEScvVYuebutTJnjkhamihFUIuPpToUnxLqOy9TyuDss0W+++7YdXJcOXL6O6cLkxDfx31l6rKpkp2bfVz9zJghcuaZnjebrNws+WjtR9LjjR6F/9GwqWHy9YavK/BJLE5fv3l59mZZNPpBdXHggEjnznaedzzk5eXJrLhZ0u4/7Qq/14s/vVj+2v+XNfF99pndpFDAf/5jJ6xFNZLVq60s7969sGjyZJG5ncZaGZ2SUu7x1AaZsn27yEMPWSNU0VtJVbN1q3sRor4oPlcBv5Wnbu/gYM+dMSIip58uEhzsqST83//Zj/ef/7jLFi60Zeef73m+v78tL6p5X3mlLfvvf91lH39sy665xl128KBIy5bFFZf77rO7e+Li3GU//WSVrMWL3WXp6SJffeW520bE7sjZt6/c1pHyzASycrMkK9cd2+W1Va9J1GtR4vu4bzHFpu2LbUXE6o1ffCHSZ9xj0mLwexLSbaX88/o0+eADa7xRjk1NLbPVJmpI8Sm/THFA8UlOFmnSxFoXymL679Ol40sdZdXOVWVXLoHcXBuupagYKSAvL0++/ftbOfPdM8XncR97g64gTlsXpk2zYrLoBsrq5K+/7Lx10aJjVEpOtstM+Ts6X1j+gvg/iCzoiKzpGCCLNxf50s891345RX+IgthWBQFnRKyMf/HFQq1482a7ur+57A1fJdJQZUpiov3eRGqZ4oN1lvYDngI+yn9ebJ0dGAK0zH/eBVgHPFqePnqDXUgvSteu9qOsW+cumzzZqodFl4XWrRMZPtwuNxXlqafsfsKiUis21m5zLqrSZmTYpaeiClItwXMmkCcffbNRZvw5Qx5Z8ohc8dkVEvlapPg87uMxA3xm2TMeis7QT4bK2Pn3yoRPP5CbJ66W00+3wnzwYLtNce3a6jFpKvWLygipapEpDig+n38uMmRI+esXnYBUhA8+sG5wpZGXlydxiXEer0fOHSmLNh3rru+Jk9aF7dutIeT33yveRqVYvFjkww/lx/mHpEULG61BXnzROo3MmOGuN3euvZcMHSoiIkkZSdLppY6S65OvAWZkuOs+/LCd3K5c6S5LTraT1lIcivLyrJvllClV8BnrORkZ9joUqX2KzyRAjjomARHYuBoR+fWeA/blOyNuBh4HfMvTR+9OnYr/AxMTrbnQCe+1OkRmTqas3btWftjyg4jYr+WxydnifWv/YhYcJiFmkpHXVr1WeP721O2yaudqWbHmkDz3nMiFF1pFp29fkQcfFPnhB5EjR2rmsyn1h0oqPlUvUxxQfEaMEHnpyWOikgAAIABJREFUpZLfSzuSJjEfxsjqXasr3U8B2dl2Xlf0nnssZsfPLpQDwz8dLn8fKJ9nsRPWhbw8O3k6OgTWceNyeVrA160TeeUVTxPOpk12TeuMMzzP7dzZ3u7Wr5d33xXp1Enk8J0TbFm+FuLKc8mXMx6TtZ2CJXecO4xyritX5Pvv7WS4kjFyvvrKWutUrh4/LpeIMfaxsoqPESs06gx9+vSR2NjYmh5GtbMtdRvLdyy3GcXz81BtTN5InuRxUvBJbB+7vbBux5c7YjBEtYgiMsxGMO4a1pWu4V0J8A1g5053gs9Fi+zO9EGDbMyL886zWZEVxSmMMWtEpE9Nj6M0KitTROCkk2DJEs/QSwCuPBfDZwxn/t/z6dO6D6tuXeXYlvPXXoPvv4c5c8qum5mTyX9W/ocnlz3JoexDNPJuxD1n3sPEcyeWe/t1RXnvPTvWX38tIQ6MiI2BVbB12+WyEcr377f7vAu+q6uvtrFsvv7aHe7hzTdtGIuRI+Htt21ZYiK0bGmTfe3f7+5n7Fj73uOPQ8eOjB8PO37czIcv7Mf3lA6sytrM/y34P1btWgXA9Eumc0OPGxz9HtLTbSTkDz6wETOU4ycw0P6MQUGVkymq+NQiDuccZsP+DcQn2SSbl3S5hNPbnA7Ac8uf476F93nU9zJedArtRGR4JJ//83N8vGwsmty83MLnYP9wS5e6FZ3ERBuYqkDZad++2j6iUs2UFFq/uqnvis+6dTbI26ZNxQPxTVg4ganLpxLqH8rqkavpENKhkqN1k5lpQ1B99507rl1Z7Dm4hwcWP8D0tTbOVOsmrXlx8ItcGXWlY+MCrAJjDLv2eNGzJ6x85kc6bv/B3vEL0swvWWKVmOhoq8GBVYQCA+2HS093xwu7/nobR+vjj200PYCVK23wmHPPtYoR2OA4f/1lY14dI9OpywWXXw6NQvcSePGDTPv9AwBaBbViasxUrut+neMxkUaMsNfHu+862my1U5MyJTzcZtRp2bJyMkVzddUgIsLEJRNZl7iO+KR4NqdsRnArok0aNSlUfM5ocwaXdrnU5qDKz0V1Stgp+PkUD2AlLh+WLXdbdf74A844wyo6H38Mp51WNUHDlNrFihVWwc3OtkEcFy+uOeWnPvPddyXn0Fq0eRFTl0/Fx8uHWf+c5ajSAzbo3T332EB9M2aU75xWTVox7ZJp3NbnNu789k5W7VrFxuSNFRtARobNC5WZaS0vBQwYAMuWIb+v5faHu3HbbdBx80K3BadA8QkNteGVDx1yn2sMTJhQ3DT02mvWdFQ0CuGZZxZPA+7lBV26lDl0b28YfP973PHNWPJ+P4ivly/39LuHiedMpEnjJsf5RZTNnDk2DuHatY43Xa3UtEwJDHQmerMqPlXIoexDrE9aX2jBiU+KJzkzmeUjlgNgjGHGuhlsSd0CgI+XD51DO9M1vCtR4VGc1/68wrbOaXsO57Q9p8R+RGyCu4UL7fHTTza3ZUyMzXfZv3+RyKBKg+Ho0PpLl6riUxUsWgSjRnmWpR1J45Y5twDw6IBHPf7LTnLbbdbqs369zWJQXs448QxWjFjBzHUzubTrpYXlS7YsoXtGEOE7k2208pNOsm/Mmwf33WdnTwXRxrOy4OabrVWmqOLj4wN5efz8RSIbNtjEoSwfaN8bMMBdr3t3dzLfojz6aPEBV0FI4CD/RuT5HiRgx0U82OcFJg7qXPZJFSAx0ebt/ewztwGrrlLTMsWp6M2q+DjAwayDuMRFMz+bEGb2+tnc8909bEvbVmL91COphXUnnzcZX29fosKj6Ny8M428G5Wrz717rcAtOLy9raJz3XXw/vsNMruBchTR0QXpOuxjdHRNj6j+4XLB8uXw0Uee5fd8dw870nfQp3Uf7u9/f5X1HxQEd99trT5Hj6HEwaamFi4BeRkvrpkWCxs+gf/+lxRfF1d+fiUvzUzjut9yyX7jVRqNud2ea4zVrgoUIYCQELjxRutTk5vrTvvy+eek5ARxTa9GzJyZb6Q57zx7FMXbu1pnZMt3LGdd4jpG9bZa6nWnXkfbZm05IetcoqOhUwhcdZWzfebk2DZvvtmm6qvr1LRMUYtPDZCelU58Ury14CTGEb/fPu5I38GU86fw4DkPAhDoG8i2tG34evlyStgpHstTkeGRNGnkVvuvO/W6cvWdkWEtOQV+Ojt22IsuJgYmTrT5NetImh6lmujXz5qia9rHpz6zdq3NPxsW5ll+QccL+G7Td0y/ZLqHv11VcMcd1sL799/5OXA3brTCokMH951p/XrrCNS5M8THu0+eNw82bIDt2zkcEcLZEWfza4u5nNAePv31Ec46w58be9yId//+9sNGRLjPNQamTSs+oNBQxo+0fk/9a0Ea6j/3/cnDPzzMnA1zaOzdmMEdB9O2WVu8jBfntrXLbt9+CxdcYPWw4cOd6/vuu62VYvJk59qsSWpapqjFpwpJO5JGXFIcG5M3enj29367d4nr4Y28G5GelV74un9EfxJuT6BDSAd8vUtJZ1sGLhesWeP204mNtTkzBw2Cd96xz33011PKoF8/VXiqkp9+crusFOWqbldxaddLy23BLRcuF+ze7Wl1eeYZgufN49nhU3jyyXP44APsnWnMGJtVskDxadXKWmWysz3bfOopq8CcdBJtgpsy5+o5LDljCfd+fy//2/s/3ps7gueWP8ek6Elc0f0KvEzZzoE//mgViXXrHPvkFWJ90nom/zSZGetmIAgBvgGM6zeO0P9v797jo6zuPI5/fgTCJYCCIAgURQTlDoJKqgiCKVhrUaRuC7q13kpV9NVaF+8i6qJUq912l13qbb23W7W1dq2uFBRaUFCIiAi1CoiABJQQEAgkZ/84ExJiQjKTZ+Z5nsz3/XrlRTI5M/PLSebHb85zLi2/umx14EB46SX45jf9CeMTJzb8+WfP9vN6Fi3yg1uNRZg5RSM+Afl0x6f86e9/OmgezsaSjQe+/63e3zrwQjnxqBPJa5Z3YJl4345+qfix7Y496F1dXm4ex3c4Pqk4nPOrQirm6cyb599JFhT4w8hHjPDD2iISHQsW+NVBFUrLSg8UOykXPV984d/xAHznO/5f5/yw0vbt/qNizsvq1bBgARdMWMX1d49g9Wo4fsgQuOiig6+tHH64n4TcotpiiPPOo7rRPUaz9IqlPPves9z8l5tZtXUV9/71Xr7T9zt1hr5nj5/v9Mtfpvek7kPZV7aPyc9P5nfv/w6HIzcnlx8O/SE3jbiJzq0713q/YcP84rKzz/ZTCa6+OvUY/uu//Fzu+fPD64fGqFUrFT71tu3LbQcVNsO7DWfSgEkAvF/0Pj986YcHtW/RtAUndDiBfh37sXvfbkhchv7NxN8EGtfWrf7NWcWozr59fkRnwgS/iOGoowJ9OhEJkHO+8HnwQf918Z5iBv3nIC4ceCG3j7y95tHe8nL/UTFc++qrfrVSQQFcdpm/bcMGuOACOP74ysLHDLp29YXLli2V/5tOnQqTJ9Nq4ECu2+PnBT/77Ml+mXd11YueQ2hiTZg0YBIT+07kkWWP0Kt9rwPLu9dsW8NfPv4LFw28iLzcvIPud9dd0L8/nHtuvZ8qEGXlZTSxJpgZzXKasXv/bprlNOOyIZcx7bRpdD+se90PAgweDAsX+lV6q1fDrFnJT0O6/3741a/8yFfPnin8MFIrXeqqw91v3M3cj+eysmglW3ZtOeh7RV8WHSh8BnQawIUDL6Rfx34H5uEcc/gx5DQJfmxy927/oqqYp/OPf/hh8oICv79Wnz6apyMSF6tX+6H3iitPMxfOZF3xOuZ/PI87u/0zrF3rJ45UuPhiv+7897+v3IRv/Xq/3Kd588rCp0cPGD/+q8uyly376jLvIUMOfDp1qp/Cs2zZQTc3SG5OLlOGTTnotpkLZ/LY8se4ae5NXDLkEi4dcil9OvahsNDvI7h8eTDPXR8bdmzg8cLHmfP2HB4Z/wije/idAR8Y+wCtmrWiS5suST9mjx5+i6ApU+Ckk/z2QYMG1X2/rVvhmmv8z//GGwdfkZRgZPWlri27tlROMK4ykrPqqlUc0cqvWFi6aSnz1s4D/GTjiiXifTv2Jb9b5QXKzq0788R5dS2HSE15uU9CFSuvFi/215ILCvyK0FNOqWEnUxGJhQUL4Oxhn8GDz7CTffzyy18CcP837sf6nOjfmm7bVrkVem6uXwK+YUPlg4we7UdnBg+uvK11a18cVVdHssjLg5tugltu8XOW0+XsXmfzwdYPWLxhMfcvup/7F93P8K75bHj5e9xw9/l06ZJ8sZGMol1FvLj6RZ5+72nmfTzvwN5nv3v/dwcKn+PaH9eg52jXzteoTz5ZudHrDTfUvFFkcbFvO306TJrkNyis2IhaghXUiE/sdm5u2q2pK7u8rMbvvX7x6wdm6S9cv5CSvSX06diH7od1r9ekvCCsXVs5ojN3rl9WXlDgP0aOhLZtMxKGSGTEdufm/fv99ayKguOPf/TXoM8+G6ZO5aKLYPxxK5k4vT/buranw+WfM+64cbw8+WXfZs8ev7fE0Uf7+2/d6kd20riZy969fqDo0UfTv9R4yadL+PU7v+aZ955hZ6nfhPCn+dfzs2/MAvwq2Nyc3Bo3WU3VlJem8Ot3fk25Kwf8iNS3j/82lw25jIKeBWnJ8zt2+NMxHnjA5+9TTvG/0u3b/eraefP8pn7XX6+FBOl2223+KvHtt2fZzs1l5WW0bd6WPh0qR3D6Hen//VrbyrHF07pnZh3lF1/4ndcr5umUlPh3CGedBffdp+FOkcjbt89PyDj99MprzT/4gb/G8cILvogBX7i88oofwZk6lQUL4Nbre1L66SXM2vwMADePuNm3rWnIpfqa9zRo3tzPS7n2Wr8qNJ0rP0/qehIndT2Jy7s/wOgr/8DXL/sfvtu/ciOc2Utmc+u8WxnceTADjhxA3459ObbdsXRp04VubbvRtW1XwO9gX/RlESV7S9iyawubdm7iw88/ZM22NSzbvIyHznmIIUf5a3ftWrSjaZOmjOkxhvNOOI+JfSfSrmW79P2Q+GLnX/4FrrvO7wTw5pt+0K5XLzj1VF/b6nzDzGjVyv+f21CxK3wGdBpA4bTCpM5RCfJskb17/YZlFZevVq3yf/xnnuk3L+3fv+7jIKJwfpKIJLz3nn8xbtlSufNny5a+IKp6WaqgwF+C6t+fF1+EoiLYurMFL/xzb2bN3c2I7iMy9oaruqo5ZeJEvyR7zhy48sr0Pu/evXD59/N4cOokLv3BpIO+t7FkI/vL97Nk4xKWbFxy0PeGdRnGksv9bXv276HTfZ1qfY43P33zQOHz4/wfc+OIG2nbPPND5zk5frPpAQMy/tSSkJcHn37a8MeJXeGTm5ObdNHTkLNFnIMVKypHdP76Vz8JuaAA7rkHvv71g4+PSXc8IhKw1q39O5bi4srC58474Wc/85m2Qrdu0K0bixb5xValpf4NT/7Nfg+vA6M9GVZTTvm3f/O3/dM/HfKszga77TY/GfiSS776vV+c9QvuHH0nb29828/B3LqKdcXr2FSyiR6HV56MnJuTS4dWHchrlken1p04Mu9IerbrSe8jetOvYz+Gdhl6oO2ReUem74eRyNOqrnpK5WyRDRsqC53XXvOX5CtWmz79tJ/4ViHZ0ZuwzzqJE42MSUb06uXf0VR1iGph/nw/GASJ4qfJ3dx7+XkMPWporfdJRhA55cYbfdFzww1+w9N0mD/fH5NRWFj7atS2zdtyRo8zDnlWWU6THIquL0pPkNUop8RbVq/qSkZ9zhYpLvYvhrlzfbFTVOQXWxQU+H0pevT46n0gtdGbsM86iQuNjElUjRrl/6M3q3wND+sSzNztIHPKXXf5Zdgvv+znHAZp40Z/LuCjj8bnXEDllPjTiE891XS2yL59foJaxS7J774Lw4f7QufJJ/0eGHXN04HURm/CPuskLjQyJlF18sl+L8AfXPk5w0d9QX5+cLvUBZlTDjvMFyYXXuhzXFCXvEpL/aW+KVNg7NhgHjMTlFPiTyM+SRg+3CeB117zpxi/8YbfUfPMM+GOO/xBeqkcEpzq6I3OT6qbRsYkqlat8pso7x0xjYuWPsS2Ix7k2uHXBvLYQeeUM87wl7yuvNLvNdPQDVKdg5/8xBdRN4czpSllyinxF8kRHzO7GrgYGAA845y7+BBtfwxMwx8I8RzwI+fc3qBi2by5cuXV//2fX9ZZUODf/TzySDDDsxq9SR/1rUC0ckqFt96CwcO389SKpwAYd9y4wB47HX/3d9/tF2HMmgXTpjXsse65x8e2cGH9RsWjRDkl/qI64rMRuAsYy4ETrr7KzMYCNwCjE/d5AbgjcVtKdu3yW3FUFDobNvh3OwUF/p3Jccel5zgIjd6kj/pWCDGn1ObNN6F8wBPs/nI3Y3qMSfpA4roE/XffsqU/eTw/H445xo8ApWL2bL8r8YIF/szTOFJOibdIjvg4554HMLNhQLdDNP0+8LBzbmWi/Z3AUySRpPbv9xt0Vay8evttOPFEX+g89BAMHZrezbtEJP0ymVPq6623YO8J/hDQK4ZeEfTDp0XXrn7j6TPP9JvtFRTU/77O+dPWZ83y0wTSfCKFSK2iOuJTX/2AP1T5uhDoZGZHOOe2VW9sZlcAVwC0b388Eyb4bcK7dfMv4GnTYMQIvx2HSHVawpoVUs4p3bvX7+Ru8En3g62r2bNjKW1y23BO73MaGHbmDBoEzz3nD36/7bb6bW64d69vt2SJH+mpbYVrtlFOCUckR3yS0BoorvJ1xedtgK8kKefcHGAOQIcOw9yECX5n0s6d0x6nxJyWsGaNlHPKsGHD6n1g4dtvQ/uRT7ERmNh3Ii2bpbAqIkSnn+63LDrnHD9yNWMG1FT3OedP55g2zS8E+dvf9MaygnJKeOJe+OwEqu45XvF5SV13POYYP0FZpD60hDVrpJxTkrFkCRzVpZyS3DZcODCeiahnT1i82E96HjIEvv1tf4Dyscf618iSJf6osW3b/F5AEyakZ35kXCmnhKdZM390SHl5wx4nrHn5K4FBVb4eBHxW05C0SENULGHNydES1kYuIznlnXfgqj53sfmnmxl59MggHzqj2raFe++Fv//dH8Hz2mt+l+cZM3zBc911/qie889X0VOdckq4WrVq+GMEvZy9aeIxc4AcM2sB7HfO7a/W9HHgMTN7CtgE3AI8FmQskrzGeN1aS1jjLWo55e23/UndrZoFkH0joH17//OkU2PLK8op4crL86ctNETQl7puAW6v8vWFwB1m9gjwPtDXObfeOfdnM5sFzKNyz43bv/JoMRa3F3tjvm6tJayxFpmcsn3Hfj5q9ieOPq4AyHzhE7ecAo03ryinhCdyIz7OuenA9Fq+fdDUOOfcz4GfB/n8URHHF7uuW0sURSmnPPH6QkrPP5eRjw9i+ZTl6XqaGsUxp4DyigQvL6/hjxGzvTfjoaYXe9TpurXIoT238vcAjO2Z+QOq4phTQHlFghe5ER/x4ngmjK5bi9TOOcfSXS9AUzivz3kZf/445hRQXpHgBTHio8InDeL6Ytd1a5GaLd+8nF1N19Oh+VGc3PXkjD9/XHMKKK9IsK67zq9CbAgVPmmiF7tI4/HbFS8AcF7f8TSxcGYIKKeIwLgAzgTWHB8RkTr8T6LwOb/vuSFHIiINpcJHROQQSvaWsGdPE5qVt+WMHmeEHY6INJAudYmIHEKb5m04a20hvQZtJTcnN+xwRKSBNOIjIlKHd96BEUM7hB2GiARAhY+ISC1Ky0pZveUjVq2CgQPDjkZEgqDCR0SkFm+se4MTZvckZ/L4QPYPEZHwqfAREanFKx++AkC3FieEHImIBEWFj4hILV75hy98Tjsq88dUiEh6qPCJuUWLYOZM/6+IBGdjyUZWbFlBk7JWnDPo1LDDyRjlFGnstJw9xuJ6YrNIHFRc5spZP5qTftQ85GgyQzlFsoFGfGIsric2i8TBqx+9CkDzT8bSuXPIwWSIcopkAxU+MVZxYnNOTrxObBaJg0Wf+Gs9g9qciVnIwWSIcopkA13qirE4n9gsEnWrrlrF1Hvfol3v48MOJWOUUyQbBD7iY2btzewFM9tlZuvMbFIt7S42szIz21nlY1TQ8TR2+flw441KUNJ4hZVTWjZrSXHhSIYMzpLhngTlFGns0nGp69+BUqATMBmYbWb9amm7yDnXusrH/DTEIyLxlvGc4pwDoLAQBg9O5RFEJKoCLXzMLA84H7jVObfTObcQeBG4KMjnEZHsEEZOcc4xYPYAznriHD4p2k7v3ul6JhEJQ9AjPr2BMufcmiq3FQK1vTsbYmZbzWyNmd1qZjXOOTKzK8xsqZktLSoqCjhkEYmwjOeUDz//kJVFK1n8yWL69jyMppoJKdKoBF34tAaKq91WDLSpoe0bQH/gSPw7uu8B19f0oM65Oc65Yc65YR07dgwwXBGJuIznlNfXvQ5AjybZN79HJBsEXfjsBNpWu60tUFK9oXPuI+fcx865cufcCmAGMDHgeEQk3jKeU+avnQ9Aqy0jGTQo6XhFJOKCLnzWAE3NrFeV2wYBK+txXwfo7ZWIVJXRnOKcOzDiU7JilAofkUYo0MLHObcLeB6YYWZ5ZnYqMB54onpbMzvLzDolPj8BuBX4Q5DxiEi8ZTqnrN2+lg07NtC+ZXs+XNSPgQMb/jOISLSkYzn7lUBLYAvwDPAj59xKM+ue2Feje6LdGOBdM9sF/C8+uf1rGuIRkXjLWE5ZtMHv1jywXT4djmjC4YcH9SOISFQEvl7BOfc5cG4Nt6/HT1Ss+PqnwE+Dfn4RaVwymVPyu+Xzi3G/YMPK7rTRZS6RRklndYmIJPRo14NrTrmG5h+fq/k9Io2UCh8RkWoKC1HhI9JIaWsuERHg3c/e5bcrf8u448ZRWHiaCh+RRkqFj4gI8OcP/8zdC+5m4/ZtfP75afTsGXZEIpIOsb/UtWgRzJzp/xURSVXFiq79759Du3bw5pshByQiaRHrEZ9Fi2DMGCgthdxcmDsX8vPDjkpE4sY5x6JPFsEnw3nm8XGU7fe5RTlFpPGJ9YjP/Pm+6Ckr8//Onx92RCISR2u3r+WzXZ/R6tNvUrbfcE45RaSxinXhM2qUH+nJyfH/jhoVdkQiEkeLNywGYPDwYsBo0kQ5RaSxivWlrvx8PxQ9f75PUBqSFpFUvPXpWwCMHXk4S5vBjTfC2LHKKSKNUawLH/CJSclJRBqiY15H+nToQ+eykzn6aJg+PeyIRCRdYn2pS0QkCDeNuIn3r3qf1p99Q/v3iDRyKnxERBKWL4fBg8OOQkTSSYWPiGS1fWX72FiyEdBRFSLZQIWPiGS1zbs20/XnXbnvb/ezbJlGfEQaOxU+IpLVviz9EoAuTftRVgZdu4YckIiklQofEclqX+7zhU+Tz4YyeDCYhRyQiKSVCh8RyWrlrpyvtf0aa1d21PwekSygwkdEst7QLkMpLNT8HpFsEHjhY2btzewFM9tlZuvMbNIh2v7YzDabWbGZPWJmzYOOR0TiLRM5ZehRQ1m+XCu6RLJBOkZ8/h0oBToBk4HZZtaveiMzGwvcAIwBjgGOBe5IQzwiEm9pzyn92w9j3Tro0yeokEUkqgItfMwsDzgfuNU5t9M5txB4EbiohubfBx52zq10zn0B3AlcHGQ8IhJvmcgpvTv0pvUXX6dPH38wqYg0bkGf1dUbKHPOralyWyEwsoa2/YA/VGvXycyOcM5tq9rQzK4Arkh8udfM3gsw5iB1ALaGHcQhRDm+KMcG0Y4vyrEBHN+A+2YkpxScfth7/vYGRJo+Uf79KrbURTm+KMcGDcspgRc+rYHiarcVA23q0bbi8zbAQUnKOTcHmANgZkudc8MCiTZgUY4Noh1flGODaMcX5djAx9eAu