Regression_Algorithms/MLRegressionAlgorithms.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ua-datalab/MLWorkshops/blob/main/Regression_Algorithms/MLRegressionAlgorithms.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Classical Machine Learning: Regression Algorithms.\n",
        "\n",
        "Regression analysis is the process of estimating the relationship between a dependent variable and independent variables."
      ],
      "metadata": {
        "id": "PG732HC_cxCy"
      },
      "id": "PG732HC_cxCy"
    },
    {
      "cell_type": "markdown",
      "source": [
        "We load all the required libraries"
      ],
      "metadata": {
        "id": "Rcju0_-EmzQL"
      },
      "id": "Rcju0_-EmzQL"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "47bdc9cd",
      "metadata": {
        "id": "47bdc9cd"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib as mpl\n",
        "\n",
        "from sklearn.preprocessing import add_dummy_feature\n",
        "\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.linear_model import SGDRegressor\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn.linear_model import Ridge\n",
        "from sklearn.linear_model import Lasso\n",
        "from sklearn.linear_model import ElasticNet\n",
        "\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.pipeline import make_pipeline\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "03ba8cfe",
      "metadata": {
        "id": "03ba8cfe"
      },
      "source": [
        "## Linear Regression\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6f9682cd",
      "metadata": {
        "id": "6f9682cd"
      },
      "outputs": [],
      "source": [
        "# Generate a collection of random points around a line y= 4 + 3*x\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\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5f0d3ee8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "5f0d3ee8",
        "outputId": "ab3f1ff4-9974-4ce5-e507-dff4000b6a1c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Plot previous generated data\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.title('Random set of points')\n",
        "plt.axis([0, 2, 0, 15])\n",
        "plt.grid()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "24009594",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "24009594",
        "outputId": "8c34cdb8-2cbc-4f95-ed86-eb91ec3c993c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [2.77011339]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "# Using Linear Algebra to solve the best parameters (Intersection & Slope)\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\n",
