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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Chapter 4 – Training Models**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "# Setup"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This project requires Python 3.7 or above:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import sys\n",
+ "\n",
+ "assert sys.version_info >= (3, 7)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It also requires Scikit-Learn ≥ 1.0.1:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from packaging import version\n",
+ "import sklearn\n",
+ "\n",
+ "assert version.parse(sklearn.__version__) >= version.parse(\"1.0.1\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As we did in previous notebooks, let's define the default font sizes to make the figures prettier:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "plt.rc('font', size=14)\n",
+ "plt.rc('axes', labelsize=14, titlesize=14)\n",
+ "plt.rc('legend', fontsize=14)\n",
+ "plt.rc('xtick', labelsize=10)\n",
+ "plt.rc('ytick', labelsize=10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And let's create the `images/training_linear_models` folder (if it doesn't already exist), and define the `save_fig()` function which is used through this notebook to save the figures in high-res for the book:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from pathlib import Path\n",
+ "\n",
+ "IMAGES_PATH = Path() / \"images\" / \"training_linear_models\"\n",
+ "IMAGES_PATH.mkdir(parents=True, exist_ok=True)\n",
+ "\n",
+ "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
+ " path = IMAGES_PATH / f\"{fig_id}.{fig_extension}\"\n",
+ " if tight_layout:\n",
+ " plt.tight_layout()\n",
+ " plt.savefig(path, format=fig_extension, dpi=resolution)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Linear Regression"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## The Normal Equation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "np.random.seed(42) # to make this code example reproducible\n",
+ "m = 100 # number of instances\n",
+ "X = 2 * np.random.rand(m, 1) # column vector\n",
+ "y = 4 + 3 * X + np.random.randn(m, 1) # column vector"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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BoeUIQQCMxjfwloslTLakFy7Ww092BCd6E72NEATAeG7/Bl5eLpWW+nToUGunmxJWtGEy1l64WA8/2TVBI72J3hZ1CHrooYfk8/n0pz/9KeTvly5dKp/Pp9mzZ7e4cQBguvqd97BhrXTLLcO0eLHP6SaFFW2YjKUXLpbDT3afBUhvondFHYIGDRokSXr33Xcb/e7o0aOaMWOGevbsqcLCwpa3DgAMdvLO27J8mjIl1fFxMPEUbXByYvxRJNzem4jQog5BAwYMUGpqqt55551GvysqKtKBAwc0b948ZWRkRPR4tbW1uvfee5WXl6c2bdqoZ8+eeuCBB2SdfPEWADBM6J23z+hT+CM9/HTi+B/G7SCcqGeM/t73vqe+ffuqrKxM3377rdLT0yVJO3bs0OOPP65hw4bpiiuuiPjx5s6dq+LiYi1dulR9+vTRpk2bNGHCBHXo0EG33XZbtM0DgKQRenZlS716ufeQWCI0N6NzqFnAFy6sOwRWW8u4HRwX02UzBg8erLKyMr3//vu68MILJUnTp0+XZVmaP39+VI+1YcMGXXnllRo5cqQk6fTTT9fy5ctDHm4DgGR38qUnTtx5p6QE9OSTAWVnc8WjcJdkCDf+Z+/eun+JuhQGvCGms8MGDx4sScFDYi+99JLWrFmjadOm6Zxzzon6sdauXauPP/5YkvT+++/rzTff1IgRI2JpGgB4VqgzmOoH3ZaUfKeFC0s0YUJihwq4ZT6eSG3YEH78D+N2cLKYvk6cODi6pqZGhYWFOu200zRz5syoH2vGjBmqrKzU2WefrdTUVNXW1uqhhx7SddddF/Y+NTU1qqmpCd6urKyUJPn9fvn9/qjb4GX19ZpWt0TtJ/40hd11l5dLu3b51KuXlfAdZV0PRisFAnWHuup6MCz95CffKTtb6tjRr6qqbxK6zRcv9mny5FQFAj6lpFgqLq5NeAiTIt/u9e2VGh4uTE21lJv7nbz4cfHiZz1en6NE1OyzYhyB3K1bN3Xo0EHjx4/Xf/3Xf2nhwoW65ZZbon6cFStW6K677tJvf/tb9enTR2VlZZo+fbrmzZun8ePHh7zPrFmzVFRU1Gj5smXL1LZt26jbAAAlJT305JP9ZVk++XyWpkwpU0HBvoQ9/7ZtnXXvvRc1Wv7AA2+qb9/DCWtHvUOHWuuWW4bJso4HipSUgBYuLFHnzt8kvD3NCdVeSfL5Apoy5f2EbkuTxfNzVF1drbFjx6qiokKZmZlxbmmdmEPQVVddpdWrV6tNmzbq3bu3Nm3apJSTh99HICcnRzNmzNDUqVODyx588EE999xz+uijj0LeJ1RPUE5Ojvbv369OnTpFX4yH+f1+lZSUqKCgQGlpaU43J6Go3bza7aq7vFzq1et4L4xU13uwc+d3CesRaq4Nid7mpaU+DRvW+GBBScl3uuSSxPYGRVJ7uPYuW/adfvYz755t7KXPerw/R4cPH1ZWVpatISjm0XWDBw/WqlWrVF1drccffzymACTVJb2T75uamqrAyQd1T5CRkRHyFPy0tDTXv0nsQu3UbpJ41713b+hT0T/9NE15eXF7mibl5YU6g8mnvLyGdSZqm59zTqgz06Szz26lpp7+5IHd8dRU7eHa+6MfNd1er/DCZz3en6NE1BvzZTPy/r+ia6+9VhdffHHMDRg1apQeeugh/fWvf9XevXu1cuVKzZs3T1dddVXMjwkA0XDLPDJumnk4lstB2HVpikhkZ0vjxjVcdv31DIJOJLd8jqIRUwiyLEuPPvqo2rZtq4cffrhFDfj973+vn/3sZ5oyZYrOOecc3XnnnZo0aZIeeOCBFj0uAETKTdd/ctMZTNGEMrsvTdGc8nLpj39suOy557xzVlsycNPnKFIxHQ4rLi7Whg0bNHfuXGW3sLr27dtr/vz5Uc8vBADx1NwEfKYKNx/PyZq6NEUiXkunnx91vPY5ijgElZeX67nnntPHH3+sP/7xj7r44ov1y1/+0s62AUBCRbrDR2OhZ7dO3KEQp58fx3npcxTx4bDXXntN99xzj1avXq0xY8Zo9erVSq3v8wIQ5LXJ5YB4cPpQiNPPD2+KuCfopptu0k033WRnWwDPC3XNIicHtwKJ5PShEKefH94T89lhABpyemAo3M2UHkI3DOyObfY7mIgQBMRJUwMzYTYnTx03Ca8zokUIQkxM+VYbDS/OkQH70UOYGLzOiAUhCFHj21boEMjAzMiZFKLpIUwMXmfEghCEqPBtq+kQ6KYZf93KtBBND2Fi8DojFoQgRMX0b1uRhEA3DAx1KxNDND2EicHrjFjEfAFVmMn0CcmYlbZlTH39OHU7MXidES16glzCK2MkTP+2RZd7yyT69XPT58pNPYRuel3izU2vM9yPEOQCXhsjYfK4F9NDYEsl8vXz2ueqJaIJNSa9LkBzCEEO8+oYCZO/bZkcAuu1pCchEa+fVz9XsYgm1Jj0ugCRIAQ5zPSBxl5lSggMFXbi0ZNg9+tnyucq2lBjyusCRIoQ5DDGmMCtQoUdr/QkmPK5ijbUmPK6AJEiBDmMMSZwo3BhZ8MGb/QknPy5SkmR5sxx1+cqHoOTow01/L0BGiIEuQBjTOA24XoYfD7v9CRMnCjNnl3X5kBAuvtu9wwCjtfg5FhCDX9vgOMIQS5hyhiTZJcspx6H62EYNMg7PQnl5dKMGcevKO6WQ3fxPqQYS6jh7w1QhxAExEkynXrcVA+DV3oS3DoI2I52EWqA2DBjNBAH4b7dDx/u3R1TU7PvZme7v654z25eXl4XYM48s2W1mz7rOuAm9AQBceDWXoeW8nIPQzwHAcezl4/ByYB70BMExAHf7t0pHteSsqOXj2tcAe5ATxAQB3y7d6+W9mbZ1cvn5V42IFnQEwTESby+3cdr7Anig14+IHnREwTEUUu/3SfTGWbJgl4+IHkRgpA0vD5HT6Tzx5SXS6WlPh061DrxjTSUV6YFABAdDochKSxadDxApKTUfXP32o6qqbEn9b0Ox+tsJZ9vmGpra3XrrYlvq1vZeSjRC9MCAIgOPUHwPK9c1LM5zV0H6uQ6LcunKVNSPVenXTiUCCBahCB43q5dvqSYo6e5sSehe4p8CanT7YcakyUIA0gsQhA8r1cvyzMX9WxOU2NPQvcUWbbX6XQPSyQBLFknqwRgL1eEoM8//1zXX3+9OnXqpDZt2qhv377atGmT081CGG7rFUi2s3fCnWF2cp0pKQE9+WStrXU63cNycgBbvNgXcr3mDiUCQCiOh6Cvv/5aF110kdLS0vTKK6/oww8/1O9+9zudeuqpTjcNITjdKxCOKWfv1NdZUvKdFi4s0YQJlq3P52QPS6gANmVKasiz4rwWhN32RQIwleNnh82dO1c5OTlavHhxcFleXp6DLUI4br9IqCln72RnS127Wvrb376x/bmcnCgw3Bio/fvbhVzfK5eiSIYzGYFk4XhP0EsvvaQLLrhAP//5z9WlSxf94Ac/0NNPP+10sxAC4y6c4WSvgZM9LOHGQGVlVYW9j9svReH04UUADTneE/TJJ5+ouLhYhYWF+s///E+99957uu2225Senq7x48eHvE9NTY1qamqCtysrKyVJfr9ffr8/Ie12i/p6E1H36adLKSmtFAgcH5eRmmopN/c7OfGyt6T28vK6s8p69bIi2mFGu368LF7s0+TJqQoEfEpJsVRcXKsJE6yEbvcbbqg7/Ll7t089e9bVn4jt3bWrVFxcNw1Aba1PqamWfv/7b9W58zee/Zz/858+BQIN/+zW1kofffSdunZt+tBmIre521C72bXbyWdZlr2DCpqRnp6uCy64QBs2bAguu+222/Tee+9p48aNIe8za9YsFRUVNVq+bNkytW3b1ra2nujQodbav/97yso6ps6d7T8s4RYlJT1UXNxPgUCKUlICmjz5fRUU7HO6WVEpKemhJ5/sL8vyyeezNGVKWZM1RLt+vBw61Fq33DJMlnU8dKakBLRwYYlR77m6z1o7ZWVVeb5utikQuerqao0dO1YVFRXKzMy05TkcD0G5ubkqKCjQf//3fweXFRcX68EHH9Tnn38e8j6heoJycnK0f/9+derUyfY2h/t27gS/36+SkhIVFBQoLS0tIc9ZXt6wVyDa+8arRyWW2svLpV69Gvdm7dz5Xcj2RLt+PJWW+jRsWOPO2pKS7zR48LcJ3+5Oqn/fnH66Xx9++Jqn6168uGHv1pNPRvb3w4nPultQu5m1Hz58WFlZWbaGIMcPh1100UXasWNHg2Uff/yxcnNzw94nIyNDGRkZjZanpaXZ/iYpL5cmTz7xmL5PU6a00uWXOzsOIRG118vLq/sXLbsGhEZT+969oQfbfvppmvLyGl92obn17XTOOaEHJZ99diulpdXtNBO53Z3S8H2TqsmTe+jyy71b9623SpdfXj+A26fs7Oj+DJuwzcOhdrNqT0S9jg+MvuOOO/T222/rN7/5jXbt2qVly5Zp4cKFmjp1qtNNC4nBwbFxy4DQpuaTCXX6v5Pzz3jttG87NH7f+FRc3K/Z943bT0F3+wBuwBSOh6ALL7xQK1eu1PLly3XuuefqgQce0Pz583Xdddc53bSQmJStaeF2Pm4Jj+GChRQ6pEnOBhFT5j8KJ9T7JhBI0e7doSdNlNw7lxUA93H8cJgk/fSnP9VPf/pTp5sRkfqd6KRJdTtxE7+dh9PU4S4n55s5Waj5ZNatCx/SnJ5/xpT5j0IJ9b5JSQmoZ8/QY2jcPpdVPTuvdg8gco73BHmR09/O3djV39zhLrcd2jn5cERzPXxeOXzhxvdGSzR+31iaPPn9sNvBLT2OTaGnCnAPQlCMnNopRnotpUSLZOfjdHhsittCWiySded64vtm587vmpyewO2Hq90yNg5AHUKQi538rT6aayklWqQ7Hzf3qLg5pDUn2Xeukb5v3B5mvdBTBZjEFWOC0Fio8TVnnBHdtZQSKVnGSnl1/E1TO1cv1tMSTo/haoqbxsYBoCcoyE1jKcJ9q//e96K/llIiebknxevcfhgo0dza4+j2nirANIQguW8sRbhv9VVVjf+APvlkbczT7dsR/Ny483FTwLWL23auJrzmseLLAuAexocgN46laOpb/cl/QGO9XIfbgp9dTKlTcs/O1aTXPFZu/LIAmMj4EOTGgYrNfatv6R/QSIOf17/NuzHg2s3pnauJrzkA7zI+BLl1LIWd3+ojCX7hvs17KRi5MeAmO15zAF5ifAhy21iKE8WjxydUYGku+IX7Nv/b33rrMEc8A66Xwp+T3PqlAgBCMT4ESe4ZSxFPTY3LaC74hfs2f/fd3jrMEa+AyxiXyLn5SwUAnMyoeYKaul5PS+aHcdt1gCK5flJTc6mEvl6TN+ehaemcMV65FpWbuHmeHgA4kTE9QXZ9m3djL0Gk4zLCHW4L9W1+7lzvHuZoyWFFxrjExukB2gAQCSNCkF1nrLj1TJh4jMs4+RDhnXeaeZgj0WNcGHsEAIljRAiy69u8W3sJ4jUu4+Rv85GOnUqmHXmo13L27LptH+/63NirCADJzIgxQXZdr8fN1wGya1xGc2OnQl3zzOsDzU98LTdtOj5APJ71MfYIABLPiJ4gu85YcfuZMIkel+HWw4PxkJ1dFyajOUMumh4xt/YqAkAyMyIESfadBu/l0+vjfdgq2Xfk0dQX7aEt5tcBgMQzJgRJsfWMRBIUQj1uebn0wgt1/+zoCWlpgLFj/Emy78gjrS+WHjG39yoCQDIyKgRFK5qgcGIoWbRI6tFDuuaaun89esR3kOuJ7erVq5VKSnpEdX+7Dlsl+4480vpi7RHzcq8iAHiREQOjYxHNQNUTBwP7fHXLrBMu7m5Zdb+PxyDXxu3yqbi4n375y1rl5UX2GE3tpFvavmSfKC+S+loyYL4lk3YCAKKTdD1B8RrnEum3+ZNDiWU1DED1AoH4jI0J1a5AIEW7d/sifgy7D1sl+0R5zdWX7D1iAJAskioEPfecL27jXCINCqFCSSgpKfEJGaHalZISUM+eIZJXGOyk7cehLQBwv6QKQXfckRq305cjDQqhQonPd/ywWP3thQvjEzIat8vS5MnvR/3Y7KTtl+w9YgDgdUk1JsiyGh4SCjfOJdIJ/SIZ/1EfSiZNqnu++rA0fLi0cWPdOoMGxXdHeGK7cnO/0wcf7JN0btSPw/gTAIDJkioE+XxWg/E40Zy+HG7QciRBIVxY+vnPY6+lOfXt8vulDz6w73kAAEhWSXU47NFHa207fbk5HPrwvmS65hkAoHlJFYKuv95qdpxLsk/oh9hw8VIAME9ShSCJ05cRvWS+5hkAILykGhMUqWSf0A/RsXPySACAexkZgiTOjMJxLZnhGQDgXa47HDZnzhz5fD5Nnz7d6abAEBwiBQAzuaon6L333tMf/vAHnXfeeU43BYbhECkAmMc1PUHHjh3Tddddp6efflqnnnqq081xJU7hthfTHACAWVzTEzR16lSNHDlS+fn5evDBB5tct6amRjU1NcHblZWVkiS/3y+/329rO52yeLFPkyenKhDwKSXFUnFxrSZMsIL1JmvdTaF282o3tW6J2k/8aRJqt5fPskJd8zyxVqxYoYceekjvvfeeWrdurSFDhqh///6aP39+yPVnzZqloqKiRsuXLVumtm3b2tzaxDt0qLVuuWVYg8uCpKQEtHBhiTp3/sbBloV26FBr7d//PWVlHXNl+wAA7lddXa2xY8eqoqJCmZmZtjyH4z1Bn332mW6//XaVlJSodevWEd3nnnvuUWFhYfB2ZWWlcnJyNHToUHXq1MmupjqmtNTX6LpogUCKcnMv1eDB36qkpEQFBQVKS0tzqIXHheuxsoPf73dV7Ylkau2m1i1RO7WbV/vhw4dtfw7HQ9DmzZv15Zdf6vzzzw8uq62t1fr16/XEE0+opqZGqfWn7fy/jIwMZWRkNHqstLS0pHyTnHNO6FO4zz67ldLS6gKGG2ovL5cmTz5x0kGfpkxppcsvt3ecjRtqd4qptZtat0Tt1G6ORNTr+MDoSy+9VNu2bVNZWVnw3wUXXKDrrrtOZWVljQKQibxyCrdd12UDAMAOjvcEtW/fXueee26DZe3atVOnTp0aLTeZF07hZtJBAICXON4ThMi5/RRur/RYAQAguaAnKJTS0lKnm4AYeaHHCgAAyaUhCN7GddkAAF7A4TCHMPszAADOIgQ5YNEiKTdX+slP6n4uWuR0iwAAMA8hKMHKy6Vbbz1xLh1p0iR6hAAASDRCUDPifdiKuXQAAHAHQlAT7DhsVT+XzomYSwcAgMQjBIVh12GrRM+lwwBsAABCIwSFYedhq4kTpb1768LJ3r11t+3AAGwAAMIjBIVh92Eru2d/ZgA2AABNIwSF4fVLQDAAGwCApjFjdBO8fAkILmYKAEDT6AlqhtsvWhqO13uyAACwGz1BSczLPVkAANiNEJTkuJgpAAChcTgMAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAAMBIhCAAAGAkQhAAADASIQgAABiJEAQAAIxECAIAAEYiBAEAACMRggAAgJEIQQAAwEiEIAAAYCRCEAAAMJIrQtDs2bN14YUXqn379urSpYtGjx6tHTt2ON0sAACQxFwRgt544w1NnTpVb7/9tkpKSuT3+zVs2DBVVVU53TQAAJCkWjndAElas2ZNg9tLlixRly5dtHnzZv34xz92qFUAACCZuSIEnayiokKS1LFjx5C/r6mpUU1NTfB2ZWWlJMnv98vv99vfQBepr9e0uiVqP/GnKUytW6L2E3+ahNrt5bMsy7L9WaIQCAR0xRVX6MiRI3rzzTdDrjNr1iwVFRU1Wr5s2TK1bdvW7iYCAACbVVdXa+zYsaqoqFBmZqYtz+G6EDR58mS98sorevPNN5WdnR1ynVA9QTk5Odq/f786deqUqKa6gt/vV0lJiQoKCpSWluZ0cxKK2s2r3dS6JWqndvNqP3z4sLKysmwNQa46HDZt2jS9/PLLWr9+fdgAJEkZGRnKyMhotDwtLc24N0k9aqd2k5hat0Tt1G6ORNTrihBkWZZ+8YtfaOXKlSotLVVeXp7TTQIAAEnOFSFo6tSpWrZsmVavXq327dvrwIEDkqQOHTqoTZs2DrcOAAAkI1fME1RcXKyKigoNGTJEWVlZwX/PP/+8000DAABJyhU9QS4bmw0AAAzgip4gAACARCMEAQAAIxGCAACAkQhBAADASIQgAABgJEIQAAAwEiEIAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAAMBIhCAAAGAkQhAAADASIQgAABiJEAQAAIxECAIAAEYiBAEAACMRggAAgJEIQQAAwEiEIAAAYCRCEAAAMBIhCAAAGIkQBAAAjEQIAgAARiIEAQAAIxGCAACAkQhBAADASIQgAABgJEIQAAAwkmtC0IIFC3T66aerdevWGjhwoN59912nmwQAAJKYK0LQ888/r8LCQs2cOVNbtmxRv379NHz4cH355ZdONw0AACQpV4SgefPm6ZZbbtGECRP0/e9/X0899ZTatm2rZ555xummAQCAJOV4CPr222+1efNm5efnB5elpKQoPz9fGzdudLBlAAAgmbVyugGHDh1SbW2tunbt2mB5165d9dFHH4W8T01NjWpqaoK3KyoqJElfffWVfQ11Kb/fr+rqah0+fFhpaWlONyehqN282k2tW6J2ajev9vp9umVZtj2H4yEoFrNnz1ZRUVGj5WeddZYDrQEAAHY5fPiwOnToYMtjOx6COnfurNTUVB08eLDB8oMHD6pbt24h73PPPfeosLAwePvIkSPKzc3Vvn37bHuh3KqyslI5OTn67LPPlJmZ6XRzEorazavd1Lolaqd282qvqKhQjx491LFjR9uew/EQlJ6erh/+8Idau3atRo8eLUkKBAJau3atpk2bFvI+GRkZysjIaLS8Q4cOxr1J6mVmZlK7gUyt3dS6JWqndvOkpNg3fNnxECRJhYWFGj9+vC644AINGDBA8+fPV1VVlSZMmOB00wAAQJJyRQi65ppr9L//+7+67777dODAAfXv319r1qxpNFgaAAAgXlwRgiRp2rRpYQ9/NScjI0MzZ84MeYgs2VE7tZvE1Lolaqd2areDz7Lz3DMAAACXcnyyRAAAACcQggAAgJEIQQAAwEiuDUELFizQ6aefrtatW2vgwIF69913m1z/z3/+s84++2y1bt1affv21d/+9rcGv7csS/fdd5+ysrLUpk0b5efna+fOnXaWEJNo6n766af1ox/9SKeeeqpOPfVU5efnN1r/xhtvlM/na/Dvsssus7uMmERT+5IlSxrV1bp16wbreGWbS9HVPmTIkEa1+3w+jRw5MriOV7b7+vXrNWrUKHXv3l0+n0+rVq1q9j6lpaU6//zzlZGRoV69emnJkiWN1on270eiRVv3iy++qIKCAp122mnKzMzUoEGD9OqrrzZYZ9asWY22+dlnn21jFbGJtvbS0tKQ7/cDBw40WM/t21yKvvZQn2Ofz6c+ffoE1/HCdp89e7YuvPBCtW/fXl26dNHo0aO1Y8eOZu+XiP26K0PQ888/r8LCQs2cOVNbtmxRv379NHz4cH355Zch19+wYYOuvfZaTZw4UVu3btXo0aM1evRobd++PbjOww8/rMcff1xPPfWU3nnnHbVr107Dhw/XN998k6iymhVt3aWlpbr22mu1bt06bdy4UTk5ORo2bJg+//zzButddtll2r9/f/Df8uXLE1FOVKKtXaqbPOzEuj799NMGv/fCNpeir/3FF19sUPf27duVmpqqn//85w3W88J2r6qqUr9+/bRgwYKI1t+zZ49GjhypoUOHqqysTNOnT9fNN9/cIBDE8l5KtGjrXr9+vQoKCvS3v/1Nmzdv1tChQzVq1Cht3bq1wXp9+vRpsM3ffPNNO5rfItHWXm/Hjh0NauvSpUvwd17Y5lL0tT/22GMNav7ss8/UsWPHRp91t2/3N954Q1OnTtXbb7+tkpIS+f1+DRs2TFVVVWHvk7D9uuVCAwYMsKZOnRq8XVtba3Xv3t2aPXt2yPWvvvpqa+TIkQ2WDRw40Jo0aZJlWZYVCASsbt26Wb/97W+Dvz9y5IiVkZFhLV++3IYKYhNt3Sf77rvvrPbt21tLly4NLhs/frx15ZVXxrupcRdt7YsXL7Y6dOgQ9vG8ss0tq+Xb/dFHH7Xat29vHTt2LLjMK9v9RJKslStXNrnOr371K6tPnz4Nll1zzTXW8OHDg7db+nomWiR1h/L973/fKioqCt6eOXOm1a9fv/g1LAEiqX3dunWWJOvrr78Ou47XtrllxbbdV65cafl8Pmvv3r3BZV7c7l9++aUlyXrjjTfCrpOo/brreoK+/fZbbd68Wfn5+cFlKSkpys/P18aNG0PeZ+PGjQ3Wl6Thw4cH19+zZ48OHDjQYJ0OHTpo4MCBYR8z0WKp+2TV1dXy+/2NrrNSWlqqLl26qHfv3po8ebIOHz4c17a3VKy1Hzt2TLm5ucrJydGVV16pf/zjH8HfeWGbS/HZ7osWLdKYMWPUrl27Bsvdvt1j0dxnPR6vpxcEAgEdPXq00Wd9586d6t69u8444wxdd9112rdvn0MtjL/+/fsrKytLBQUFeuutt4LLTdnmUt1nPT8/X7m5uQ2We227V1RUSFKT1wRL1H7ddSHo0KFDqq2tbTRbdNeuXRsdA6534MCBJtev/xnNYyZaLHWf7O6771b37t0bvCkuu+wyPfvss1q7dq3mzp2rN954QyNGjFBtbW1c298SsdTeu3dvPfPMM1q9erWee+45BQIBDR48WOXl5ZK8sc2llm/3d999V9u3b9fNN9/cYLkXtnsswn3WKysr9a9//SsunyMveOSRR3Ts2DFdffXVwWUDBw7UkiVLtGbNGhUXF2vPnj360Y9+pKNHjzrY0pbLysrSU089pb/85S/6y1/+opycHA0ZMkRbtmyRFJ+/nV7wxRdf6JVXXmn0Wffadg8EApo+fbouuuginXvuuWHXS9R+3TUzRqNl5syZoxUrVqi0tLTBAOExY8YE/9+3b1+dd9556tmzp0pLS3XppZc60dS4GDRokAYNGhS8PXjwYJ1zzjn6wx/+oAceeMDBliXWokWL1LdvXw0YMKDB8mTd7pCWLVumoqIirV69usG4mBEjRgT/f95552ngwIHKzc3VCy+8oIkTJzrR1Ljo3bu3evfuHbw9ePBg7d69W48++qj++Mc/OtiyxFq6dKlOOeWU4IXG63ltu0+dOlXbt293zbgl1/UEde7cWampqTp48GCD5QcPHlS3bt1C3qdbt25Nrl//M5rHTLRY6q73yCOPaM6cOXrttdd03nnnNbnuGWecoc6dO2vXrl0tbnO8tKT2emlpafrBD34QrMsL21xqWe1VVVVasWJFRH/o3LjdYxHus56Zmak2bdrE5b3kZitWrNDNN9+sF154odGhgpOdcsopOuusszy/zUMZMGBAsK5k3+ZS3VlQzzzzjMaNG6f09PQm13Xzdp82bZpefvllrVu3TtnZ2U2um6j9uutCUHp6un74wx9q7dq1wWWBQEBr165t8M3/RIMGDWqwviSVlJQE18/Ly1O3bt0arFNZWal33nkn7GMmWix1S3Wj4x944AGtWbNGF1xwQbPPU15ersOHDysrKysu7Y6HWGs/UW1trbZt2xasywvbXGpZ7X/+859VU1Oj66+/vtnnceN2j0Vzn/V4vJfcavny5ZowYYKWL1/eYDqEcI4dO6bdu3d7fpuHUlZWFqwrmbd5vTfeeEO7du2K6AuPG7e7ZVmaNm2aVq5cqddff115eXnN3idh+/WohnQnyIoVK6yMjAxryZIl1ocffmjdeuut1imnnGIdOHDAsizLGjdunDVjxozg+m+99ZbVqlUr65FHHrH++c9/WjNnzrTS0tKsbdu2BdeZM2eOdcopp1irV6+2PvjgA+vKK6+08vLyrH/9618Jry+caOueM2eOlZ6ebv3P//yPtX///uC/o0ePWpZlWUePHrXuvPNOa+PGjdaePXusv//979b5559vnXnmmdY333zjSI3hRFt7UVGR9eqrr1q7d++2Nm/ebI0ZM8Zq3bq19Y9//CO4jhe2uWVFX3u9iy++2LrmmmsaLffSdj969Ki1detWa+vWrZYka968edbWrVutTz/91LIsy5oxY4Y1bty44PqffPKJ1bZtW+uuu+6y/vnPf1oLFiywUlNTrTVr1gTXae71dINo6/7Tn/5ktWrVylqwYEGDz/qRI0eC6/zyl7+0SktLrT179lhvvfWWlZ+fb3Xu3Nn68ssvE15fU6Kt/dFHH7VWrVpl7dy509q2bZt1++23WykpKdbf//734Dpe2OaWFX3t9a6//npr4MCBIR/TC9t98uTJVocOHazS0tIG79/q6urgOk7t110ZgizLsn7/+99bPXr0sNLT060BAwZYb7/9dvB3l1xyiTV+/PgG67/wwgvWWWedZaWnp1t9+vSx/vrXvzb4fSAQsO69916ra9euVkZGhnXppZdaO3bsSEQpUYmm7tzcXEtSo38zZ860LMuyqqurrWHDhlmnnXaalZaWZuXm5lq33HKL6/4w1Ium9unTpwfX7dq1q3X55ZdbW7ZsafB4XtnmlhX9+/2jjz6yJFmvvfZao8fy0navP/355H/19Y4fP9665JJLGt2nf//+Vnp6unXGGWdYixcvbvS4Tb2ebhBt3ZdcckmT61tW3VQBWVlZVnp6uvVv//Zv1jXXXGPt2rUrsYVFINra586da/Xs2dNq3bq11bFjR2vIkCHW66+/3uhx3b7NLSu29/uRI0esNm3aWAsXLgz5mF7Y7qFqltTgs+vUfp2ryAMAACO5bkwQAABAIhCCAACAkQhBAADASIQgAABgJEIQAAAwEiEIAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAXGfQoEHy+XzauHFjg+WVlZXq37+/MjIyVFJS4lDrACQLQhAA15k7d64k6de//nVw2bfffqurrrpKH3zwgZYuXaqCggKnmgcgSRCCALjOj3/8Y40cOVKvv/66SktLZVmWbrzxRr3++ut69NFHNWbMGKebCCAJcBV5AK60bds29e/fX4MHD9aAAQM0b9483XPPPfrNb37jdNMAJAlCEADXGj9+vJ599llJ0k033aRFixY1WufFF19UcXGxNm/erK+//lp79uzR6aefnuCWAvAiDocBcK3TTjtNktS+fXstWLAg5DpVVVX68Y9/rPvvvz+RTQOQBFo53QAACOWJJ57Q7373O3Xt2lUHDx7U0qVLNWnSpEbrjRs3TpK0ffv2RDcRgMfREwTAdV544QXdfvvtGjp0qLZu3aoOHTqoqKhI1dXVTjcNQBIhBAFwlbVr12rcuHHq27evVq1apaysLN1xxx3av3+/HnvsMaebByCJMDAagGts2bJFQ4YMUadOnbRhwwZlZWVJqpskMS8vT7W1tfrkk0/UsWPHRvfdvn27+vbty8BoABGjJwiAK+zevVuXX3650tPTtWbNmmAAkqTMzEzdfffdqqio0OzZsx1sJYBkQk8QgKRATxCAaHF2GABP++qrr7Rv3z7t3r1bkvThhx/qyJEj6tGjR8jDZgBQj54gAJ62ZMkSTZgwodHyxYsX68Ybb0x8gwB4BiEIAAAYiYHRAADASIQgAABgJEIQAAAwEiEIAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAAMBIhCAAAGAkQhAAADASIQgAABjp/wDZgfvVd3oOwwAAAABJRU5ErkJggg==",
+ "text/plain": [
+ "<Figure size 600x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# extra code – generates and saves Figure 4–1\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.plot(X, y, \"b.\")\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.axis([0, 2, 0, 15])\n",
+ "plt.grid()\n",
+ "save_fig(\"generated_data_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.preprocessing import add_dummy_feature\n",
+ "\n",
+ "X_b = add_dummy_feature(X) # add x0 = 1 to each instance\n",
+ "theta_best = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21509616],\n",
+ " [2.77011339]])"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "theta_best"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21509616],\n",
+ " [9.75532293]])"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "X_new = np.array([[0], [2]])\n",
+ "X_new_b = add_dummy_feature(X_new) # add x0 = 1 to each instance\n",
+ "y_predict = X_new_b @ theta_best\n",
+ "y_predict"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 600x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "plt.figure(figsize=(6, 4)) # extra code – not needed, just formatting\n",
+ "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
+ "plt.plot(X, y, \"b.\")\n",
+ "\n",
+ "# extra code – beautifies and saves Figure 4–2\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.axis([0, 2, 0, 15])\n",
+ "plt.grid()\n",
+ "plt.legend(loc=\"upper left\")\n",
+ "save_fig(\"linear_model_predictions_plot\")\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(array([4.21509616]), array([[2.77011339]]))"
+ ]
+ },
+ "execution_count": 11,
+ "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": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21509616],\n",
+ " [9.75532293]])"
+ ]
+ },
+ "execution_count": 12,
+ "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": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21509616],\n",
+ " [2.77011339]])"
+ ]
+ },
+ "execution_count": 13,
+ "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": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21509616],\n",
+ " [2.77011339]])"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.linalg.pinv(X_b) @ y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Gradient Descent\n",
+ "## Batch Gradient Descent"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21300182],\n",
+ " [2.77196257]])"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "eta = 0.1 # learning rate\n",
+ "n_epochs = 1000\n",
+ "m = len(X_b) # number of instances\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "theta = np.random.randn(2, 1) # randomly initialized model parameters\n",
+ "\n",
+ "# IMPLEMENT THE BATCH GRADIENT DESCENT\n",
+ "prev = theta\n",
+ "gv = 2/m * X_b.T @ (X_b@theta - y)\n",
+ "theta = theta - eta * gv\n",
+ "\n",
+ "while np.linalg.norm(theta - prev) > 0.0001:\n",
+ " prev = theta\n",
+ " gv = 2/m * X_b.T @ (X_b@theta - y)\n",
+ " theta = theta - eta * gv\n",
+ "\n",
+ "theta"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The trained model parameters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[4.21509616],\n",
+ " [2.77011339]])"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "theta"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "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": [
+ "# extra code – generates and saves Figure \n",
+ "\n",
+ "import matplotlib as mpl\n",
+ "\n",
+ "def plot_gradient_descent(theta, eta):\n",
+ " m = len(X_b)\n",
+ " plt.plot(X, y, \"b.\")\n",
+ " n_epochs = 1000\n",
+ " n_shown = 50\n",
+ " theta_path = []\n",
+ " for epoch in range(n_epochs):\n",
+ " if epoch < n_shown:\n",
+ " y_predict = X_new_b @ theta\n",
+ " color = mpl.colors.rgb2hex(plt.cm.OrRd(epoch / n_shown + 0.15))\n",
+ " plt.plot(X_new, y_predict, linestyle=\"solid\", color=color)\n",
+ " gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
+ " theta = theta - eta * gradients\n",
+ " theta_path.append(theta)\n",
+ " plt.xlabel(\"$x_1$\")\n",
+ " plt.axis([0, 2, 0, 15])\n",
+ " plt.grid()\n",
+ " plt.title(fr\"$\\eta = {eta}$\")\n",
+ " return theta_path\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "theta = np.random.randn(2, 1) # random initialization\n",