2d1ToFox6fYUhfl+KIcGzQ4pwQ+x2cn0LbabW2Bknq0rfi8prYikp2UU0QkUEEXPmuApmbWq8ptg4CVNbRdmfhe1XafVR+SFpGsppwiIoEKtPBxzu0CngdmmFmemZ0KjAeeqKH548ClZtbXzNoBtwCP1eNp5gQVbxpEOTaIdnxRjg2iHV+UY4MGxKecAkQ7PsWWuijHF+XYoIHxmXMuqED8A5q1Bx4BCvDX1W9wzj1tZt2B94G+zrn1ibY/AaYBLYHngCnOub2BBiQisaacIiJBCrzwEREREYkqHVkhIiIiWUOFj4iIiGSNyBU+UT/rq77xmdnFZlZmZjurfIxKc2xXm9lSM9trZo/V0TajfVff2ELqt+Zm9nDi91liZsvM7KxDtM9Y3yUTWxh9l3jeJ81sk5ntMLM1ZnbZIdpG9jUb9fiUU1KLTTmlYfGF1H/pzSnOuUh9AM8Av8FvRnYafhOyfjW0Gwt8ht+ttR0wH7gnQvFdDCzMcN9NAM4FZgOPHaJdxvsuidjC6Lc8YDr+fKcmwLfwe78cE3bfJRlbxvsu8bz9gOaJz08ANgNDw+67Ks+rnJJ6bMopqcUW2ZySQnxh9F9ac0rGfpAkfhmlQO8qtz1R0w8CPA38a5WvxwCbIxRfxv9Yqjz3XXUkgoz3XRKxhdZv1eJ4Fzg/Sn1Xj9hC7zv8VvKbgAui0HfKKYHFqZzS8Dgjm1PqiC/U/ktHTonapa7azuX5yknMidsKq7XrZGZHRCQ+gCFmtjUxVHermQV9REiqwui7ZITab2bWCf+7rmmTvFD7ro7YIKS+M7P/MLMvgQ/wSep/a2gW9dds1OMD5ZRUKaccQhTzSjpzStQKn6DO5UmXZOJ7A+gPHIk/Xfp7wPVpjC0ZYfRdfYXab2bWDHgK+G/n3Ac1NAmt7+oRW2h955y7Et8HI/AbDta0d07UX7NRj085JTXKKYcQ1bySzpwStcIn6ufy1Ds+59xHzrmPnXPlzrkVwAxgYhpjS0ZkzzQKs9/MrAn+MkMpcHUtzULpu/rFydsfAAADkklEQVTEFvbfnHOuzDm3EOgG/KiGJpF+zdbQNlLxhf37rYNySg2inFMg+nklXTklaoVP1M/lSSa+6hxgaYkqeXE60ygj/WZmBjwMdMJf595XS9OM910SsVUX1t9cU6BnDbdH/TUb9fiqU05JTdbnlCTjqy6Mv7tgc0pYE5YOMZHpWfwqhzzgVGpf4TAOP9O7L34291/IzAqM+sZ3FtAp8fkJwHvA7WmOrSnQApiJr+JbAE2j0HdJxJbxfks8138Ci4HWdbQLo+/qG1sYf3NHAt/FDznn4FdZ7ALGR6HvEs+rnJJ6bMopqccX2ZySZHwZ7b9M5JS0dmyKP3R74PeJH3Q9MClxe3f8sFb3Km1/gl/KtgN4lMTytyjEB9yXiG0X8BF+eLBZmmObjq/Gq35Mj0Lf1Te2kPrt6EQ8exKxVHxMDrvvkoktpL7rCLwObE/0xwrg8ppeE2H83SWeUzkl9diUU1KLLbI5Jdn4Mt1/mcgpOqtLREREskbU5viIiIiIpI0KHxEREckaKnxEREQka6jwERERkayhwkdERESyhgofERERyRoqfERERCRrqPARERGRrKHCR0RERLKGCh/JCDNraWYbzGy9mTWv9r2HzKzMzL4bVnwiEj/KK5IKFT6SEc653cDtwNeAKytuN7OZwKXAVOfcsyGFJyIxpLwiqdBZXZIxZpYDFOJP3z0WuAx4AH/S74wwYxOReFJekWSp8JGMMrNvAX8E5gKjgV85564JNyoRiTPlFUmGLnVJRjnnXgLeAcYAvwGurd7GzK4ys7fMbI+Zzc9wiCISM8orkoymYQcg2cXMLgAGJ74scTUPOW4C7gFOAvIzFZuIxJPyiiRDhY9kjJl9A3gCeAHYB1xiZg8451ZVbeecez7RvnvmoxSROFFekWTpUpdkhJmdAjwP/BWYDNwClAMzw4xLROJLeUVSocJH0s7M+gB/AtYA5zrn9jrn/gE8DIw3s1NDDVBEYkd5RVKlwkfSKjGs/CpQDJzlnNtR5dszgN3ArDBiE5F4Ul6RhtAcH0kr59x6/OZiNX1vE9AqsxGJSNwpr0hDqPCRyDGzpvi/zaZAEzNrAZQ750rDjUxE4kp5RSqo8JEougW/DX2F3cDrwKhQohGRxkB5RQDt3CwiIiJZRJObRUREJGuo8BEREZGsocJHREREsoYKHxEREckaKnxEREQka6jwERERkayhwkdERESyxv8Djpb9tv39lU4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\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": "markdown",
   "metadata": {},
   "source": [
    "**Note**: to be future-proof, we set `max_iter=1000` and `tol=1e-3` because these will be the default values in Scikit-Learn 0.21."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.47012588])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", max_iter=1000, tol=1e-3, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mislav/anaconda3/envs/tf2/lib/python3.7/site-packages/sklearn/linear_model/coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 2.802867703827423, tolerance: 0.0009294783355207351\n",
      "  positive)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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), random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 44,
     "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": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 45,
     "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": 46,
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Early stopping example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\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(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, 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, y_val_predict)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = deepcopy(sgd_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, 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, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\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": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239,\n",
       " SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
       "              eta0=0.0005, fit_intercept=True, l1_ratio=0.15,\n",
       "              learning_rate='constant', loss='squared_loss', max_iter=1,\n",
       "              n_iter_no_change=5, penalty=None, power_t=0.25, random_state=42,\n",
       "              shuffle=True, tol=-inf, validation_fraction=0.1, verbose=0,\n",
       "              warm_start=True))"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\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], [1, -1], [1, 0.5]])\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": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_vs_ridge_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 727.2x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.05, n_iterations = 200):\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) + l2 * theta\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10.1, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 2., 0, \"Lasso\"), (1, N2, 0,  2., \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * 0.5 * 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(np.array([[2.0], [0.5]]), Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    ax = axes[i, 0]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, N / 2., levels=levelsN)\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.set_title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "    ax.set_ylabel(r\"$\\theta_2$\", fontsize=16, rotation=0)\n",
    "\n",
    "    ax = axes[i, 1]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    ax.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.plot(t1r_min, t2r_min, \"rs\")\n",
    "    ax.set_title(title, fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename']"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\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",
      "                \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",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\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",
      ".. topic:: 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"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris virginica, else 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: To be future-proof we set `solver=\"lbfgs\"` since this will be the default value in Scikit-Learn 0.22."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='warn', n_jobs=None, penalty='l2',\n",
       "                   random_state=42, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd05ad58b10>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": {},
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.66066066])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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(solver=\"lbfgs\", 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": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='multinomial', n_jobs=None, penalty='l2',\n",
       "                   random_state=42, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 63,
     "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": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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)\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": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# My exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These were theoretical questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename']"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note: I looked at the solution a bit for the below code that adds the bias."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def train_test_split(X, y, val_ratio=0.2, test_ratio=0.2):\n",