        "theta_best\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a832f4bb",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a832f4bb",
        "outputId": "2ec70910-0ec7-49fe-b667-0543923227c1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [9.75532293]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "# Predict y values for X=0 and 2\n",
        "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\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7bc560e9",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "7bc560e9",
        "outputId": "b55f1b4a-6a5a-4f2f-b1c1-1c4691642cac"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEYCAYAAABcGYHrAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAAsTAAALEwEAmpwYAAAtaUlEQVR4nO3de3wU9b3/8deHkHC/iMYrFfACFhQDorJKMIjHWq/Vah96bNGqpbTaaqtWrbXV+lN7OT21x57zsNRqtfXY8tNqL7/aqsiWVOIFMCBgFbWoeMNyD5eEJJ/fHzObbGIum2RmL+H9fDz2sZud3ZnPDsP3M/OZ73zH3B0REZE+uQ5ARETygxKCiIgASggiIhJSQhAREUAJQUREQkoIIiICKCFIL2Zm5Wb2Sq7jALDAfWa20cyez6fYRFJM1yFIoTOzNcBl7v5UrmNpj5mVAw8B49x9WxvT15Dnv0F6Px0hiETMzPq28fYoYE1byUAkXyghSK9lZhVmtjbt7zVmdo2ZLTezzWb2WzPrnzb9dDOrNrNNZrbIzCamTbvezF43s61mtsrMzk6bdrGZPWNmPzaz9cDNreK4FLgHSJhZjZndkh6bmf0KOBD4Yzj9G3GtE5GOtLUnI9KbfQY4BdgJPANcDNxtZpOAe4EzgMXAZ4E/mNk4d68FXgfKgfeB84Bfm9kh7v5eON9jgd8A+wDF6Qt091+YWQNBSWgaBMkqbfrnwpKSSkaSUzpCkN3Nf7n7u+6+AfgjUBa+Pxv4mbs/5+4N7n4/UAtMBXD3/xt+r9HdfwusBo5Jm++77n6Xu9e7+47s/RyR6CghyO7m/bTX24HB4etRwNVhuWiTmW0CPgbsD2Bms9LKSZuAw4G90ub1duyRi8RMJSORwNvAbe5+W+sJZjYK+DkwE6hy9wYzqwYs7WM97a6n7n6SczpCkN6i2Mz6pz26urPzc2COmR0bXjMwyMxOM7MhwCCCBvtDADP7PMERQpQ+AA6KeJ4iXaKEIL3Fn4EdaY+bu/Jld18MfAH4KbAReI3ghDPuvgr4EVBF0HAfQXBCOkp3AN8KS1LXRDxvkYzowjQREQF0hCAiIiElBBERAZQQREQkpIQgIiKAEoKIiITy6sK04cOH+yGHHJLrMDq1bds2Bg0alOswOqU4o1MIMYLijFqhxLlkyZJ/uXtpT+eTVwlhn332YfHixbkOo1PJZJKKiopch9EpxRmdQogRFGfUCiVOM3szivmoZCQiIoASgoiIhJQQREQEyLNzCG3ZtWsXa9euZefOnbkOpcmwYcN4+eWXcx1Gp7oSZ//+/Rk5ciTFxcWdf1hEeqW8Twhr165lyJAhjB49GjPr/AtZsHXrVoYMGZLrMDqVaZzuzvr161m7di1jxozJQmQiko/yvmS0c+dO9txzz7xJBr2RmbHnnnvm1VGYiGRf3icEQMkgC7SORaQgEkKuFRUVUVZWxuGHH855553H9u3buz2viy++mIcffhiAyy67jFWrVrX72WQyyaJFi5r+vvvuu3nggQe6vWwRkY4oIWRgwIABVFdXs2LFCkpKSrj33ntbTK+vr+/WfO+55x7Gjx/f7vTWCWHOnDnMmjWrW8sSEelMJAnBzO41s3VmtqKNaVebmZvZXm19t9CUl5fz+uuvk0wmKS8v58wzz2T8+PE0NDRw7bXXcvTRRzNx4kR+9rOfAcEJ2yuuuIJx48Zx0kknsW7duqZ5VVRUNF2Z/Ze//IXJkydz5JFHMnPmTNasWcPdd9/Nj3/8Y8rKyqisrOTmm2/mP/7jPwCorq5m6tSpTJw4kbPPPpuNGzc2zfO6667jmGOOYdKkSVRWVgKwcuVKjjnmGMrKypg4cSKrV6/O5moTkQIQVS+jXxLcerBFPcPMPgacDLwVyVKuugqqqyOZVZOyMrjzzow+Wl9fz+OPP950KfvSpUtZsWIFY8aMYe7cuQwbNowXXniB2tpajj/+eE4++WRefPFFXnnlFVatWsUHH3zA+PHjueSSS1rM98