+ "\n",
+ "plt.figure(figsize=(10, 4))\n",
+ "plt.subplot(131)\n",
+ "plot_gradient_descent(theta, eta=0.02)\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.subplot(132)\n",
+ "theta_path_bgd = plot_gradient_descent(theta, eta=0.1)\n",
+ "plt.gca().axes.yaxis.set_ticklabels([])\n",
+ "plt.subplot(133)\n",
+ "plt.gca().axes.yaxis.set_ticklabels([])\n",
+ "plot_gradient_descent(theta, eta=0.5)\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 = [] # extra code – we need to store the path of theta in the\n",
+ " # parameter space to plot the next figure"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "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": [
+ "n_epochs = 50\n",
+ "t0, t1 = 5, 50 # learning schedule hyperparameters\n",
+ "\n",
+ "def learning_schedule(t):\n",
+ " return t0 / (t + t1)\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "theta = np.random.randn(2, 1) # random initialization\n",
+ "\n",
+ "n_shown = 20 # extra code – just needed to generate the figure below\n",
+ "plt.figure(figsize=(6, 4)) # extra code – not needed, just formatting\n",
+ "\n",
+ "for epoch in range(n_epochs):\n",
+ " for iteration in range(m):\n",
+ "\n",
+ " # extra code – these 4 lines are used to generate the figure\n",
+ " if epoch == 0 and iteration < n_shown:\n",
+ " y_predict = X_new_b @ theta\n",
+ " color = mpl.colors.rgb2hex(plt.cm.OrRd(iteration / n_shown + 0.15))\n",
+ " plt.plot(X_new, y_predict, color=color)\n",
+ "\n",
+ " # IMPLEMENT SGD HERE\n",
+ " \n",
+ " theta_path_sgd.append(theta) # extra code – to generate the figure\n",
+ "\n",
+ "# extra code – this section beautifies and saves Figure 4–10\n",
+ "plt.plot(X, y, \"b.\")\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.axis([0, 2, 0, 15])\n",
+ "plt.grid()\n",
+ "save_fig(\"sgd_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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/html": [
+ "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SGDRegressor</label><div class=\"sk-toggleable__content\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre></div></div></div></div></div>"
+ ],
+ "text/plain": [
+ "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)"
+ ]
+ },
+ "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-5, penalty=None, eta0=0.01,\n",
+ " n_iter_no_change=100, random_state=42)\n",
+ "sgd_reg.fit(X, y.ravel()) # y.ravel() because fit() expects 1D targets\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(array([4.21278812]), array([2.77270267]))"
+ ]
+ },
+ "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": "markdown",
+ "metadata": {},
+ "source": [
+ "The code in this section is used to generate the next figure, it is not in the book."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "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": [
+ "# extra code – this cell generates and saves Figure 4–11\n",
+ "\n",
+ "from math import ceil\n",
+ "\n",
+ "n_epochs = 50\n",
+ "minibatch_size = 20\n",
+ "n_batches_per_epoch = ceil(m / minibatch_size)\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "theta = np.random.randn(2, 1) # random initialization\n",
+ "\n",
+ "t0, t1 = 200, 1000 # learning schedule hyperparameters\n",
+ "\n",
+ "def learning_schedule(t):\n",
+ " return t0 / (t + t1)\n",
+ "\n",
+ "#IMPLEMENT MINI BACTH GRADIENT DESCENT"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Polynomial Regression"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "np.random.seed(42)\n",
+ "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": 25,
+ "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": [
+ "# extra code – this cell generates and saves Figure 4–12\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.plot(X, y, \"b.\")\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.axis([-3, 3, 0, 10])\n",
+ "plt.grid()\n",
+ "save_fig(\"quadratic_data_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([-0.75275929])"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.preprocessing import PolynomialFeatures\n",
+ "\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": 81,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([-0.75275929, 0.56664654])"
+ ]
+ },
+ "execution_count": 81,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "X_poly[0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
+ ]
+ },
+ "execution_count": 28,
+ "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": 29,
+ "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": [
+ "# extra code – this cell generates and saves Figures\n",
+ "\n",
+ "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",
+ "\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.plot(X, y, \"b.\")\n",
+ "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.legend(loc=\"upper left\")\n",
+ "plt.axis([-3, 3, 0, 10])\n",
+ "plt.grid()\n",
+ "save_fig(\"quadratic_predictions_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "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": [
+ "# extra code – this cell generates and saves \n",
+ "\n",
+ "from sklearn.preprocessing import StandardScaler\n",
+ "from sklearn.pipeline import make_pipeline\n",
+ "\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "\n",
+ "for style, width, degree in ((\"r-+\", 2, 1), (\"b--\", 2, 2), (\"g-\", 1, 300)):\n",
+ " polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
+ " std_scaler = StandardScaler()\n",
+ " lin_reg = LinearRegression()\n",
+ " polynomial_regression = make_pipeline(polybig_features, std_scaler, lin_reg)\n",
+ " polynomial_regression.fit(X, y)\n",
+ " y_newbig = polynomial_regression.predict(X_new)\n",
+ " label = f\"{degree} degree{'s' if degree > 1 else ''}\"\n",
+ " plt.plot(X_new, y_newbig, style, label=label, linewidth=width)\n",
+ "\n",
+ "plt.plot(X, y, \"b.\", linewidth=3)\n",
+ "plt.legend(loc=\"upper left\")\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$\", rotation=0)\n",
+ "plt.axis([-3, 3, 0, 10])\n",
+ "plt.grid()\n",
+ "save_fig(\"high_degree_polynomials_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Learning Curves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "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": [
+ "from sklearn.model_selection import learning_curve\n",
+ "\n",
+ "train_sizes, train_scores, valid_scores = learning_curve(\n",
+ " LinearRegression(), X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
+ " scoring=\"neg_root_mean_squared_error\")\n",
+ "train_errors = -train_scores.mean(axis=1)\n",
+ "valid_errors = -valid_scores.mean(axis=1)\n",
+ "\n",
+ "plt.figure(figsize=(6, 4)) # extra code – not needed, just formatting\n",
+ "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
+ "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
+ "\n",
+ "# extra code – beautifies and saves Figure 4–15\n",
+ "plt.xlabel(\"Training set size\")\n",
+ "plt.ylabel(\"RMSE\")\n",
+ "plt.grid()\n",
+ "plt.legend(loc=\"upper right\")\n",
+ "plt.axis([0, 80, 0, 2.5])\n",
+ "save_fig(\"underfitting_learning_curves_plot\")\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.pipeline import make_pipeline\n",
+ "\n",
+ "polynomial_regression = make_pipeline(\n",
+ " PolynomialFeatures(degree=10, include_bias=False),\n",
+ " LinearRegression())\n",
+ "\n",
+ "train_sizes, train_scores, valid_scores = learning_curve(\n",
+ " polynomial_regression, X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
+ " scoring=\"neg_root_mean_squared_error\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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OOeXIj7FvH8yZE0rfvnDWWb055hjo3fvIjy0iEhXvhagbzWwQcDyww923VqlyJ7A52cFJfOIZhNCtG5xwArRsWXu9tWth1aqK7Q0bYMOGY5gzB84+O7SKvvCF0EoSETkScc8F5+6HgBU1PFbtfkmPs86CN94I981g4EAYOhROOimUIUOgS5f4juUOy5bBQw/Bo4/CRx9V7H/uuVCaN4devaBHj8qle/eK+926QUFBCt6siOSNuBKQmd0YTz13v+fIwpH6+NnPQqukTRsYPLjuVk5tzEI33imnwD33wIIF8P/+3y6WLWv/ySwL+/eHltLatTUfp3t3uP9++Nzn6h+LiOS3eFtAdwM7gWJqXozOASWgDGjcGD772eQft1kzmDwZunR5jX79RvPwwzB7Nrz1Vt3P3bo1JMU//hE+//nkxyYiuS/eBPQS4fzP08Bv3H1J6kKSbHT00XDrrXDLLbBrF2zZEpLMli2Hl/XrYc8eKC2FiRNh7ly44IJMvwMRyTbxDkIYaWbHA1cC88zsQ+A3wBx3fz+VAUp2MYMOHUI58cTq67z7LowZExJRaSlcfLGSkIgcLu7ZsN39DXe/kXBB6m3AaGCjmS0ws6Ypik9yUM+eUFQExx4btqNJaMGCjIYlIlkm4eUY3L3U3ecCPwGWAp8Dmic5LslxRx99eBKaNElJSEQqJJSAzKyPmX3PzN4Bfg38A+jv7h+lIjjJbdEk1K9f2FYSEpFY8a4HdJmZPQesAgYCVwN93P277v52KgOU3FZdElJ3nIhA/KPgfgtsInS77STM/XacVbkEX9cBSXV69AhJaPToMCnqoUMhCT30EIwYAU2bhtKsWcX9RlqrVyTvxZuANhGu87m0ljq6DkhqFE1CY8aE64gOHYIvf7nm+o0bh0TUoUNoRfXoEW5jS3T2hcLCtL0NEUmieIdh96mrjpn1POJoJK/16AGLF1ckodocOhTK3r2waVPN9czCcPDx48OsCyNHJjdmEUmduOeCq4mZdQVuJ1wjpNFwUqtoS+jWW8OccwcOVJSSkor78XKHFStC+cEPoF07GDr0U2zeDOeeC506peytiMgRincuuKOA+4CxQCnwQ+DnwB3AdMLghK+mJkTJN927hyl9auIeBiuUlMD27WF2hc2bK5fovvfe45M56gA+/BCef74Lzz8fWkcjRoTW0ZlnwrBh0LZtyt+e1KKsLExwu2tX5fLBB+EWwkzrLVqEOQ2ru9+uHXTsGCbFldwWbwvoLsIy3HOA84B7gc8CLYFx7v631IQnDZEZNGkSSps2FSPoqrNnT5ih++mn4ZlnwvRAUe5hcb6lSyv29esXEtHJJ4cydCi0b5+69xKrtBSWLIGdO6Fr11C6dUvsGO6we3dItIWF0KpV+HJuHOf/ZPfQwty9O/zt9u8PrcROnRIb+HHwYCNWroQ33wxl69awjtS+feGY1d3fvTskn9gfDEeiZcuQiDp1qvm2Uyfo3BmKixvjHt/SJZI+8SagzwFXuPuzZvYLwsJ06939hpRFJhKH1q3hwgtDcQ+rv/785xtYs6YvL7wA5VUWil+3LpTHH6/Yd8wxMHw4jB0bJk6Nd+mKeJSVwd/+Br//fZiY9YMPDq/TrNmZnyxhEU1MUNE6+PDDyvervicIrYFWrSpK69ahtbB/f0g0u3dXJJ3S0sOfX1hYeaBH7P1WrcLfLJps1q6Fd945M2mJpL727g3lnXfiqX0GhYUVialzZxgwAI4/Pswgf/zxYcCLpFe8Cag7oZsNd99gZiWEC1FFsoZZWPvo8ss3MXp0X3btgr/+FZ59Fl5+GVauDAMbqnr77VD+8IdwjFGjQkKbMCGsrZSo8nL45z/hscfCHHjbt9dev6SkgPXrw9x59bV/fyg7dtTv+aWlsHFjKPGpf1OibdvQ6uzQIdxGS7t2oSW3d29Fq2nfvsrbxcUhCe/YUX0irU1pKWzbFgqEz0Wsrl0rJ6SBA0Mrq7AwlCZNKt9GR1/GJvjqSnl5SHyxpVOn8P6bVjOJWWkpfPxxYzZurHycXbtC6zladuyovL1rV4i3c+eKEk220dKxY6gTvewheulD7G061/GKNwE1Ipz7iSoD9iXyQmb2IHA+sN3dB1fzuAE/BcZHjj3V3Zcn8hoisdq3h0suCQVC19Prr4dktHx5uH39dTh4sOI57vDCC6FMnx6+hKLJaOTI0E1VWlrxpbNnT+Xyz3+GRLZlS/Ux9egRugB37Ajnr7ZtS2zQBYQWyVFHhdZVcXEoibRGCgtDEmjTJnyZvv9++FJPhJnTp48xcGBoSfTpE+Jq3rziXE20RPe1alWRZI6Ue/h7R7+EY2+r3t+xA7ZtO8T+/bW/8HvvhfLcc0ceX7xatw5JoVGjis9USQnAGfU63scfhxLPkik1KSgIn5HGjRMr9RHv0wz4nZlF/6s0A35tZpWSkLvXNt/xbGAW8HANj48D+kfKSOB/I7ciSdG0aehqGz68Yt/Bg2E12aKiMDvDP/5RuYtr7Vr40Y9CadkytKASTRhdu4YLbydPhtNOq3yuxR2efnoJ/fqd8ckX4LZtoU5syyB6/6ijQtKI5V7ROiguDl9kxcWh5dC8eUg00dK6dfW/uvfurRjYUXXQx+7doZsymmwGDoTNm//B2LFnJfaHSCKzivcUnW+wNkVFSxg1avQnCWnr1rD0/BtvhJbx6tWhBZlu0R8u2aSsLJR0iDcBzamy/btEX8jd/25mfWqpMgF42N0d+LeZHWVm3dx9W6KvJRKvJk3CQIShQ+Gb3wy/nJ9+OiSjhQvDF3vU3r3xH7djx7AW0uTJYcn0mro1zKBVq0MMGgSDBtXvPZiF5NiyZf3PX7VsGZLLgAHx1d++vZoTUVmuWbMwU3vPnqEVev75FY+VlYVu2GhCWrkydEcePBhavFVvo/ehcoKPJvnYbfdw7i+2uyxaqvuiLyiAFi1KadeusNIx27c/vCsvdtBFu3bhM7p9e0XZsaPy9s6dIdHGXvZQUlL5fjrP7cV7IeoVqQ6EsMzDuzHbmyP7lIAkbTp2hK98JZT9+8N5ggUL4MknK86vNGpU8SXTunXl0r17WPfo7LOT09Uk6VFQEEZI9usXulvTwT10l+3cGVrd0WTTvDn87W//ZPTo0Qkfs1mzcG7pU5+qf0ylpSExRi8Gj7ecdlrir2eexnQXaQE9VcM5oKeAH0ZXW41Mfjrd3ZdVU/cq4CqATp06nfx47JCmHFBcXEyrVq0yHUbcFG/4gtizp5CmTcto2rQ8qcN5c+3vC7kXs+JNvTFjxrzs7sPrrlkhm36jbQFip/M5OrLvMO5+P3A/wMCBA70+vxQyqaioqF6/bjJF8aZWrsULuRez4s1O2TTn8JPAFAtGAR/r/I+ISP5KWwvIzB4lLOPd0cw2A3cChQDu/kvgGcIQ7HWEYdjpOO8kIiIZkrYE5O61LeVAZPTbtWkKR0REMiybuuBERKQBUQISEZGMUAISEZGMUAISEZGMUAISEckXM2ZkOoKEKAGJiOSLmTPrrlNXkkpjEsummRBERPLPjBnxfeknWqesLKy7ELu2CITJ7KJL5VYtrVqFJHXeeWGBoC5dwv5YM2fWKwkdHdaNS4gSkIg0THV96R9J4igvD2t5LF0avtC7dq2YbTS6GFP0tk2byl/67uH5ZWXhfnR75sywLkY04bz6avVTtD/5ZN3v/dRTK+63aFF51TqAG2+sOdbYfS1bfrLOeRdIcIF5JSARaajq+qUfT0sgWmfHjpBsli6Ff/8bXnopTHUd9fWv1x1PzAy3o2uqM3Vq5e3o2hInnwwnnRSmYp83r2K98mhZuDCsllhVQUFYc6Tqcrj33lt3vBCmho8mpnpQAhKR9IinRZGs41RXp7wc1q2DV14Jq9EBXHNNWHdj376Kdc2jBcLqhVXXrI69BejbNywmFI9+/UK31+7d8M474bYmZjUvznP55XDPPWExoKq+8IXD9333u9Uf1z2sXrh9e1gad/v28Py77w4JdPfuw29j7+/bBx99FEp9uHtOlwEDBniuWbx4caZDSIjiTa2MxnvnnfV62mExx3OcMONW7ZJ1HHB/5RX33/zGfdo0/2jwYPdWraIdWqkpvXu733yz+7x57lu2xB9veXmoU1YW7nsNn4l0/f3ieZ2ogwfdP/jAfcMGPzkyo1oiRS0gkYYsnm6m6loT7mH98LfeCmXmzNAdc+hQxWpmVW8Bpk0L3T4FBWHFvqr3Z84Mv66j64pXvS0uDsfp0aPiuQUF4bWj96Nrqg8d+km4baN3evQI+088Ee66C2bNCivANW8ezoVE7zdvDqecErrSalo69MCB0IJ69VU4/vj6r0AY7XqLXau9vuJpYd5555E9HquwsGK9+HpQAhJpqNavD7c/+EHlL9/o/ejtzJlw7LHw5pufJJwz1qypvF45xPfFdd99ddf5yU/qrrN1a911os45hxVjxzJk6tSKk+wQEtC1dcx/PLyO9dWuuQaGDKm9Tjx/l2TViUeKhmG/X4/Vq5WARBqab3879PFH3Xpr3c+ZMqXSZmMI50AOHDi87pgxMHbs4a2badPgZz+raBVFy6JFUFR0+HEuugiuuCIMHW7dumJocc+e8O674bnR0WKxxT0khZjzJx8WFVVOPpCclkA8deL5Qk9WnQzaDAn8KgiUgEQair17Q+viV78K29GT0dOnH34SfsWKihZSrAsvhJtv5p/bt3P6BRdUdB/VdsI8ato0uO66w/fHJsB4jgNw9NF116lLMloCWZ4Usp0SkEg+mzEDbr8dZs+GO+6AbZFekvHj4Yc/DOdCfvjD2o9RTVIoLSqqNGw4LsnqQkpnd5WklKbiEclGyfj17R7O35x4Ivznf4bkM3w4PP88PP00nHBCepNCMk6Qx3sctUxyglpAIulW03UsxcWwaVMoM2eG0VpmYXRU1WIW6nzqU4ePEouW1avDcVevDlfQ33UXfPGLlUdbpTMpxEOJo0FRAhJJl0OHYOXKkDhatPgk2QxftQp27YIPP6xc/8IL6z7mJZfE99pvvw1r1tRvqK+SgqSIEpBIvBK5At89jNSKTs+ydGmYvyt6hf306Z88pVX0TkFBGMVVVf/+4Qr68vIwDHrDhsPrjBgBn/lMGCkWLW3bwsSJ8Z3UF8kAJSCReLz/fkW3WHT4b3QIcPR+dMLIV16BF18MF2rW5YtfZNnZZzP8oougY8fERpXFO2JMJEspAUnDUJ95yPbuhfnz4Xe/C9eqQHzdYtHZiNu1g5EjK8qIEdChw2GJo7ioqPo5vZJBo8EkiykBSX7bvx8eeyy0TC65JEwc2aTJ4fWiCerQoTBK7He/q5hVuDqDBoVRZI0awRtvhHM7VV13XXwLhFUnnRdBimSIEpDkr9JSmDQpDDmGMGKsoCCMCBswIJSBA8PtzJlhdt9HH63cdXbqqWHm4S9+MbRSktEtpqHGIoASkOQr9zCZ5IoVlfeXlYUp+detg2eeqfxYdA2Ufv1C0rn88jAHWrIpcYgAuhBV8tWtt4bk06JFWCAMQlLavz90l82bB+ecU/1zv/Sl0Eqpmnx0Bb5IUqkFJHmnx9y5YdblggKYOzcMAIhq1ixMnX/88ZUX7oqn60zdYiJJpRaQ5JfHHqN/dMr/Bx+EcePCfbVMRLKOEpDkj0WLKpYN+J//qbyEQF0tEyUokbRTApL8sGxZWD+mtJR3J02Cm25K7PnqOhNJOyUgyX3XXReWFyguhssuY/3Xvpb4UgEiknZKQJLd6mqZvPcezJoFO3aEVTgffLB+E26KSNppFJxkt5kzQxI6cCCsZ7N1ayjR+wsWhHqnnAJ//GP1sxyISFZSApLMqTo/W1lZmO15xYpQXnst7O/QISxXUJuXXoLWrcNggtGjUxSwiCSTEpBkxt69oXXTsWNFwlm5smK5gljR5NO6dZhOp3t36NYt3PboAV/9auVreIqK0vIWROTIpDUBmdl5wE+BAuABd/9hlcenAj8GtkR2zXL3B9IZo6TY66/DL34Bv/1t2L7uusqP9+oFQ4ZUlEmTwlIIHTvWfG7nq19NbcwikhJpS0BmVgDcB3wW2Ay8ZGZPuvuqKlV/7+7T0hWX1EOiSxscPBjOz/ziF7BkSfV1vvIVuOceaN/+8Mc6d679+LqGRyQnpXO40AhgnbtvcPeDwGPAhDS+viRLPEsMzJgRlpy+7Tbo2TPMr7ZkSehGmzYtLGEAoevMHWbPrj75aMkBkbyVzi64HsC7MdubgZHV1JtoZmcBbwLfdPd3q6kjmfLKK+H2+uuhcWMoLAy3saWgICSp//qvsEoohLVzrr0WLrssLBcdLyUXkbxlnqYlfc3sYuA8d/+PyPaXgZGx3W1m1gEodvcDZnY1MNndz67mWFcBVwF06tTp5Mcffzwt7yFZiouLaZXIl3CGFRcXM3juXPrMmZPQ88obN2bHWWex9cIL+Xjw4MMuDu0zezYbp05NYqRBLv59cyleyL2YFW/qjRkz5mV3H57Ic9KZgE4FZrj7uZHtWwDc/Qc11C8Adrl729qOO3DgQF+7dm2yw02poqIiRufQUOGioiJGDx8Oo0ZVdJ395Cdh2PShQxXluefg738//AB33pnWlkxO/n1zKF7IvZgVb+qZWcIJKJ1dcC8B/c3sGMIot0uAL8VWMLNu7r4tsnkBsDqN8UlN3OHKK0PyGTQI1qyBb3zj8Hp33FFxP57lDUSkQUtbAnL3Q2Y2DVhIGIb9oLu/YWbfA5a5+5PA9WZ2AXAI2AVMTVd8UrOj//AHePzxMIDgiSfgsccyHZKI5IG0Xgfk7s8Az1TZd0fM/VuAW9IZk9Rh8WKO/dWvwv05c0ILKJ7uNA2NFpE6aNZGqdm778LkyVh5OdxyS+UVROui0WsiUgclIKnegQNw8cWwYwe7hg8PQ6pFRJJICUiqd/318OKL0Ls3q26/PVzbIyKSRJqMVA73wANw//3QrBnMm8eh3bszHZGI5CG1gKSy//zPMGMBwC9/CcOGZTYeEclbSkANTU2DAz7+GF54IbR+Dh6Ea64JE4SKiKSIuuAakvLyMEfbqFHhYtI1a2Dt2nD73nsV9U49Fe69N3NxikiDoATUEJSXh4QSncV63Lja67/wAjRtmvYpdESkYVECynfbtsEZZ8CGDYc/du658M1vhotLe/YMC75pCh0RSRMloHz29NMwdSrs3BlWFH3oIfj855VgRCQraBBCPiopCdfxnH9+SD6f+Qy89lrYroum0BGRNFECyiczZoQZq0eMgJ//PCwW9+Mfw8KF0K1bqFNXgtE5HxFJE3XB5Qv3MMjgRz8KLaD+/eHRR+HkkyvXU4IRkSyhFlA+2LQJLrww3C8pga9+FZYvPzz5iIhkESWgXPbRR3D66dC7Nzz5ZMX+Bx+Eu+/OWFgiIvFQAspFBw6E63qOPRb+9a+w75JLwq17KOpqE5EspwSUS8rLw3mdQYPgxhth1y749KfDrNWPPprp6EREEqJBCLni+efh5pvh5ZfD9vHHhwEH48eHi0dBQ6hFJKeoBZTtXn89JJlzzgnJp3v3MGHoihXwuc9VJB9Qt5uI5BQloGw0YwZs3hxGsw0ZAn/+M7RuDf/93/DWW3DllVogTkRynrrgss3evZWv52ncGL7+dfjud6FTp0xHJyKSNEpA2eaqq8JtSQlMmgR33QX9+mU2JhGRFFAXXLaYMSOcz/m//6vY94c/wO9+l7GQRERSSS2gbDFjBrzySsUFpZqxWkTynFpA2WLp0pB8WrTIdCQiImmhFlC2+O53w+3114fVSEVE8pwSUDb4299g0SJo0wa+/W1o3z7TEYmIpJy64DLNHW6/Pdz/1reUfESkwVACyrSFC2HJEujQAW64IdPRiIikjRJQJsW2fqZPD11wIiINhBJQJs2fH+Z369oVrr0209GIiKSVElCmlJVVjHy7/XYNvxaRBkcJKFN+/3t44w3o1Qv+4z8yHY2ISNopAWWAHTpUsXbPnXfquh8RaZCUgDKgy8KFsG4d9O8PU6ZkOhwRkYxIawIys/PMbK2ZrTOz71TzeFMz+33k8aVm1ied8aXFgQP0+e1vw/2ZM8NyCyIiDVDaEpCZFQD3AeOA44BLzey4KtWuBD50937AvcCP6vViVVcGjWel0HTV+fWvafb++zB4MEyeXPfxRETyVDp/fo8A1rn7BgAzewyYAKyKqTMBmBG5PxeYZWbmHufU0B98ABs3hpbF5z9fsb/qdnXSUaesLKxqCvBf/wWN1AMqIg1XOhNQD+DdmO3NwMia6rj7ITP7GOgA7IzrFZ5+Gr7ylXB/+PDKj1Xdrk4660yYUHcdEZE8lpMnIMzsKiCydCgHzGzl0dC9C3Sr67nvw7bNsBWgpuekpU6k9RNbJ4t1JN4fAdlB8aZersWseFNvYKJPSGcC2gL0jNk+OrKvujqbzawx0Bb4oOqB3P1+4H4AM1vm7nE0ObJHrsWseFMr1+KF3ItZ8aaemS1L9DnpPAnxEtDfzI4xsybAJcCTVeo8CUT60LgYeD7u8z8iIpJT0tYCipzTmQYsBAqAB939DTP7HrDM3Z8EfgP81szWAbsISUpERPJQWs8BufszwDNV9t0Rc78EmJTgYe9PQmjplmsxK97UyrV4IfdiVrypl3DMph4uERHJBF2IIiIiGZHTCaiuqX0yzcweNLPtZrYyZl97M1tkZm9FbttlMsZYZtbTzBab2Soze8PMvhHZn80xNzOzF81sRSTmmZH9x0Smc1oXmd6pSaZjjWVmBWb2ipk9FdnO2njNbKOZvW5mr0ZHOmXzZwLAzI4ys7lmtsbMVpvZqdkas5kNjPxto2W3md2QrfECmNk3I//fVprZo5H/hwl/hnM2AcU5tU+mzQbOq7LvO8Bz7t4feC6ynS0OAd9y9+OAUcC1kb9pNsd8ADjb3YcAJwHnmdkowjRO90amdfqQMM1TNvkGsDpmO9vjHePuJ8UMDc7mzwTAT4G/uPsgYAjhb52VMbv72sjf9iTgZGAf8ARZGq+Z9QCuB4a7+2DCoLJLqM9n2N1zsgCnAgtjtm8Bbsl0XNXE2QdYGbO9FugWud8NWJvpGGuJfQHw2VyJGWgBLCfMsLETaFzdZyXThXAN3HPA2cBTgGV5vBuBjlX2Ze1ngnD94NtEznHnQswxMY4F/pnN8VIxY017wkC2p4Bz6/MZztkWENVP7dMjQ7Ekoou7b4vcfw/okslgahKZiXwosJQsjznSnfUqsB1YBKwHPnL3Q5Eq2fbZ+AlwM1Ae2e5AdsfrwF/N7OXILCSQ3Z+JY4AdwEORbs4HzKwl2R1z1CXAo5H7WRmvu28B7gY2AduAj4GXqcdnOJcTUM7z8FMh64Yhmlkr4I/ADe6+O/axbIzZ3cs8dF8cTZj0dlBmI6qZmZ0PbHf3lzMdSwLOcPdhhO7ua83srNgHs/Az0RgYBvyvuw8F9lKl+yoLYyZyzuQC4A9VH8umeCPnoiYQEn13oCWHn2qISy4noHim9slG75tZN4DI7fYMx1OJmRUSks8j7j4vsjurY45y94+AxYTm/1GR6Zwguz4bpwMXmNlG4DFCN9xPyd54o794cffthHMTI8juz8RmYLO7L41szyUkpGyOGUKCX+7u70e2szXezwBvu/sOdy8F5hE+1wl/hnM5AcUztU82ip1u6CuE8yxZwcyMMBvFane/J+ahbI65k5kdFbnfnHDOajUhEV0cqZY1Mbv7Le5+tLv3IXxmn3f3y8jSeM2spZm1jt4nnKNYSRZ/Jtz9PeBdM4tOjnkOYdmXrI054lIqut8ge+PdBIwysxaR74zo3zfxz3CmT2gd4cmw8cCbhD7/2zIdTzXxPUroIy0l/Cq7ktDf/xzwFvAs0D7TccbEewahmf8a8GqkjM/ymE8EXonEvBK4I7K/L/AisI7QpdE007FWE/to4KlsjjcS14pIeSP6/yybPxOR+E4ClkU+F/OBdtkcM6Eb6wOgbcy+bI53JrAm8n/ut0DT+nyGNROCiIhkRC53wYmISA5TAhIRkYxQAhIRkYxQAhIRkYxQAhIRkYxQApIGy8xmR2ejTuA5RWY2K1UxZRMz62NmbmbD664tkjgNw5asZ2Z1fUjnuPvUehy3LeH/wEcJPKc9UOruexJ9vXQys9mECUTPP4JjFACdgJ1eMceXSNKkdUlukXrqFnP/fODXVfbtj61sZoUepgiplbt/nGgg7r4r0efkKncvI0yCKZIS6oKTrOfu70UL8FHsPqAZ8JGZXWpmz5vZfuBqM+sQWShrs5ntjyyedUXscat2wUW6135hZneZ2U4LiwnebWaNqtSZFbO90cxuN7NfRRYS22xm367yOgPM7G9mVmJhAcXxZlZsZlNres9mdoKZPRc5ZrGFBffGxDx+nJk9bWZ7InE+amZdI4/NIEyF8rlIF5qb2ehEX6dqF1zkvXs1ZXTk8SZm9qPI32Cfmb1kZufW9B5FlIAkX/wA+AVhccL5hMS0nNBiOp4w4eevzOycOo5zGWFhvtOAacANwOQ6nvNN4HXChJc/Av7HzE4FiCSvJyLHHAVMBe4kTF1Sm/8jTOM0gjCtzAygJHLMbsDfCdOgjCBMDtkKWBB5vbuBxwnTt3SLlH8l+jrVuCjmeN2AXwLvE6ZkAXgI+DTwJWAwMAf4k5kNqeO9SkOV6TmFVFQSKYTJDj1muw9h/rpvxfHcx4AHYrZnE5mLLbJdBLxQ5TmLqjynCJgVs70ReLTKc94Cbo/cP5eQfHrEPH5aJOaptcS6G/hKDY99j7BSZuy+dpFjjqjuvdXzdaJ/2+HVPDaZ0PU5KrJ9LGF9o15V6s0HfpHpz41Kdha1gCRfLIvdsLBI3W1m9pqZfWBmxYRf8L3qOM5rVba3Ap2P4DmDgK0eWdIg4iUqFqOryT3AA5FuxdvMLHaNo5OBsyJdZsWR9xZdnPHYOo6byOtUK9Il9yBwpbv/O7J7GGFl11VV4vpcPWKSBkIJSPLF3irbNwHfAn5MmC7+JMKv8SZ1HKfq4AWn7v8n9XlOrdx9BhXdiacBr5nZVyMPNwKeJryn2NKfsDxysl7nMGbWnTDN/j3u/n8xDzUivO9TqsT0KaDG40nDplFwkq/OAP7k7r+FT9Y6GkBkEEMarQG6m1l3d98a2TecOBKUu79F6M77mZn9L/AfhJbHcuCLwDte82i/g0BBPAHW8jqVmFkzQqL6F3BHlYdfIbSAurr74nheV0QtIMlXbwLnmNkZkW6lWYQlhNNtEbAWmGNmQ8xsFKHb6xA1LLFsZs3N7D4zGx0ZiTaSkFBXRarcB7QFfm9mI82sr5l9xszut8jicYRzU4PNbKCZdbSw0m2ir1PVryKvOx3oYmZdI6WJu78JPALMNrOLIzENN7ObzOyihP9q0iAoAUm++j5hcaw/E0aM7SV8QaaVu5cDXyCMenuRMDLsvwnJp6bRZmWEQQWzCcnrCeAF4MbIMbcSlkAuB/5CWCjuPuBApEC4Vmo14dzYjkj9hF6nGp8mtCLXE0bORctpkcevIIyE+x9Cy+8p4CzgnRqOJw2cZkIQSbPIsORXCaPLXs5wOCIZowQkkmJm9gVCC+wtwtDmewjnS4a6/gNKA6ZBCCKp15pwgWpP4EPCtUTfVPKRhk4tIBERyQgNQhARkYxQAhIRkYxQAhIRkYxQAhIRkYxQAhIRkYxQAhIRkYz4//YyORdoVEfkAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# extra code – generates and saves Figure 4–16\n",
+ "\n",
+ "train_errors = -train_scores.mean(axis=1)\n",
+ "valid_errors = -valid_scores.mean(axis=1)\n",
+ "\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
+ "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
+ "plt.legend(loc=\"upper right\")\n",
+ "plt.xlabel(\"Training set size\")\n",
+ "plt.ylabel(\"RMSE\")\n",
+ "plt.grid()\n",
+ "plt.axis([0, 80, 0, 2.5])\n",
+ "save_fig(\"learning_curves_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Regularized Linear Models"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ridge Regression"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's generate a very small and noisy linear dataset:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# extra code – we've done this type of generation several times before\n",
+ "np.random.seed(42)\n",
+ "m = 20\n",
+ "X = 3 * np.random.rand(m, 1)\n",
+ "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
+ "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "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": [