    "    train_length = int(len(X) * (1 - val_ratio - test_ratio))\n",
    "    val_length = int(len(X) * val_ratio)\n",
    "    \n",
    "    random.shuffle(X)\n",
    "    random.shuffle(y)\n",
    "    X_train = X[:train_length]\n",
    "    y_train = y[:train_length]\n",
    "    X_val = X[train_length:(train_length + val_length)]\n",
    "    y_val = y[train_length:(train_length + val_length)]\n",
    "    X_test = X[(train_length + val_length):]\n",
    "    y_test = y[(train_length + val_length):]\n",
    "    \n",
    "    return X_train, y_train, X_val, y_val, X_test, y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, y_train, X_val, y_val, X_test, y_test = train_test_split(X_with_bias, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90\n",
      "90\n",
      "30\n",
      "30\n",
      "30\n",
      "30\n",
      "[[1.  1.4 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.3 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.3 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.3 0.2]\n",
      " [1.  1.5 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.4 0.1]\n",
      " [1.  1.3 0.2]\n",
      " [1.  1.7 0.4]\n",
      " [1.  1.6 0.2]\n",
      " [1.  1.4 0.3]\n",
      " [1.  1.7 0.4]\n",
      " [1.  1.3 0.2]\n",
      " [1.  1.7 0.3]\n",
      " [1.  1.4 0.3]\n",
      " [1.  1.4 0.3]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.5 0.3]\n",
      " [1.  1.5 0.3]\n",
      " [1.  1.5 0.4]\n",
      " [1.  1.3 0.4]\n",
      " [1.  1.9 0.2]\n",
      " [1.  1.4 0.3]\n",
      " [1.  1.4 0.1]\n",
      " [1.  1.6 0.4]\n",
      " [1.  1.5 0.4]\n",
      " [1.  1.5 0.2]\n",
      " [1.  1.7 0.2]\n",
      " [1.  1.9 0.2]\n",
      " [1.  1.5 0.3]\n",
      " [1.  1.5 0.2]\n",
      " [1.  1.6 0.2]\n",
      " [1.  1.5 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.  0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.6 0.2]\n",
      " [1.  1.5 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.3 0.3]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.4 0.1]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.5 0.4]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.3 0.2]\n",
      " [1.  1.6 0.2]\n",
      " [1.  1.6 0.2]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.2 0.2]\n",
      " [1.  1.9 0.2]\n",
      " [1.  1.4 0.3]\n",
      " [1.  1.1 0.1]\n",
      " [1.  4.6 1.5]\n",
      " [1.  1.5 0.4]\n",
      " [1.  4.6 1.3]\n",
      " [1.  4.2 1.5]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.5 0.4]\n",
      " [1.  1.6 0.2]\n",
      " [1.  4.2 1.5]\n",
      " [1.  4.  1.3]\n",
      " [1.  4.  1. ]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.5 0.2]\n",
      " [1.  4.  1. ]\n",
      " [1.  1.5 0.2]\n",
      " [1.  1.5 0.1]\n",
      " [1.  1.4 0.2]\n",
      " [1.  1.6 0.2]\n",
      " [1.  1.5 0.3]\n",
      " [1.  1.6 0.6]\n",
      " [1.  1.3 0.2]\n",
      " [1.  4.5 1.5]\n",
      " [1.  1.3 0.4]\n",
      " [1.  3.8 1.1]\n",
      " [1.  1.4 0.2]\n",
      " [1.  3.9 1.1]]\n",
      "[2 2 2 0 1 0 2 1 2 1 0 2 2 1 1 2 0 1 1 0 2 0 1 0 1 2 1 1 2 0 0 0 1 1 1 2 0\n",
      " 2 1 0 2 0 1 2 2 1 0 2 1 1 1 1 0 1 1 0 2 2 2 0 1 1 0 1 1 2 0 1 1 0 0 2 1 2\n",
      " 0 1 1 2 1 0 2 0 2 0 1 2 1 1 2 0]\n"
     ]
    }
   ],
   "source": [
    "print(len(X_train))\n",
    "print(len(y_train))\n",
    "print(len(X_val))\n",
    "print(len(y_val))\n",
    "print(len(X_test))\n",
    "print(len(y_test))\n",