MPP+QLX/gCCxcuZMyYMWzYsIERI0YwZ84cBg8ezDXXBHdUnD9/ftN3Zs2axV133cUJJ5zAt7/9bW655RbuDH9HfX09zz//PA8//DC33HILTz31FHfffTdXXnklF154IXV1dTQ0NPR0zYlILxNJQnD3hWY2uo1JPwa+Afw+iuXkyo4dOygrKwOCI4RZs2bx0ksvccwxxzR103ziiSdYvnx50/mBzZs3s3r1ahYuXMgFF1xAUVER+++/PyeeeOJH5v/ss88yffr0pnmNGDGiw3g2b97Mpk2bOOGEEwC46KKLOO+885qmn3POOQBMmjSJNWvWAJBIJLjttttYu3Yt55xzDoceemj3V4iI9EqxXYdgZmcB77j7so56sJjZbGA2QGlpKclkssX0YcOGsXXr1uCPW2+NJ9jU/NsxYMCAptILQENDA9u3b6dfv35Nse3atYvvf//7nHTSSS2++9hjj7Fz586mz9XX17Njxw62bt1KQ0MD27ZtY8eOHezatav5d4Zqa2spLi5uej/9b3dver+mpobGxsamedbX17eIa+vWrZxxxhlMmDCBv/71r5xyyin85Cc/aUooKTt37vzI+s+GmpqanCy3KwohRlCcUSuUOKMSS0Iws4HANwnKRR1y97nAXIBx48Z565EFX3755by4CCw9hq1btzJw4ED69u3b9P5pp53G/fffz+mnn05xcTGvvvoqBxxwACeddBI/+9nP+OIXv8i6deuorKxk1qxZDBkyhKKiIgYNGsSMGTO4+uqr+de//tWiZLTXXnuxZcuWpmX069ePfv36MXLkSEaMGEF1dTXl5eU8+uijzJgxo8U8hwwZwvr16zEzhgwZwhtvvMHEiRM58sgjWbduHa+99hqnn356i9/Yv39/Jk2alL2VGiqEESULIUZQnFErlDijEtcRwsHAGCB1dDASWGpmx7j7+zEtM6cuu+wy1qxZw+TJk3F3SktLeeyxxzj77LN5+umnGT9+PAceeCCJROIj3y0tLWXu3Lmcc845NDY2svfee/Pkk09yxhlncO655/L73/+eu+66q8V37r//fubMmcP27ds56KCDuO+++zqMb968efzqV7+iuLiYfffdl29+85uR/n4R6QXcPZIHMBpY0c60NcBenc1j7Nix3tqqVas+8l6ubdmyJdchZKSrceZqXS9YsCAny+2KQojRXXFGrVDiBBZ7BO14VN1OHwKqgHFmttbMLo1iviIikj1R9TK6oJPpo6NYjoiIxEdXKouICFAgCSEokUmctI5FJO8TQv/+/Vm/fr0arBh5eD+E/v375zoUEcmhvL9BzsiRI1m7di0ffvhhrkNpsnPnzoJoPLsSZ+qOaSKy+8r7hFBcXJx3d/FKJpM5uYCrqwolThHJD3lfMhIRkexQQhAREUAJQUREQkoIIiICKCGIiEhICUFERAAlBBERCSkhiIgIoIQgIiIhJQQREQGUEEREJKSEICIigBKCiIiElBBERARQQhARkVCPE4KZ3Wtm68xsRdp7PzSzf5jZcjN71MyG93Q5IiISryiOEH4JnNLqvSeBw919IvAqcEMEyxERkRj1OCG4+0JgQ6v3nnD3+vDPZwHdm1FEJM9ZFDevN7PRwJ/c/fA2pv0R+K27/7qd784GZgOUlpYeNW/evB7HE7eamhoGDx6c6zA6pTijUwgxguKMWqHEOWPGjCXuPqXHM3L3Hj+A0cCKNt6/EXiUMPF09hg7dqwXggULFuQ6hIwozugUQozuijNqhRInsNgjaMv79jijtMPMLgZOB2aGAYuISB6LJSGY2SnAN4AT3H17HMsQEZFoRdHt9CGgChhnZmvN7FLgp8AQ4Ekzqzazu3u6HBERiVePjxDc/YI23v5FT+crIiLZpSuVRUQEUEIQEZGQEoKIiABKCCIiElJCEBERQAlBRERCSggiIkBVFdxxR/C8u4pt6AoRkUJRVQUzZ0JdHZSUwPz5kEjkOqrs0xGCiOz2kskgGTQ0BM/JZK4jyg0lBBHZ7VVUBEcGRUXBc0VFriPKDZWMRGS3l0gEZaJkMkgGu2O5CJQQRESAIAkUQiKoqoovcSkhiIgUiLhPfuscgohIgYj75LcSgohIgYj75LdKRiIiBSLuk99KCCIiBSTOk98qGYmIZGB3GNpCRwgi0iNxdoPMF5n07ukN60EJQUS6bXcZA6it3j3pvzOO9ZCLBBNJycjM7jWzdWa2Iu29EWb2pJmtDp/3iGJZIpI/dpcxgDrr3RP1ekglmJtuCp6zVaaK6hzCL4FTWr13PTDf3Q8F5od/i0gvsruMAZTq3XPrrW3v/Ue9HnKVaCMpGbn7QjMb3erts4CK8PX9QBK4LorliUh+2J3GAOqod0/U6yGVYFIlqGwlWnP3aGYUJIQ/ufvh4d+b3H14+NqAjam/W31vNjAboLS09Kh58+ZFEk+campqGDx4cK7D6JTijE4hxAiKM2q5jHPlyqFUVw+nrGwTEyZs6fCzM2bMWOLuU3q8UHeP5AGMBlak/b2p1fSNnc1j7NixXggWLFiQ6xAyojijUwgxuivO1hYtcr/99uC5OwplfQKLPYJ2PM5eRh+Y2X7u/p6Z7Qesi3FZIiIt5GsPqMh7D73/fgQzCcSZEP4AXAR8