+ "# extra code – a quick peek at the dataset we just generated\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.plot(X, y, \".\")\n",
+ "plt.xlabel(\"$x_1$\")\n",
+ "plt.ylabel(\"$y$ \", rotation=0)\n",
+ "plt.axis([0, 3, 0, 3.5])\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.55325833]])"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.linear_model import Ridge\n",
+ "\n",
+ "ridge_reg = Ridge(alpha=0.1, solver=\"cholesky\")\n",
+ "ridge_reg.fit(X, y)\n",
+ "ridge_reg.predict([[1.5]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 648x252 with 2 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# extra code – this cell generates and saves Figure 4–17\n",
+ "\n",
+ "def plot_model(model_class, polynomial, alphas, **model_kwargs):\n",
+ " plt.plot(X, y, \"b.\", linewidth=3)\n",
+ " for alpha, style in zip(alphas, (\"b:\", \"g--\", \"r-\")):\n",
+ " if alpha > 0:\n",
+ " model = model_class(alpha, **model_kwargs)\n",
+ " else:\n",
+ " model = LinearRegression()\n",
+ " if polynomial:\n",
+ " model = make_pipeline(\n",
+ " PolynomialFeatures(degree=10, include_bias=False),\n",
+ " StandardScaler(),\n",
+ " model)\n",
+ " model.fit(X, y)\n",
+ " y_new_regul = model.predict(X_new)\n",
+ " plt.plot(X_new, y_new_regul, style, linewidth=2,\n",
+ " label=fr\"$\\alpha = {alpha}$\")\n",
+ " plt.legend(loc=\"upper left\")\n",
+ " plt.xlabel(\"$x_1$\")\n",
+ " plt.axis([0, 3, 0, 3.5])\n",
+ " plt.grid()\n",
+ "\n",
+ "plt.figure(figsize=(9, 3.5))\n",
+ "plt.subplot(121)\n",
+ "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
+ "plt.ylabel(\"$y$ \", rotation=0)\n",
+ "plt.subplot(122)\n",
+ "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
+ "plt.gca().axes.yaxis.set_ticklabels([])\n",
+ "save_fig(\"ridge_regression_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([1.55302613])"
+ ]
+ },
+ "execution_count": 38,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sgd_reg = SGDRegressor(penalty=\"l2\", alpha=0.1 / m, tol=None,\n",
+ " max_iter=1000, eta0=0.01, random_state=42)\n",
+ "sgd_reg.fit(X, y.ravel()) # y.ravel() because fit() expects 1D targets\n",
+ "sgd_reg.predict([[1.5]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[1.55321535]])"
+ ]
+ },
+ "execution_count": 39,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# extra code – show that we get roughly the same solution as earlier when\n",
+ "# we use Stochastic Average GD (solver=\"sag\")\n",
+ "ridge_reg = Ridge(alpha=0.1, solver=\"sag\", random_state=42)\n",
+ "ridge_reg.fit(X, y)\n",
+ "ridge_reg.predict([[1.5]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0.97898394],\n",
+ " [0.3828496 ]])"
+ ]
+ },
+ "execution_count": 40,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# extra code – shows the closed form solution of Ridge regression,\n",
+ "# compare with the next Ridge model's learned parameters below\n",
+ "alpha = 0.1\n",
+ "A = np.array([[0., 0.], [0., 1.]])\n",
+ "X_b = np.c_[np.ones(m), X]\n",
+ "np.linalg.inv(X_b.T @ X_b + alpha * A) @ X_b.T @ y"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 82,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(array([0.97944909]), array([[0.38251084]]))"
+ ]
+ },
+ "execution_count": 82,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "ridge_reg.intercept_, ridge_reg.coef_ # extra code"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Lasso Regression"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([1.53788174])"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.linear_model import Lasso\n",
+ "\n",
+ "lasso_reg = Lasso(alpha=0.1)\n",
+ "lasso_reg.fit(X, y)\n",
+ "lasso_reg.predict([[1.5]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 648x252 with 2 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# extra code – this cell generates and saves Figure 4–18\n",
+ "plt.figure(figsize=(9, 3.5))\n",
+ "plt.subplot(121)\n",
+ "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
+ "plt.ylabel(\"$y$ \", rotation=0)\n",
+ "plt.subplot(122)\n",
+ "plot_model(Lasso, polynomial=True, alphas=(0, 1e-2, 1), random_state=42)\n",
+ "plt.gca().axes.yaxis.set_ticklabels([])\n",
+ "save_fig(\"lasso_regression_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {},
+ "outputs": [
+ {
+ "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": [
+ "# extra code – this BIG cell generates and saves Figure \n",
+ "\n",
+ "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) * ((T @ Xr.T - yr.T) ** 2).sum(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(J.argmin(), J.shape)\n",
+ "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
+ "\n",
+ "t_init = np.array([[0.25], [-1]])\n",
+ "\n",
+ "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 @ (X @ theta - y)\n",
+ " + 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",
+ "\n",
+ "for i, N, l1, l2, title in ((0, N1, 2.0, 0, \"Lasso\"), (1, N2, 0, 2.0, \"Ridge\")):\n",
+ " JR = J + l1 * N1 + l2 * 0.5 * N2 ** 2\n",
+ "\n",
+ " tr_min_idx = np.unravel_index(JR.argmin(), JR.shape)\n",
+ " t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
+ "\n",
+ " levels = np.exp(np.linspace(0, 1, 20)) - 1\n",
+ " levelsJ = levels * (J.max() - J.min()) + J.min()\n",
+ " levelsJR = levels * (JR.max() - JR.min()) + JR.min()\n",
+ " levelsN = np.linspace(0, N.max(), 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(theta=np.array([[2.0], [0.5]]), X=Xr, y=yr,\n",
+ " l1=np.sign(l1) / 3, l2=np.sign(l2), core=0)\n",
+ " ax = axes[i, 0]\n",
+ " ax.grid()\n",
+ " ax.axhline(y=0, color=\"k\")\n",
+ " ax.axvline(x=0, color=\"k\")\n",
+ " ax.contourf(t1, t2, N / 2.0, 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(fr\"$\\ell_{i + 1}$ penalty\")\n",
+ " ax.axis([t1a, t1b, t2a, t2b])\n",
+ " if i == 1:\n",
+ " ax.set_xlabel(r\"$\\theta_1$\")\n",
+ " ax.set_ylabel(r\"$\\theta_2$\", rotation=0)\n",
+ "\n",
+ " ax = axes[i, 1]\n",
+ " ax.grid()\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)\n",
+ " ax.axis([t1a, t1b, t2a, t2b])\n",
+ " if i == 1:\n",
+ " ax.set_xlabel(r\"$\\theta_1$\")\n",
+ "\n",
+ "save_fig(\"lasso_vs_ridge_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Elastic Net"
+ ]
+ },
+ {
+ "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",
+ "\n",
+ "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
+ "elastic_net.fit(X, y)\n",
+ "elastic_net.predict([[1.5]])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Early Stopping"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's go back to the quadratic dataset we used earlier:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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IpJalOiMlU2RUUTkj/6TiARtlJkwAr9UO3by74fQ6kFK5T/ny5ZO34sWL++w7f/48xYsX5+OPP6Zjx46EhYUxbdo0jh07Rp8+fahcuTJhYWFcffXVzJw50+d5U3bBRUVFMXz4cB599FFKly5N2bJlGTNmjM8CcCm74KpXr87TTz/NPffcQ9GiRalcuTIvvPCCz+ts376dDh06EBoaSp06dViwYAERERHptto2bNhAp06dKFq0KBERETRu3JjFixcnH9+8eTPdu3enSJEilC1blj59+nDw4EEAJk+ezPvvv88333yDMQZjTJ4b3Zm/AlA6vAPQb785Vw6l1OUbP348w4cPZ/Pmzdx8882cP3+eZs2aMX/+fDZt2sSoUaO45557+PHHH9N9ng8//JCgoCCWLVvG66+/ziuvvMKnn36a7mNefvllGjZsyB9//MG4ceN45JFH+M31zyQpKYlbbrmFoKAgfv/9d2bNmsUTTzzBhQsX0n3OO++8kwoVKrBixQrWrl3L5MmTCXVNXIyNjaV9+/Y0aNCAFStW8MMPPxAXF0evXr1ISkpizJgx/Otf/6Jz587ExsYSGxtL27Zts1CbuYCI5Omtdu3a4mPDBpHnnhP57juf3Rs3etZnLFlSJDFR8rXFixc7XYRcq6DUzebNmy/dmc7CpeemTvWcN21a+oucemvWLHPnZcHnn38ueD1+9+7dAsiUKVMyfGzv3r1lyJAhyfcHDBgg3bt3T77foUMHadOmjc9jOnfu7POYDh06yP333y8iIqdOnZJq1arJHXfc4fOYyMhIeeqpp0REZOHChRIYGCj79u1LPv7rr78KIDNnzkyzrEWKFJFZs2aleuzxxx+Xjh07+uw7fvy4ALJ8+fJU31tOSPXvyAVYJVfw/zv/tYB+/BHGjYPPPvPZXb8+uNdjOn4c1q71f9GUUlemRQvfpWcSExN55plnaNSoEaVKlSIiIoI5c+ZkuMBao0aNfO5XrFiRw4cPX/Zjtm7dSsWKFalUqVLy8ZYtW2a4yuhDDz3E3XffTceOHXnmmWfY6pWwcvXq1fz8889EREQkb1VcC5plZRny3Cz/BSD3H2iKCz3G+I5N+OknP5ZJqdwinXZN/KBBnvOGDUv3XB+rV2fuvGwQHh7uc3/KlCm8+OKLjB07lh9//JG1a9dy8803c/HixXSfJ+XgBWOMzzWg7HpMRiZPnpzcnbhs2TIaNWrEjBkzANut1717d9auXeuz7dixI8vDynOr/BeAmjSxK6Ju3Ajnzvkc6tTJczuDLmKlVB6wdOlSbrrpJvr160eTJk2oWbMm27dv93s56taty4EDBzhw4EDyvlWrVmUqQNWqVYuRI0fyzTffMGTIEKZPnw5As2bN2LRpE9WqVSMyMtJnc2dmCA4OJjExMWfelB/kvwAUHm7XYEhIgPXrfQ55B6Cff4bz5/1cNqVUtqpduzY//vgjS5cuZevWrYwYMYLdu3f7vRzXX389derUYcCAAaxbt47ff/+dhx56iKCgoDTnN507d47777+f6OhoYmJiWL58OUuXLqV+/foA3H///Zw8eZLevXuzfPly/vzzT3744QeGDRuWnJuuevXqbNy4kW3btnH06FHi4+P99p6zQ/4LQJBmRoTq1e3q3QBnz8J33/m3WEqp7PXYY4/RqlUrbrzxRtq3b094eDh9+/b1ezkCAgKYO3cuFy5coFWrVgwYMIAJEyZgjEke1ZZSYGAgJ06cYODAgdSpU4dbbrmFa665hpdeegmw15h+/fVXAgIC6Nq1K1dffTX3338/ISEhhLgW4Bw6dCj16tWjRYsWlClThl9//dVv7zlbXMkIhtywXTIKTkTktddsD/SgQZccGj/e00Hdt2+agzvyvIIy0utyFJS6SW/0UmpOnTqVQyXJ2y63XtauXSuArFq1KptL5F86Ci6rWrSAypXBNZnN27/+5bn91VeXXCZSSqnLMnfuXL777jt2797N4sWLGThwII0bN6ZZs2ZOFy1HZMcYk/yVisetdWvYuzfVQ40b2264HTsgLg6+/RZuvdXP5VNK5TunT59m3Lhx7N27lxIlShAVFcXLL7+cYY67vObECXjuOfs/9ErlzwCUzi/cGNsKeuYZe//ttzUAKaWuXP/+/enfv7/Txcgx587B66/Df/5jg1B2yJ9dcG4nT4LXsEi3oUPtSG2A77+HzZv9XC6llMojRGDGDLvc2iOPZF/wgfwcgP73P3sNaPz4Sw5VqwY33+y5P3Wq30qllF9JDkwGVQWDCJw4IezfD0OGwL59nmM1a8LHH1/5a+TfAFSnjv2Zxgp0I0d6bs+cCTt3+qFMSvlRYGBgnpsXonKH06ft2mm7dp3j4EFPBohy5eCNN2yv0R13XPnr5N8A1KgRhITA1q02+VsK7dtDu3b2dny8TR+nVH5SvHhxDh06dMXpYlTBce6cHVywbZsQF3eWI0f28+abZYmIgCeftF/Uhw+H4ODseb38OQgBIDQU2rSBJUts2gPvPjfsYIQXX7QD5gDmzIGvv4abbvJ/UZXKCaVLl2bfvn1s27YtU+efP38+zUmTBVlBqJeEBPj7bzhzxt5PSoJjxwrxzjvlaN26KPPmQZky2f+6+TcAgV32dMkSiI6+JAABtGoFffvChx/a+4MG2SzZlSv7sYxK5ZCAgACqVq2a6fOjo6Np2rRpDpYob8rP9XL8ODz7rB3d5r10kTH2f+MHH8BVV+Xc6+ffLjiADh3sz3RWCZw61RNwjh2DG2+0P5VSKr86f972ANWsaX96B58bb4Q1a+w4rpwMPpDfA1CbNrazcsMGOyQ7FaVK2RZQYKC9v3EjXHcd5JPlNpRSKllSkh29Vq8ejBlju93cWrWCxYthwQI7Yd8f8ncACguzqQ5iY6FYsTRPa98e3n/fM391wwZo3tw2S3UQkVIqP1iyxF7zvvNOiInx7K9ZEz7/HH7/3V618Kf8HYDArkJXtmyGp/Xta4OQe3THyZPwwANQowZMnAgrVthvD0oplZds2QI9e9rg4r1OZ6lS9hLE5s1w223pJpDJMX4bhGCMqQJ8AJQDBHhHRKamOCcK+ApwL+gxR0Se9FcZ+/WDunWhTx9PF9y+ffDUU3YrUsSO7q5bF6pUsdeOKlWyW8WKULKkM79EpZRK6eBBmDwZpk8H7zXrQkJg9Gj4979TzdfsV/4cBZcAPCwifxhjigCrjTHfi0jKRDi/iEj2rjd7zz02586KFVC6dLqntmxprwNNnQovvQTey8SfPg2//mq31AQHQ4UKNhi5tzp14Oqr7ZYTwxiVUsrbmTN2YMHzz3uGVYP9cnzXXfD005CFwZE5ym8BSERigVjX7dPGmC1AJSDnM7H9+Sfs3m2DUJ8+GZ4eGmonpo4eDfPn2+3bb+HQofQfd/Ei7Nljt9RUqADXXmsnwLZrZ1cPdw9+UEqpK5GYaLO6TJxoL3t769QJXngBcttockfmARljqgNNgeWpHL7GGLMOOACMEZFNV/yCXbvCDz/AwoWZCkBuISHwz3/aTcT+Utevt7Fs3z7PFhtrc56mMdAuWWwsfPGF3cA2xrp3t/2zXbpARMQVvEelVIEkYr8