    "print(X_train)\n",
    "print(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    y_one_hot = []\n",
    "    for value in y:\n",
    "        if value == 0:\n",
    "            y_one_hot.append([1, 0, 0])\n",
    "        elif value == 1:\n",
    "            y_one_hot.append([0, 1, 0])\n",
    "        elif value == 2:\n",
    "            y_one_hot.append([0, 0, 1])\n",
    "    return y_one_hot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the y vector had more options, the above function would get tedious to write (because I could have [0, 0, ..., 1 ..., 0]. That would be a pain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_one_hot = to_one_hot(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2 2 0 1 0 2 1 2 1 0 2 2 1 1 2 0 1 1 0 2 0 1 0 1 2 1 1 2 0 0 0 1 1 1 2 0\n",
      " 2 1 0 2 0 1 2 2 1 0 2 1 1 1 1 0 1 1 0 2 2 2 0 1 1 0 1 1 2 0 1 1 0 0 2 1 2\n",
      " 0 1 1 2 1 0 2 0 2 0 1 2 1 1 2 0]\n",
      "[[0, 0, 1], [0, 0, 1], [0, 0, 1], [1, 0, 0], [0, 1, 0], [1, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 1], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0], [1, 0, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [0, 0, 1], [0, 0, 1], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [1, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0]]\n"
     ]
    }
   ],
   "source": [
    "print(y_train)\n",
    "print(y_train_one_hot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(s):\n",
    "    numerator = np.exp(s)\n",
    "    denominator = np.sum(np.exp(s), axis=1, keepdims=True)\n",
    "    return numerator / denominator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note: For the function above I looked at the solution a bit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.57611688 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.57611688 0.21194156 0.21194156]\n",
      " [0.21194156 0.21194156 0.57611688]\n",
      " [0.21194156 0.21194156 0.57611688]]\n"
     ]
    }
   ],
   "source": [
    "print(softmax(y_one_hot))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y))   # == 3 (3 iris classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(90, 3)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "print(len(np.unique(y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for the gradient descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 0; loss: 1.1254676117494151\n",
      "Iteration: 500; loss: 1.1013337854756082\n",
      "Iteration: 1000; loss: 1.09892832055843\n"
     ]
    }
   ],
   "source": [
    "eta = 0.01\n",
    "n_iterations = 1001\n",
    "epsilon = 1e-7 # so we don't try to take the log of 0\n",
    "m = len(X_train)\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(softmax(y_proba + epsilon)), axis=1))\n",
    "    error = y_proba - y_train_one_hot\n",
    "    if ((iteration % 500) == 0):\n",
    "        print(\"Iteration: \" + str(iteration) + \"; loss: \" + str(loss))\n",
    "    gradients = 1/m * X_train.T.dot(error)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note: For the above function I consulted the official solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23333333333333334"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_val.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_val)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "(without using Scikit-Learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's set the random seed so the output of this exercise solution is reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(2042)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 78,
   "metadata": {},
   "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": {},
   "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": 79,