gP/IIbErx37JBA9sS6to1d14eMP5OVmiMiQCWAM+IyJwUx4oCSSISZ4zpBkwVkVqpPMcwYBhAmTJlmn/22Wfpvmbh3btpNXgwF0uUYNkXX3hSYWezc+cCOH48hKNHgzl2LIRDh0LYsyecmJjC7NkTzvnzaTd3goMTadfuKF27HqRZsxNX3DKKi4sjQiNaqrRuUqf1krrcXC/bt0fw9ts1WbOmhM/+UqUuMGjQbrp2PZijvSzXXXfdahFpcdlPcCXLqWZ1AwoBi4CHMnl+DFA6vXNSXZI7paQkkcqV7Trcf/yR8fk5ICFBZN06kTfeEOnTR6R8ec/S4Cm3SpVEJk4UOXjw8l+voCw7fTm0blKn9ZK63Fgv+/aJ9O9/6f+OiAiRJ58UiYvzTznIK0tyG7ss4HvAFhF5KY1zyrvOwxjTCjtM/MrzEhhj26Bgu+EcEBhoR9ANHw4ffQT799sxEY89ZpvJ3vbvt4n/qlaFgQNh3TpHiqyUymXOnoUnnrBr83zwgWd/YCDce69NFvr44xAe7lwZs8Kf84CuBfoBHY0xa11bN2PMvcaYe13n3AZsdF0DehW4wxVlr5zDASilgAA74u6pp+zE1zVr7KAH70F6Fy/auUlNmtjrRH/84VRplVJOSkqC2bPtqNrJk20gcrvpJvs/5K237HIJeYk/R8EtBdK9DCYirwOv50gBOnWCRx+1V/1zoSZN7Pb88zYz9yuv2JnJbl9/bbdevewfYJMmjhRTKeVny5bBgw/aHhNvjRrByy/bufZ5Vf7PhOBWvDg88wy0bet0SdJVqBD07g2//Wa3lDOUv/rKDqXs2xf27nWunEqpnLVnj1307dprfYNP2bLw7ru2RyQvBx8oSAEoD2rTxuZoWr/eBiJvH31km+MTJ0JcnDPlU0plv9OnYcIE+/n+9FPP/uBgm71gxw64++78MYewYAWgpCR49VXo1s03/3gu16CBDUTr1vkua3TunL2GVKeO7R/284h6pVQ2SkyEGTPsAINnn/X9F3X77XZx5//8B4oWda6M2a1gBaCAAPsb/vZb+PFHp0uTZY0awdy5Nqtts2ae/QcO2Dx2XbrYUTBKqbwlOhpatIAhQ2wON7fmze2Czp99lvNr8zihYAUggFtusT/nznW2HFegfXtYudKm3ahQwbP/hx9sa+mZZyA+PhdOe1ZK+di1C2691a5BtnatZ3/FinYE7IoV8I9/OFa8HFdwA9C8eb4pYvOYgAA7R2jbNjtCxp3c4cIFO7do6NAWLFvmaBGVUmk4eRLGjoX69X2/C4eF2eu627dD//45lrQl18jnby8VDRvatuzhw2mntc5DihSxWbtXrPDtltuzJ5x//MMmVT1/3rnyKaU8EhLg7behVi2YMsXO9XPr29d+oXziibwzkfRKFbwAZIy9ogfwySfOliUbNW8Oy5fbeQHuP96kJDuvqEULncSqlNO+/97O37vvPjhyxLO/TRs752/2bLvOWEFS8AIQeDJif/55vlpzOyjIZlPYvBmaNz+evH/TJrsU7xNP5Ku3q1SesHUr9OhhBwl5Z6uuUgU+/thONG3d2rnyOalgBqDGje1wkylT8uXY5apV4fnn1/PGG1C4sN2XkGAzKFxzjf1AKKVy1vHjMGqU7fX/5hvP/vBwuyjctm12omluXCbBXwpmADLGrlM7YICd3ZUPBQTYxKfr1tmZ1G6rV9vuuvfey5exVynHxcfb6YaRkfZnQoLdbwwMGmQnkk6YYAccFHQFMwAVIJGRdt7QCy94Yu3Zs3Ymde/e8PffjhZPqXxDxLZ0Gja0LZ8TJzzH2reHVavsNETvqRMFXcEOQH/8Ya8IereP86HAQBgzxs4dqlfPs//zz21vZD4YDKiUozZuhBtusNd6tm3z7K9RA7780k409R6lqqyCHYB++cWOiXzzTadL4heNGtlvYffc49n311/229kTT3i6CpRSmXPkiP0O27ixHeXmVrSoHYG6ebOdaFqQr/Okp2AHoL59bfrphQvtKnAFQOHCNuZ++SWUcK3im5RkByh06mTT+iil0nfhgh3DFBlpP09JSXZ/QID9grdjh51oGhLibDlzu4IdgEqXtgvsJCX5Li9YANx6qx2g0L69Z9/PP9ulHvJgmjyl/ELEZi64+mobYE6d8hzr3Nmm03n7bbtkgspYwQ5AAIMH258zZhS4YWFVqsBPP9nuN3fKj8OH4frrbYsoD2cqUirbrVlj19+59Vabw82tdm27WOR339kBCCrzNAB16QKVKtk00r/84nRp/C4w0Oae+uEHz3K+IjYo3XADHDrkbPmUctqxY8EMGWKnL0RHe/aXKGFXLt640Q4+0Os8WacBKDDQZvUE23YuoNzZeKOiPPt+/NF2yS1Z4lSplHLOuXN2XZ5+/Vr5dJAEBsLIkfY766hR9jKyujwagACGDbOzNh97zOmSOKp8edsSevxxz7e52Fjb7fDss54LrUrlZyJ2JdJ69eyE0XPngpKPde9uWzxTp0LJkg4WMp/QAAQ2d80bb9jc6AVcYCA8+aRds690absvKcl+ELt3h6NHnS2fUjlpxQpo186myNmzx7P/6qth0SKYPx/q1nWufPmNBqCURArcYITU3HCDvejarp1n38KFtktO1xnKOyIiIpg1a1amz581axYRERE5V6Bcau9eOyujdWvfv+/SpeHBB7ezdq29XKyyl98CkDGmijFmsTFmszFmkzFmVCrnGGPMq8aYncaY9cYY/84dnj8fWrXKV8s0XInKle0ouUce8ezbtw86dIAXX8w7cXrgwIEYY5K3Xr160aNHD7ZmY1bWmJgYjDGsWrUq255T5by4ONvlXLs2fPSRZ3+hQvDww3Y+T8+eBwgKSvs51OXzZwsoAXhYROoDbYD7jTEp+7xuBGq5tmHAW34sn52MumoVvPaaX182NytUCJ57zg4zdU9cTUiwqX1uucU331Vu1rlzZ2JjY4mNjeWFF17g3Llz3OJeHVcVOElJdkn72rVtZmrvRRtvvRW2bLETTYsXd6yIBYLfApCIxIrIH67bp4EtQKUUp/UCPhDrd6C4McZ/qfvuuguKFYPffrOJ01SyHj1sl1yrVp59X31l81vlhS/9ISEhlC9fnvLly1O7dm0efPBBtm7dyrlz55LP2b9/P3fccQclSpSgRIkSdO/enR07diQf37t3L7169aJkyZIULlyYunXr8omrtXzVVVcB0LJlS4wxRHkPJ/Tibil98skndOjQgbCwMJo2bcr69evZuHEjbdu2JTw8nHbt2rF7926fx06bNo3IyEiCg4OJjIzk3Xff9Tm+c+dOoqKiCA0NpU6dOsyfP/+S18/oPRYES5bYRRoHD7aDbNyaNbPDrL/8EmrWdKx4BUqmApAx5lljTGGv+92MMWFe94saYzKdSsAYUx1oCixPcagSsNfr/j4uDVI5JzzcjogD+7Vf+ahWzU6VGj3asy8mxi738MYbeadL7uzZs3z66ac0bNiQMFdO/LNnz3LdddcRGhrKkiVL+O2336hQoQKdO3fm7NmzAAwfPpyzZ8+yePFiNm3axCuvvEJx11fkFStWALBw4UJiY2OZM2dOumWYNGkS48aNY82aNRQvXpw+ffrwwAMP8Mwzz7BixQrOnz/PyJEjk8+fO3cuI0aMYPTo0WzcuJFRo0YxfPhwvv76awCSkpK45ZZbSEpK4rfffmPGjBlMnjyZCxcu+LzvjN5jfrZzp23dREXZL1NuFSrY1tDKlbZ7WflPZns2xwGvAO6/0k+AJsCfrvthQF+gf0ZPZIyJAL4ERovIqYzOT+M5hmG76ChTpgzR3rPDrlBw69a0KVQIM2cOK99/n7PVqmXbc/tTXFxcttaLt169oHjx0rzwQl3OnAni4kUYMQK++OIwY8ZsIzw8d6VQOHjwIN9//31ysDl//jxly5blv//9b3IdLViwgLNnzzJgwACOH7eryfbp04fPP/+c5557juuuu47NmzfTvn17Tpw4wYkTJwgNDQUgOjqagwcPAraFE5JOAjD3ed27d6dw4cIcPHiQLl268Oijj9K7d2+MMRw5coTOnTszderU5PI9/vjjdO7cmQYNGnDgwAEaNmxIp06dePTRRylSpAgrV65k8+bNfPTRR5w8eRKAAQMGMHLkSLZu3Up0dHSG77Fly5Zs3bqVxMTEHPvbcUJcXBAffFCNuXMrkZDg+c4dEpLIv/61lz599hIWlsjPP6f1+Jz7LBV4IpLhBiQBZb3unwZqeN0vByRm4nkKAYuAh9I4Pg3o43V/G1AhveesXbu2ZLt777Vj4QYMyP7n9pPFixfn+Gvs3CnStKl72KDdatUSWbs2x186SwYMGCDXXXed7NixQ3bs2CFvvfWWDBw4UCpUqCB//fWXiIgMHz5cAgMDJTw83Gczxsizzz4rIiLTp0+XoKAgadOmjUyYMEFWrVqV/Bq7d+8WQFauXJluWdznLVu2LHnfihUrBJDt27cn71uwYIEAcubMGRERKVGihEyfPt3nud59910pUaKEiIi88sorUqVKFZ/jFy9elICAAJk5c2am3uPixYtl5syZEh4enpXqzbXi40Vef12kVCnfv1EQuesuEdevPkP++CzlVcAqyUQMSWvz5yg4A7wHbBGRl9I4bR7Q3zUarg1wUkRi0zg354wdayfEfPedXb1NpapmTTtk9b77PPt27IA2beDdd3NXl1zhwoWJjIwkMjKSunXrMn36dE6dOsU777wD2C6sJk2asHbtWp9t+/bt3ONav2LIkCHs3r2bQYMGsX37dtq2bcvkyZMvqzyFvKbPG9es39T2JWUw+9dkIf9LZt5jfvHtt3b5kREj4Ngxz/62bWH5cvjf/2wuROUsf46CuxboB3Q0xqx1bd2MMfcaY+51nbMA2623E3gXGO7H8nnUqGGHZO/YYdcvUGkKDbXLKX30kb2EBnZE0bBh0L+/HeaaGxljCAgISL720axZM3bu3Enp0qWTA5V7K+k15b1y5coMGzaMzz77jCeffDI5gAW7lptNzKEMrvXq1ePXFCsHLl26lPquydP16tVj//797N3ruYS6YsUKnwCW2feYl61fb+ewdetmR7K5VatmsxssXeo7kEY5Kyuj2+81xrj/nQQBQ4wx7u8WRTJ6sIgsBdL9uuZq0t2fhTLlnK5dnS5BntKnj52kevvtNlUJwOzZsHo1fPGF80kmLly4kHz9Zc+ePTzwwAPExcVx0003AdC3b1+mTJlCr169ePLJJ6latSp79+7lq6++4t5776VWrVqMGjWKG2+8kdq1a3Pq1CkWLlyYHADKli1LWFgYixYtonr16oSGhlKsWLFsK//YsWO5/fbbad68OV26dGHhwoV8+OGHyYMdOnfuTN26denfvz8vv/wy586d48EHHyTIawJLRu8xL9u3z87nef9935Z3kSLw6KN24Izrkp3KTTLTTwfEALsz2q6kL/Bytxy5BuTt5EmRr7/O2dfIAU71W585IzJ4sG9/e+HCIh98kPFjc8qAAQMESN4KFy4sLVu2lC+++MLnvIMHD8rAgQOlTJkyEhwcLNWrV5dBgwbJkSNHRERkxIgREhkZKSEhIVK6dGnp3bu37Nu3L/nx7777rlSpUkUCAgKkQ4cOqZYltWtFK1euFEB2796dvO/bb78VQE6fPp2876233pKaNWtKUFCQ1KxZU9555x2f5962bZu0b99egoODJTIyUr766isJDw9PvgaU0XvMi9eATp4UGT9eJDTU928uIEBk6FCRgwev/DX0GlDauMJrQH4PGNm95WgAOn1apFw5kaAgkR07cu51coDTH5qZM0XCwnz/Kdx9tw1QTnO6bnKrvFQvFy+KvPaaSOnSvn9jINKtm8iGDdn3WnmpXvztSgOQ5oJLT0SE7UxOSLCL5qhMGzjQJnb0Ttw4fbqdALhunWPFUnmcCMyZY5ODPvCAb3LcZs3sEiLffAMNGjhXRpV5mZ2I2tgYc12KfX2NMX8aYw4bY942xgTnTBEdNnkyBAfDxx/bBXNUpjVoYCf33XmnZ9+WLfYi8Cuv6PIOKmuWLbPJcf/5Tzs+yK1qVXu9ceVKu3SIyjsy2wJ6GkjOi+zK4TYT2AF8jJ2EOi7bS5cbVK1q1woCGD/e2bLkQRER9p/D9OmeAYUXL8KDD9rlHXTFVZWRHTvgtttsxg3vTNXFi8MLL8C2bTaTdYD25+Q5mf2VNQO+87p/B7BZRG4QkVHAaKB3Npct93j0USha1K5HsGCB06XJc4yBIUPgjz9sN4nbwoV2roZWqUrNvn12OH+9ejY/m1uhQvYLzM6dNimujm7LuzIbgEoBB7zutwe+9rofDVTNpjLlPmXKwKRJ9vaoURAf72x58qg6dWye17FjPfsOH7YtoVGjfDMS51dbtmyhW7du3HDDDcnbe++953SxcpWjR21giYy0E5q9p1bdcYdt8bz0EpQq5VwZVfbI7DygI7gShRpjAoHmwBSv48HYdD351wMP2Eyc992ni8BfgeBgeP55u7hX//6ebMSvvmrXHvrgAzufKL9av3490dHRPlm4AwICGDJkiIOlyh1On4aXX7bLIJw+7XusY0f473+hZUtnyqZyRmZbQNHAJGNMDeBh177FXsfrY+cK5V+FCsHcubosYjbp3NnOWu/Z07Nv40Y7QOGJJ/J3IzNIVzfzcf68DTw1atiOBu/g07IlfP+9Hd2mwSf/yWwAehy7SNxO4BngERE543W8H/BjNpctd8vG1TQLqtKl4f/+z6bycSWqJiHBDjxs3Ro2bHCydCqnJSTAe+/ZReEeesh3SLX7us/y5fbLisqfMhWARCQGqItdw6eaiKRcqXQS8Gz2Fi0XGzvWfkK+/jrjc1W6jLG9muvW2USRbmvWQPPm8J//2H9UKv9ISLApc+rWhbvvBq/0dVSrBrNm2S8ft95q/z5U/pXpgYsikiAi60TkQCrH1onIsdQely9Vcq2Rd9994Fp7RV2ZWrXg559t/797OZ34eDsA8dprtTWUH3gHnoEDYdcuz7GyZe11wG3bYMAAm4xe5X+Z6ow2xjyUmfMk7WUW8pcHHoBPPrH9A+PGwdtvO12ifCEwEB5+2I6KGzDAZlIA+7NZMzsy6vHHNUF5XpOQYOeCPf20b9ABO5dnzBg7CjIiwpHiKQdl9mroFOAoEEfaGa0FKBgBKDDQdl43bQrTpkHv3nDddRk/TmVK3brw66+2NTRpkp24mpBgR0F99pm9ZnTDDU6XUmUkvcBTooS97vPAA5CNScNVHpPZLriVQGFgCdBPRK5KZauRc8XMha6+Gh57zN7u3x9OnHC2PPlMUBD8+982+9E//uHZ/+efdqWMO+/ULAq51blztlOgTh0YNMg3+JQoYQNSTIz9+GjwKdgyOwihNdAaOAHMMcZsM8Y8Yowpl6Oly+3Gj7fDtfbtgwkTnC5NvlSvHkRH21Q+JUp49n/8sR099dJLtoWknPf333bQSPXq9vLon396jnkHngkTbGIRpbIyCGGTiDyEnZA6AYgCYowxXxljQnKofLlboUJ2KdC77oKnnnK6NPlWQIBN5bN1q8355XbqlL1m1KiRXYJZOePAAXjkEZs28dFHbXYLNw08Kj1ZnhEnIvHAF8aYU9huue5AGHAhm8uWN9SoYReYVzmubFl7TaF/f3vtYPt2u3/bNrtqRrdu8OKLvktAOC0+Pp4VK1a4F3Zkayrzx06cOMHSpUuT79eqVYty5XJ/58KmTTar+QcfXNoKrVzZfjm4+24dXKDSlqUAZIypDgwGBrh2fQAMEpG/s7dYedTFi/Dcc3b93yIZrlKuLlOXLnZY9uuv26wJp07Z/QsWwKJFdojvpElQpYqjxQRg9erVtGvXzmd57vMpkt5t3ryZHj16AHD27FlGjhzJlClTyI2Skmw9T50KP/xw6fF69ezA0D59bNolpdKT2fWA+hpjfgQ2A3WAe4DqIvK4iOzOyQLmKffcYxeuGzzYd2F6le2Cg+0oqh07YOhQz4TFxEQ7QLFWLfsN3Ht2vRNat25N/fr1OXnyZPIWnyLP0OnTp5OPBQYG8sADDzhU2rSdPm3n6dSpAzfddGnwadPGZrXYuNEOodfgozIjs9eA/gfUBF4BlmNzvz1ojHnIe8uhMuYd//63bfl88YXtC1I5rmxZeOcdWLUKrr/es//CBTtAoUYNO3foyBFnymeMYcqUKYSHh2d4blBQELfffjvVqlXzQ8kyZ+1auP9+26U2apRdAsEtIMAuDvfzz3adnl69dE0elUWZWbcbm2h0dwbbn1eyNvjlbrVr176Mlcxz0Ny5dmH6gACRb75xrBgFdR37H38UadXK/gq8t7AwkVGjRP76y/91k5SUJPXr1xfsXLk0t9DQUImJifFr2by56+XUKZF33hFp2fLSegSR4sVFxowRcbCoflVQP0uZAaySK/j/nW2BAKiSwfEZwGFgYxrHo4CTwFrXNjEzr5vrApCIyMSJtmojIkTWrHGkCAX5Q5OUJDJnjki9epf+8yxUSKRr1wOycaN/y7RgwQIJDw9PM/gEBQVJv379/FsoL0lJIm+8sVqGDrV/tqkFnrp1Rd58UyQuzrFiOqIgf5Yy4ngAAsoDrwPnMjivPXZl1fQC0Pysvn6uDEBJSSJ33mmrt2JFkX37/F4E/dCIJCSIfPqpSJMmqf9DjYoS+fxzkYsXc74sGbWCnGr9bNki8thjIjVqpF5HISH2T3nxYvtnXRDpZyltVxqAMjsIobgx5kNjzBFjzAFjzEhjTQL+BNpgR8el19X3M3A8M6+X5xkDM2bYKfwtW9qEV8rvAgPhX/+yS4EvWOCbUQHsBNfbb4errrKj5ryvb2S39K4FBQUFcdttt/nt2s/u3fYSZfPmdtTa00/7ThoFu//ll2H/fvjwQ4iK0szUKgdkJkoBbwJ7sTnhNgKJ2CW5fwI6ZDbaAdVJvwV0DFgHfAtcnZnnzJUtILeTJ+3XcAfot7bULV0q0qHDIQkMTP0bf9u2Im+/LXLsWPa/dlqtoJxu/SQl2Z7gSZNEGjdO/X2DSHh4vAwebOuooLZ2UqOfpbRxhS0gY58jfcaYPcAQEfnBtSrqTuBVERmdlWDnmkc0X0QapHKsKJAkInHGmG7AVBGplcbzDAOGAZQpU6b5Z599lpViOCLgwgWqfvghf911F0l+GKMaFxdHhM4ATFVcXBznzpXi668rMH9+RU6cuPT3ERiYRJMmf3PttUe59tpjlC2bPfOsly9fzuTJk5PnAgUGBtKxY0ceffTRbHl+t5Mng/jjjxKsXl2CVatKcuhQaKrnFSqURJs2x+jc+RANGvxFyZKaajwl/Syl7brrrlstIi0u+wkyE6WAeKCi1/2zZLKFkuJ5qpNGCyiVc2OA0hmdl6tbQN5697ZfM7t2FTl7NsdfTr+1pc27bi5csNeBevYUCQpKu3XQtKnI2LEiCxaInD59+a+dshWUXa2fgwftAMxHHhFp3lzEmLTfS3CwSLduItOni5w44XkO/ZtJndZL2rjCFlBmMyEEuIKQW6IrCGUbY0x54JCIiDGmles1888id489Zhe2X7jQLngzb57mKMkFgoPhttvsduSIXeZp9mzPWkRua9bY7YUXbKbuli2hVSt7HaV5cztBMzOLqLmvBd1+++1cuHDhsub9HDpkJ3xu2GDL+fvv9rpOeooVs392N99ss4lrog6VG2Q2ABlgtjHG3Q8RCrxrjPEJQiLSM80nMOZj7HWe0saYfdhlvAu5Hvc2cBtwnzEmATgH3OGKsPlDgwawZAl06gSLF9t8MgsW6ACFXKRMGZtj7oEH7MX3efPs7P6ffvJdFjwhAX77zW5u4eE2O3etWnaLjLSpgMqWtVvp0p4AdexYVy5cqEZCwjZ++ukpPvzQk2Q1Ph6OH7cZHI4cgT17bCLPmBgbZDZvztyk2sBAGyCvv95urVvb3LlK5SaZDUDvp7g/O6svJCJ9Mjj+OnY4d/5Vvz788osNQr/9Zn8uWAB5IPFkQVOpkl1SwL3q+s8/20D000+wfv2l558542klpcYY2+oQgbg4g8g7wBL2769Gv34wfLg9z53XLqtCQqBFC7jmGruE+XXX6Vo7Kg+4kv673LDh6kv31qNHDwFk3rx5yfumTZsmgAwdOjR53/79+wWQChUq+Dy+WbNmAsiqVauS902aNEkAmTRpUvK+VatWCSDNmjXzeXyFChUEkP379yfvGzp0qAAybdo0O4U8MlIE5FmQHj16+Dw+O95TqVKl/PueXObNmyfk0HvKrt+Tu0//ct/T4cMi8+aJwCSBeVK+fNrXW3JiCw8XadDgtMC7Urny87Jihb2WdaW/p8WLF+eq35Nbfvrby2/vCX/MA1LZrFo1WLqUP3v2ZKLTZVFZVqaMTcgJTwA9iY2Fgwdh6VJo3PgV4Gn+8Y/9dOhg59OEh59P9/l8JQJHqFbtPG3bwh13wLXX/gLcQ9++/2PXLttKmjVrGzCUsmU/oWVLTf6p8qZMDcPOzerUqSPbtm1zuhhX7uRJ+OYbm8c+G2b8RUdHExUVdeXlyoecqJv4eNtN17ChXUA3pcqVbddesWLOJfTUv5nUab2kzRhzRcOwtQWUGyQl2WFYffvCoEFwNlsHGKpcoFAhO97kv/+Fwimm2hQubPeXKKHZpFXBon/uuUFAgF3mMywM3n/fXknescPpUqkc0LevXT6iWjXb0K1Wzd73XmpcqYJCA1Bu0a8fLF9ux/CuX28nl/zvf/a6s8pX+va1w6qTkuxPDT6qoNIAlJs0bGhXVrvtNrsEZf/+9ip0UpLTJVNKqWynASi3KVoUPvvMrisdEWH7aPTCgFIqH8rsRFTlT8bA4MHQsSNUqODZv2yZDUiVKjlXNqWUyib61To3q17dTnEHO/nj9tvtxJLXXvPNDaOUUnmQBqC84tw5mwHz9GkYORIaN7ZpfHSQglIqj9IAlFeUK2czY86da5fw3LzZpjfu0gXWrXO6dEoplWUagPKam2+GLVtgyhQ7s/GHH+xoOW0JKaXyGB2EkBeFhMDDD8PAgfDUU9CunSd9z/79cOKEo8VTSqnM0BZQXlaqFLzyip035Pb009CwIQ0mTIDoaG0ZKaVyLQ1A+U14OISEUHrZMrsoTLNmNr3PhQsZP1YppfxIA1B+M2UK7NnD7oED7VKca9farrpKlWDOHIcLp5RSHhqA8qNy5dgzYAD89RfMmgVNm8KxY1CzpuecbdvsEhBKKeUQDUD5WUgIDBgAq1fDhg127pDboEG2hdSrF3z0kZ1fpJRSfqQBqCAwBho08Nw/d84u/RAfD/Pm2XTMZcrArbfC7Nlw/LhzZVVKFRgagAqisDD48Uc7ZPu11+ww7gsX7CTXfv3g++8958bF6Ug6pVSO0ABUkFWoACNGwC+/2HWiX3kFrr/eZldwGzkSqla1XXmzZsGePU6VVimVz/gtABljZhhjDhtjNqZx3BhjXjXG7DTGrDfGNPNX2RR2lNyoUfDdd3ZtaLc1a2xw+uADe92oenWoUQOGDIGffnKsuEqpvM+fLaBZQNd0jt8I1HJtw4C3/FAmlZHVq+1Q7pdfhp49oVgx2L0bZsyApUs9523caLMyfP+9jq5TSmWK31LxiMjPxpjq6ZzSC/hARAT43RhT3BhTQURi/VNClaqAADt6rnFjGD0aEhNtq2jxYujc2XPewoUwcaLnfo0a9jFNmtifPXt60gUppRS5KxdcJWCv1/19rn0agHKTwEBo0cJu3q65xgao5cvhjz/gzz/tNneu7d7r1ctz7vjx9vpT3bp2q1xZV31VqgDKTQEo04wxw7DddJQpU4bo6GhnC5QLxcXF+b9eevWCXr0wCQkU3ruX8J07idi1CylUiN2usgScO0f7//7X52GJoaGcrVKFs1WqsO+f/+R0/foAmIsXkaCgbA9OjtRNHqD1kjqtl5xjxI9DbF1dcPNFpEEqx6YB0SLysev+NiAqoy64OnXqyLZt23KiuHladHQ0UVFRThfjUqdPw3vvwdatdtuyBQ4f9hz/+mvo0cPe/s9/4Ikn7DLkNWrYdZDcW/Xql7bCMinX1o3DtF5Sp/WSNmPMahG5vA8iuasFNA8YYYz5BGgNnNTrP/lQkSK2q87b8eM2NdCWLdC8uWf/oUN2ftL27XbzVquW775OnewAiUqV7Fa5MlSsaLM9VKtmX1cplav4LQAZYz4GooDSxph9wCSgEICIvA0sALoBO4GzwCB/lU05rGRJew3pmmt897/yil1eYvduu/35p/0ZE2OvIbmdOZP+kPBp02DYMHt7zhwaPfss1KljV5ktW9azlS4Nbdpk97tTSqXBn6Pg+mRwXID7/VQclVdEREDDhnZLS3Aw/Pqrzeywb5/nZ2wsHDliJ9K6bdlCydWr7fDylIoW9R1C3qKFTeJaqpQNkiVLem537GiXuwD4+2/Ytcu2wIoWtT9DQrLl7SuVn+WmLjilLk+hQtC2bebO7d+fdYUK0bh8eXvt6dAh+/Pw4UuDRkyMDUAxMZc+T2CgJwAtXQo33eR7PDjYE5CWLoXy5e3+qVNhxw7PsSJF7BpO4eG+17USEmyZ3MeC9KOq8h/9q1YFS5UqnGjVCjJzUXnHDnt9yns7dsz+9H58aKhd8uLkSTh1yv68eNG2vo4csbn33ObNS7u78J//hC++sLf37bODLdxCQmwgioiwP6dP9wTdTz+1GSzCw+1reW9lykAfr86HpUttMPM+JzTU/kxMzEwNKpVtNAAplZYSJezmvY5Sajp3tnOf3ETs4Al3QPIeAPHQQ3DzzfbYyZM22euZM/an9/Wn+Hjbajpzxm4XLtjNnancO1j8/rvNTJGa2rV9A1DXrvb5UlHl3nvtYA6A//s/O1gkZUALCbHbhx96Autrr9m1p0JCbMvPfU5IiJ3n5W4pxsXBsmW+x723smXt41WBoQFIqexmjG1VhIbagQ7eunfP3HPUqmWvYYENaOfPe4JRXJztrnPr0weuvtoeO3fOdytd2vd527Sxj0953rlzJIaGes47fjz9xLPec7M++sgGwdT06+cJQDExcMMNaT/nL7/YzOxgg9+bb3qCU3Cw7WoNDrZB7euvPY/r0sXWUaFCnnPct/v182TsWL0avvzy0nPctwcP9nR1/vKL/fJQqBDFN2/2Pa90aTvKEuwXhaNH7eMKFbI/3VtgoGb/yIAGIKVyO2M8LZCUAQWgVSu7ZcYPP6R56EB0NLXdd3r3tt2MKQPVhQu2e9G7pTJyJNxyi6eV5j7nwgXfVl1YmA0G3ud5b+HhnnPPn7f/3OPjbcD05n0e2KVFkpJSf1OtWnkC0Lp1dm5ZWgZ5DbwdO9Zm9QCapDxv4ECYOdPe3rzZpptKy2+/eergkUfs47yDlHurVw/mzPE8zh20UwtsQ4Z4Avmvv9rWaGrPGRQEEybYQAjw+eeeYBkY6PkZGGhb+S1b2vNOnbLlTu28oCA7gjTl7+AyaQBSSl0qPNxO/s0M7y6+9NSs6bvWVHrefNMO2PAOaO6A5P6H6vbDD55j8fG+57Zu7TmvWTM7rD/lee6f3gM92ra1ox3j4/n78GGKh4d7zvUeVWmM7SpNSLBbfLzndmKi73OeOmUDQGq8rxOKQHqZFzp29NzevBneSidv82OPeW4//zysWpX6eUOGeALQrl22qzYty5dn/gtPBjQAKaVyn4AAT/dbRtythYw0aZJ+a8XbSy8l31ybXiaERo08XaUppcwy8+KLNmO8O0B5b4UK+Z67ZEnq5yUk2EDqdu218MYbaZ/r3VV62212lGV8vA2OiYmeQOkOPmC/fFx/veeY93mJiXYgTDbRAKSUUjkh5fUf95D6zDyuffvMvUb9+nbLjHHjMnde7dp2VKUfaApipZRSjtAApJRSyhEagJRSSjlCA5BSSilHaABSSinlCA1ASimlHKEBSCmllCM0ACmllHKEBiCllFKO0ACklFLKERqAlFJKOUIDkFJKKUdoAFJKKeUIDUBKKaUcoQFIKaWUI/wagIwxXY0x24wxO40x/07l+EBjzBFjzFrXdrc/y6eUUsp//LYgnTEmEHgDuB7YB6w0xswTkc0pTv1UREb4q1xKKaWc4c8WUCtgp4j8KSIXgU+AXn58faWUUrmIPwNQJWCv1/19rn0p/dMYs94Y84Uxpop/iqaUUsrf/NYFl0lfAx+LyAVjzD3A+0DHlCcZY4YBwwDKlClDdHS0XwuZF8TFxWm9pEHrJnVaL6nTesk5/gxA+wHvFk1l175kInLM6+504PnUnkhE3gHeAahTp45ERUVla0Hzg+joaLReUqd1kzqtl9RpveQcf3bBrQRqGWOuMsYEA3cA87xPMMZU8LrbE9jix/IppZTyI7+1gEQkwRgzAlgEBAIzRGSTMeZJYJWIzANGGmN6AgnAcWCgv8qnlFLKv/x6DUhEFgALUuyb6HV7PDDen2VSSinlDM2EoJRSyhEagJRSSjlCA5BSSilHaABSSinlCA1ASimlHKEBSCmllCM0ACmllHKEBiCllFKO0ACklFLKERqAlFJKOUIDkFJKKUdoAFJKKeUIDUBKKaUcoQFIKaWUIzQAKaWUcoQGIKWUUo7QAKSUUsoRGoCUUko5QgOQUkopR2gAUkop5QgNQEoppRyhAUgppZQj/BqAjDFdjTHbjDE7jTH/TuV4iDHmU9fx5caY6v4sn1JKKf/xWwAyxgQCbwA3AvWBPsaY+ilOGwKcEJFI4GXgOX+VTymllH/5swXUCtgpIn+KyEXgE6BXinN6Ae+7bn8BdDLGGD+WUSmllJ/4MwBVAvZ63d/n2pfqOSKSAJwESvmldEoppfwqyOkCXA5jzDBgmOvuBWPMRifLk0uVBo46XYhcSusmdVovqdN6SVudK3mwPwPQfqCK1/3Krn2pnbPPGBMEFAOOpXwiEXkHeAfAGLNKRFrkSInzMK2XtGndpE7rJXVaL2kzxqy6ksf7swtuJVDLGHOVMSYYuAOYl+KcecAA1+3bgJ9ERPxYRqWUUn7itxaQiCQYY0YAi4BAYIaIbDLGPAmsEpF5wHvA/4wxO4Hj2CCllFIqH/LrNSARWQAsSLFvotft88DtWXzad7KhaPmR1kvatG5Sp/WSOq2XtF1R3Rjt4VJKKeUETcWjlFLKEXk6AGWU2ic/M8bMMMYc9h6CbowpaYz53hizw/WzhGu/Mca86qqn9caYZs6VPGcZY6oYYxYbYzYbYzYZY0a59hfoujHGhBpjVhhj1rnq5QnX/qtcaa92utJgBbv2F6i0WMaYQGPMGmPMfNd9rRfAGBNjjNlgjFnrHvGWnZ+lPBuAMpnaJz+bBXRNse/fwI8iUgv40XUfbB3Vcm3DgLf8VEYnJAAPi0h9oA1wv+vvoqDXzQWgo4g0BpoAXY0xbbDprl52pb86gU2HBQUvLdYoYIvXfa0Xj+tEpInXUPTs+yyJSJ7cgGuARV73xwPjnS6Xn+ugOrDR6/42oILrdgVgm+v2NKBPaufl9w34Crhe68anTgoDfwCtsRMsg1z7kz9T2NGq17huB7nOM06XPYfqo7LrH2lHYD5gtF6S6yYGKJ1iX7Z9lvJsC4jMpfYpaMqJSKzr9kGgnOt2gawrV/dIU2A5Wjfubqa1wGHge2AX8LfYtFfg+94LUlqsV4BHgCTX/VJovbgJ8J0xZrUrAw1k42cpT6biURkTETHGFNghjsaYCOBLYLSInPLOaVtQ60ZEEoEmxpjiwFygrrMlcp4xpgdwWERWG2OiHC5ObtRORPYbY8oC3xtjtnofvNLPUl5uAWUmtU9Bc8gYUwHA9fOwa3+BqitjTCFs8PlQROa4dmvduIjI38BibNdScVfaK/B978n1kl5arHzgWqCnMSYGm6G/IzAVrRcARGS/6+dh7JeWVmTjZykvB6DMpPYpaLxTGQ3AXv9w7+/vGqXSBjjp1YTOV4xt6rwHbBGRl7wOFei6McaUcbV8MMaEYa+LbcEGottcp6Wsl3yfFktExotIZRGpjv0f8pOI9KWA1wuAMSbcGFPEfRvoAmwkOz9LTl/kusILZN2A7di+7AlOl8fP7/1jIBaIx/a1DsH2Rf8I7AB+AEq6zjXYEYO7gA1AC6fLn4P10g7bb70eWOvauhX0ugEaAWtc9bIRmOjaXwNYAewEPgdCXPtDXfd3uo7XcPo9+KGOooD5Wi/J9VEDWOfaNrn/x2bnZ0kzISillHJEXu6CU0oplYdpAFJKKeUIDUBKKaUcoQFIKaWUIzQAKaWUcoQGIKXyGGOMGGNuy/hMpXI3DUBKZYExZpYrAKTcfne6bErlNZoLTqms+wHol2LfRScKolRepi0gpbLugogcTLEdh+TusRHGmG+MMWeNMXuMMXd5P9gY09AY84Mx5pwx5rirVVUsxTkDXAuBXTDGHDLGvJ+iDCWNMZ8bY84YY/5M+RpK5QUagJTKfk9g82I1Ad4BPjDGtIDknFqLgDhsYsdbgLbADPeDjTH3YNdWmYlNodMNmz7H20RsDq7GwKfADGNM1Rx7R0rlAE3Fo1QWGGNmAXcB51McekNExrlS008XkaFej/kBOCgidxljhgJTgMoictp1PAqb/LKWiOw0xuwDZotIqsvMu17jvyIy3nU/CDgFDBOR2dn3bpXKWXoNSKms+xm75LC3v71u/5bi2G9Ad9ftesB6d/BxWYZdDK2+MeYUdhGvHzMow3r3DRFJMMYcAcpmqvRK5RIagJTKurMisjMHnjcr3RHxqTxWu9RVnqJ/sEplvzap3N/iur0FaOheZ8WlLfazuEXswl/7gU45XkqlHKYtIKWyLsQYUz7FvkQROeK6fasxZiUQjV20rBPQ2nXsQ+wghQ+MMROBEtgBB3O8WlXPAC8bYw4B3wCFgU4i8mJOvSGlnKABSKms64xdDNDbfuwSxACTgX8CrwJHgEEishJARM4aY24AXsEuaHYeO5ptlPuJROQtY8xF4GHgOeA4sCCH3otSjtFRcEplI9cItdtF5Auny6JUbqfXgJRSSjlCA5BSSilHaBecUkopR2gLSCmllCM0ACmllHKEBiCllFKO0ACklFLKERqAlFJKOUIDkFJKKUf8P1l+Qsq3yHZMAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from copy import deepcopy\n",
+ "from sklearn.metrics import mean_squared_error\n",
+ "from sklearn.preprocessing import StandardScaler\n",
+ "\n",
+ "# extra code – creates the same quadratic dataset as earlier and splits it\n",
+ "np.random.seed(42)\n",
+ "m = 100\n",
+ "X = 6 * np.random.rand(m, 1) - 3\n",
+ "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)\n",
+ "X_train, y_train = X[: m // 2], y[: m // 2, 0]\n",
+ "X_valid, y_valid = X[m // 2 :], y[m // 2 :, 0]\n",
+ "\n",
+ "preprocessing = make_pipeline(PolynomialFeatures(degree=90, include_bias=False),\n",
+ " StandardScaler())\n",
+ "X_train_prep = preprocessing.fit_transform(X_train)\n",
+ "X_valid_prep = preprocessing.transform(X_valid)\n",
+ "sgd_reg = SGDRegressor(penalty=None, eta0=0.002, random_state=42)\n",
+ "n_epochs = 500\n",
+ "best_valid_rmse = float('inf')\n",
+ "train_errors, val_errors = [], [] # extra code – it's for the figure below\n",
+ "\n",
+ "for epoch in range(n_epochs):\n",
+ " sgd_reg.partial_fit(X_train_prep, y_train)\n",
+ " y_valid_predict = sgd_reg.predict(X_valid_prep)\n",
+ " val_error = mean_squared_error(y_valid, y_valid_predict, squared=False)\n",
+ " if val_error < best_valid_rmse:\n",
+ " best_valid_rmse = val_error\n",
+ " best_model = deepcopy(sgd_reg)\n",
+ "\n",
+ " # extra code – we evaluate the train error and save it for the figure\n",
+ " y_train_predict = sgd_reg.predict(X_train_prep)\n",
+ " train_error = mean_squared_error(y_train, y_train_predict, squared=False)\n",
+ " val_errors.append(val_error)\n",
+ " train_errors.append(train_error)\n",
+ "\n",
+ "# extra code – this section generates and saves Figure 4–20\n",
+ "best_epoch = np.argmin(val_errors)\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.annotate('Best model',\n",
+ " xy=(best_epoch, best_valid_rmse),\n",
+ " xytext=(best_epoch, best_valid_rmse + 0.5),\n",
+ " ha=\"center\",\n",
+ " arrowprops=dict(facecolor='black', shrink=0.05))\n",
+ "plt.plot([0, n_epochs], [best_valid_rmse, best_valid_rmse], \"k:\", linewidth=2)\n",
+ "plt.plot(val_errors, \"b-\", linewidth=3, label=\"Validation set\")\n",
+ "plt.plot(best_epoch, best_valid_rmse, \"bo\")\n",
+ "plt.plot(train_errors, \"r--\", linewidth=2, label=\"Training set\")\n",
+ "plt.legend(loc=\"upper right\")\n",
+ "plt.xlabel(\"Epoch\")\n",
+ "plt.ylabel(\"RMSE\")\n",
+ "plt.axis([0, n_epochs, 0, 3.5])\n",
+ "plt.grid()\n",
+ "save_fig(\"early_stopping_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#IMPLEMENT EARLY STOPPING THROUGH .... \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Logistic Regression"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Estimating Probabilities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {},
+ "outputs": [
+ {
+ "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": [
+ "# extra code – generates and saves Figure 4–21\n",
+ "\n",
+ "lim = 6\n",
+ "t = np.linspace(-lim, lim, 100)\n",
+ "sig = 1 / (1 + np.exp(-t))\n",
+ "\n",
+ "plt.figure(figsize=(8, 3))\n",
+ "plt.plot([-lim, lim], [0, 0], \"k-\")\n",
+ "plt.plot([-lim, lim], [0.5, 0.5], \"k:\")\n",
+ "plt.plot([-lim, lim], [1, 1], \"k:\")\n",
+ "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
+ "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\dfrac{1}{1 + e^{-t}}$\")\n",