   "metadata": {},
   "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": {},
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 2, 1, 2, 0, 1, 1])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 82,
   "metadata": {},
   "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": {},
   "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": 83,
   "metadata": {},
   "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": {},
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "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": {},
   "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": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.597130923472287\n",
      "500 1.0908127529355436\n",
      "1000 1.0869544648915044\n",
      "1500 1.0848375011351523\n",
      "2000 1.0835671826737425\n",
      "2500 1.0827229443791269\n",
      "3000 1.082105168466696\n",
      "3500 1.0816174822554023\n",
      "4000 1.081212060324179\n",
      "4500 1.0808641153835157\n",
      "5000 1.080559941470915\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": {},
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.03408702,  0.02168645, -0.31656222],\n",
       "       [-0.55509682, -0.27435129, -0.12026124],\n",
       "       [ 0.73231186,  0.02962805, -0.08082224]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3"
      ]
     },
     "execution_count": 87,
     "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": {},
   "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": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.860660829970837\n",
      "500 1.0829609680541645\n",
      "1000 1.0829105586140142\n",
      "1500 1.0829104165714163\n",
      "2000 1.0829104160040177\n",
      "2500 1.082910416001738\n",
      "3000 1.0829104160017304\n",
      "3500 1.0829104160017304\n",
      "4000 1.0829104160017302\n",
      "4500 1.0829104160017302\n",
      "5000 1.0829104160017302\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_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.51011728  0.74237601  0.53943335]\n",
      " [-0.04789373 -0.00246172  0.05035546]\n",
      " [ 0.04824824 -0.07473776  0.02648952]]\n"
     ]
    }
   ],
   "source": [
    "print(Theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3"
      ]
     },
     "execution_count": 90,
     "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": {},
   "source": [
    "Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.8817819074712805\n",
      "500 1.138176318326418\n",
      "1000 1.1362720904161314\n",
      "1500 1.1361953608989321\n",
      "2000 1.1361919982355595\n",
      "2500 1.1361918498621622\n",
      "3000 1.1361918432907514\n",
      "3500 1.1361918429982307\n",
      "4000 1.1361918429851163\n",
      "4340 1.13619184298457\n",
      "4341 1.13619184298457 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_outputs]), 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": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3"
      ]
     },
     "execution_count": 92,
     "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": {},
   "source": [
    "Still perfect, but faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the model's predictions on the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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)\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": {},
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 146,
     "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": {},
   "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": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".py",
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