+ "plt.xlabel(\"t\")\n",
+ "plt.legend(loc=\"upper left\")\n",
+ "plt.axis([-lim, lim, -0.1, 1.1])\n",
+ "plt.gca().set_yticks([0, 0.25, 0.5, 0.75, 1])\n",
+ "plt.grid()\n",
+ "save_fig(\"logistic_function_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Decision Boundaries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['data',\n",
+ " 'target',\n",
+ " 'frame',\n",
+ " 'target_names',\n",
+ " 'DESCR',\n",
+ " 'feature_names',\n",
+ " 'filename',\n",
+ " 'data_module']"
+ ]
+ },
+ "execution_count": 48,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.datasets import load_iris\n",
+ "\n",
+ "iris = load_iris(as_frame=True)\n",
+ "list(iris)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "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) # extra code – it's a bit too long"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style scoped>\n",
+ " .dataframe tbody tr th:only-of-type {\n",
+ " vertical-align: middle;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>sepal length (cm)</th>\n",
+ " <th>sepal width (cm)</th>\n",
+ " <th>petal length (cm)</th>\n",
+ " <th>petal width (cm)</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>5.1</td>\n",
+ " <td>3.5</td>\n",
+ " <td>1.4</td>\n",
+ " <td>0.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>4.9</td>\n",
+ " <td>3.0</td>\n",
+ " <td>1.4</td>\n",
+ " <td>0.2</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td>4.7</td>\n",
+ " <td>3.2</td>\n",
+ " <td>1.3</td>\n",
+ " <td>0.2</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)\n",
+ "0 5.1 3.5 1.4 0.2\n",
+ "1 4.9 3.0 1.4 0.2\n",
+ "2 4.7 3.2 1.3 0.2"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "iris.data.head(3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0 0\n",
+ "1 0\n",
+ "2 0\n",
+ "Name: target, dtype: int64"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "iris.target.head(3) # note that the instances are not shuffled"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array(['setosa', 'versicolor', 'virginica'], dtype='<U10')"
+ ]
+ },
+ "execution_count": 52,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "iris.target_names"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(random_state=42)</pre></div></div></div></div></div>"
+ ],
+ "text/plain": [
+ "LogisticRegression(random_state=42)"
+ ]
+ },
+ "execution_count": 53,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.linear_model import LogisticRegression\n",
+ "from sklearn.model_selection import train_test_split\n",
+ "\n",
+ "X = iris.data[[\"petal width (cm)\"]].values\n",
+ "y = iris.target_names[iris.target] == 'virginica'\n",
+ "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
+ "\n",
+ "log_reg = LogisticRegression(random_state=42)\n",
+ "log_reg.fit(X_train, y_train)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {},
+ "outputs": [
+ {
+ "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) # reshape to get a column vector\n",
+ "y_proba = log_reg.predict_proba(X_new)\n",
+ "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0, 0]\n",
+ "\n",
+ "plt.figure(figsize=(8, 3)) # extra code – not needed, just formatting\n",
+ "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2,\n",
+ " label=\"Not Iris virginica proba\")\n",
+ "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica proba\")\n",
+ "plt.plot([decision_boundary, decision_boundary], [0, 1], \"k:\", linewidth=2,\n",
+ " label=\"Decision boundary\")\n",
+ "\n",
+ "# extra code – this section beautifies and saves Figure 4–23\n",
+ "plt.arrow(x=decision_boundary, y=0.08, dx=-0.3, dy=0,\n",
+ " head_width=0.05, head_length=0.1, fc=\"b\", ec=\"b\")\n",
+ "plt.arrow(x=decision_boundary, y=0.92, dx=0.3, dy=0,\n",
+ " head_width=0.05, head_length=0.1, fc=\"g\", ec=\"g\")\n",
+ "plt.plot(X_train[y_train == 0], y_train[y_train == 0], \"bs\")\n",
+ "plt.plot(X_train[y_train == 1], y_train[y_train == 1], \"g^\")\n",
+ "plt.xlabel(\"Petal width (cm)\")\n",
+ "plt.ylabel(\"Probability\")\n",
+ "plt.legend(loc=\"center left\")\n",
+ "plt.axis([0, 3, -0.02, 1.02])\n",
+ "plt.grid()\n",
+ "save_fig(\"logistic_regression_plot\")\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "1.6516516516516517"
+ ]
+ },
+ "execution_count": 55,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "decision_boundary"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([ True, False])"
+ ]
+ },
+ "execution_count": 56,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "log_reg.predict([[1.7], [1.5]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 57,
+ "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": [
+ "# extra code – this cell generates and saves Figure 4–24\n",
+ "\n",
+ "X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
+ "y = iris.target_names[iris.target] == 'virginica'\n",
+ "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
+ "\n",
+ "log_reg = LogisticRegression(C=2, random_state=42)\n",
+ "log_reg.fit(X_train, y_train)\n",
+ "\n",
+ "# for the contour plot\n",
+ "x0, x1 = np.meshgrid(np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
+ " np.linspace(0.8, 2.7, 200).reshape(-1, 1))\n",
+ "X_new = np.c_[x0.ravel(), x1.ravel()] # one instance per point on the figure\n",
+ "y_proba = log_reg.predict_proba(X_new)\n",
+ "zz = y_proba[:, 1].reshape(x0.shape)\n",
+ "\n",
+ "# for the decision boundary\n",
+ "left_right = np.array([2.9, 7])\n",
+ "boundary = -((log_reg.coef_[0, 0] * left_right + log_reg.intercept_[0])\n",
+ " / log_reg.coef_[0, 1])\n",
+ "\n",
+ "plt.figure(figsize=(10, 4))\n",
+ "plt.plot(X_train[y_train == 0, 0], X_train[y_train == 0, 1], \"bs\")\n",
+ "plt.plot(X_train[y_train == 1, 0], X_train[y_train == 1, 1], \"g^\")\n",
+ "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
+ "plt.clabel(contour, inline=1)\n",
+ "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
+ "plt.text(3.5, 1.27, \"Not Iris virginica\", color=\"b\", ha=\"center\")\n",
+ "plt.text(6.5, 2.3, \"Iris virginica\", color=\"g\", ha=\"center\")\n",
+ "plt.xlabel(\"Petal length\")\n",
+ "plt.ylabel(\"Petal width\")\n",
+ "plt.axis([2.9, 7, 0.8, 2.7])\n",
+ "plt.grid()\n",
+ "save_fig(\"logistic_regression_contour_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Softmax Regression"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(C=30, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(C=30, random_state=42)</pre></div></div></div></div></div>"
+ ],
+ "text/plain": [
+ "LogisticRegression(C=30, random_state=42)"
+ ]
+ },
+ "execution_count": 58,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
+ "y = iris[\"target\"]\n",
+ "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
+ "\n",
+ "softmax_reg = LogisticRegression(C=30, random_state=42)\n",
+ "softmax_reg.fit(X_train, y_train)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([2])"
+ ]
+ },
+ "execution_count": 59,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "softmax_reg.predict([[5, 2]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0. , 0.04, 0.96]])"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "softmax_reg.predict_proba([[5, 2]]).round(2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 61,
+ "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": [
+ "# extra code – this cell generates and saves Figure 4–25\n",
+ "\n",
+ "from matplotlib.colors import ListedColormap\n",
+ "\n",
+ "custom_cmap = ListedColormap([\"#fafab0\", \"#9898ff\", \"#a0faa0\"])\n",
+ "\n",
+ "x0, x1 = np.meshgrid(np.linspace(0, 8, 500).reshape(-1, 1),\n",
+ " np.linspace(0, 3.5, 200).reshape(-1, 1))\n",
+ "X_new = np.c_[x0.ravel(), x1.ravel()]\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",
+ "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
+ "contour = plt.contour(x0, x1, zz1, cmap=\"hot\")\n",
+ "plt.clabel(contour, inline=1)\n",
+ "plt.xlabel(\"Petal length\")\n",
+ "plt.ylabel(\"Petal width\")\n",
+ "plt.legend(loc=\"center left\")\n",
+ "plt.axis([0.5, 7, 0, 3.5])\n",
+ "plt.grid()\n",
+ "save_fig(\"softmax_regression_contour_plot\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Last but not least "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Batch Gradient Descent with early stopping for Softmax Regression\n",
+ "Exercise: _Implement Batch Gradient Descent with early stopping for Softmax Regression without using Scikit-Learn, only NumPy. Use it on a classification task such as the iris dataset and (Titanic or spams or ...) ._"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.14.3"
+ },
+ "nav_menu": {},
+ "toc": {
+ "navigate_menu": true,
+ "number_sections": true,
+ "sideBar": true,
+ "threshold": 6,
+ "toc_cell": false,
+ "toc_section_display": "block",
+ "toc_window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/ML/04_entrainement/Training models.md b/ML/04_entrainement/Training models.md
new file mode 100644
index 0000000..59ab7dc
--- /dev/null
+++ b/ML/04_entrainement/Training models.md
@@ -0,0 +1,35 @@
+# Linear Regression
+- 1 poids par input
+- Représentation vectorielle : $ŷ = h_{{\theta}}(x) = \theta \cdot x$
+ - $h_{\theta}$ = fonction d'apprentissage
+ - $\theta$ = vecteur à apprendre
+Usage de la RMSE à optimiser
+## Equation Normale
+$\hat{\theta} = (X^TX)^{-1}X^TX$
+Pseudo inverse
+
+## Decomposition en valeur singulière (SVD)
+$X \rightarrow U\Sigma V^T$ et $X^+ = V\Sigma^+ U^T$
+
+## Complexités
+Eq normale : $O(n^2.4) \approx O(n^3)$
+SVD : $O(n^2)$
+
+# Descente de Gradient
+-> Recherche de minimum
+Part d'un vecteur initialisé aléatoirement
+Calcul de la dérivée de $f(\theta)$ (MSE par exemple)
+$\theta' = \theta - \alpha f'(\theta)$
+$\alpha$ = learning rate
+Si $\alpha$ est trop petit : convergence trop lente
+Si $\alpha$ est trop grand : risque de "saut de vallée" et divergence
+
+De toute façon risque de tomber dans un minimum local
+
+Normalisation capitale pour la descente de gradient
+Bien mieux que SVD et Normale
+
+GridSearch pour trouver un bon learning rate
+limiter le nombre d'époques pour éviter la convergence trop lente
+Set le nombre d'époques grand mais interrompre si $\nabla$ très petit
+$O\left( \frac{1}{\epsilon} \right)$ \ No newline at end of file
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