L3z+fYzLEhFpobOuornQ4yTlDm+8AZWVwWPhQnjttcjiiyQhmNlDBCeQ9zKztcB3CBLBPDO7FHgT+EwUyxIRyUSuTsymtHUk0DpJPfBAJ0cLjY2wcmVz419ZCe++G0wbMQKmTYMvfhGuvTaSmKPqZXRBO5NmRjF/EWlWCFfE5kOMuewB1d6RQHqS6tsX7r03SA5Nn5myC5YubW78//532LgxmOkBB8AJJ0B5efAYPx76hFcO5FNCEJHsyNe6eLp8ijFXd0Frr1yVnqTeegt+/nOnocGo29lA8nO/JPHeV2H79mAmY8fCOecEjf/06TB6NJjFGrcSgkgByce6eGuFEGPc2i1XbdxIYv0zJDZVUlW5gfsa7qKRYvr6Lir6LIRLLw0a/2nTYN99sx63EoJIAcl1XTwThRBj3JqOBP64hYqBL5B48FGYUwkvvRScGC4uhsMuxouKoNHw4n5w//2Q48SphCBSQArhyuBCiDEWqR5AYf0/sXAhiddfD6YNGgTHHQfnnhuUgI49luSdA2i4KfhaQ0N+HEkpIYgUmFzVxbsiFzFm/UR2YyOsWNGyC+h77wXT9twzKPt86UtBCaisLDgqSJOPR1JKCCJS8LJyInvXLliypLnxf+aZ5h5AI0cGLfr06cERwMc/3twDqB35eCSlhCAiBS+WE9nbtzN86dJgZpWVQdbZsSOYNnYsfPrTzT2ARo3qVg+gfDvaU0IQkYKUXiKKpPyycWPQ7z91BLBkCWX19UFDX1YGX/hC8zUA++wT5U/JG0oIIlJw2ioRdbn88u67La8AXrEiOMNbUgJHHw3XXMPy4cOZOGcODBv2keXnU6knKkoIIlJw0ktEtbVw883B44Yb2vmCO7z+essE0LoH0Gc+E+z9H3MMDBgAwIZkss1kkI0L73KRdJQQRKTgpEpEtbVBZ5+nngra+KbGOdUDKNX4L1zYPCronnsGDf+Xv9zcA6hv5k1hNi68y9XV3koIIhK5uPduUz10br45SAaNjVBX6yS/u5BE0Q+DHkCbNgUfHjkSTjyxuQfQYYe12wMok7iz0V00V1d7KyGISKSysne7bRuJ7c9y8wFvUMnnqKOIksZdVPzlehi3MbgALJUAMuwB1FbcbclGd9FcXaOghCASo9568rEjsezdbtjQ3AOosjK4HqC+nkSfPsw/5BmSe51LxWmDSFz6WLd7AHUl7ri7i+bqGgUlBJGY5NOon3FoL9ml1/f79AlK9l32zjstrwBesSJ4v6QkOOl77bXBEUAiQWLYsA6HAMo0Kbe1V15b243YI5KLaxSUEERi0ptH/ewo2SUScOedcPnlwW+/6io44ogOfrt7cNev9B5Ab7wRTBs8OOgBdP75zT2A+vePJM7W2torTyYzXlSvoIQgEpN8HKsmKp0lu/Xrg3a+sbGN6Q0NDHrttWDkz8pKquZvJ7nhCCpIktjrtaDhv+KK4LmLPYC6Gmdr+XblcLYpIYjEJB/HqolKZ8mu5XSnYs+X4PuPN90F7OjNmwGo2vssZm5+hDorpqQfzP+9kTiu5QngnpyH6c1JOQ5KCCIxyuYeZ1UVPPjggfTrF/8yO0x227aR2FbF/PP/GUx/50ESX/xbMO2ww+Azn+Hl0lI+Pns2yf8dRd1N0OBQtwuSf4PEcS1/U0/Ow/TmpBwHJQSRXiDVcNbWjuHBB7NzArsp2W3YAH/4e3P9f8kSaGgg0acPibIyOGs6lH81GA56770B+CCZ5OOjRnW6Bx/FeZjdvQzUFbEmBDP7GnAZ4MBLwOfdfWecyxTZHaUazsZGi/8E9tq1LXsArVwZvF9SAsceC9ddF9T/jzsOhg7tcFbt7cGnykR77qmSTzZ1mhDM7HBgrrsfF/49Gfihu8/s5HsHAF8Fxrv7DjObB5wP/LLHUYtIC81dPRspKekTXcPpDqtXt+wB9M9/BtOGDAka/QsuCLqAHn10l3oApbTeg29dJrrzzuAktUo+8cvkCGEVcJCZFbl7A/CfwNe7MP8BZrYLGAi8270wRaS11idb58+He+9dwyWXHNT9hrOhobn3z6Pvk3xhIBU1fyLBs7DXXsGe/1e/GjwfeWSPegC1paoqGI4iNUZRXV2QDNodtE4iZe7e+YfM5gNfAw4FznT3izKaudmVwG3ADuAJd7+wjc/MBmYDlJaWHjVv3rzMo8+RmpoaBg8enOswOqU4o9OTGFeuHEp19XDKyjYxYcKWSOJZuXIoV199JLt29aG4uJEf/WgZEyZs6XKctmsXQ155heHLlzNs+XKGrVhB323bqGIqM3maOkoo7tvAT69/ioNPHNCtm8C0pa04U7+prq4P7mDmlJR402/LhVxsm93ZXmbMmLHE3af0eOHu3umDoFH/EsF5gAMy/M4ewNNAKVAMPAZ8tqPvjB071gvBggULch1CRhRndLob46JF7gMGuBcVBc+LFkUTz+23B/OE4Pn22zOMc+tW9yeecL/pJvcTTnDv3z+YCbh//OPus2e7//rXfvs3NrY5/6i0FWf6b+rTx/3kk6NbX92V7W2zu9sLsNgzaJc7e2R6vPcsQe3/v939nQy/cxLwT3f/EMDMfgccB/w6w++LFLy4rlbOuH/9+vXBGECp+v/SpUEwffrApEkwZ05Q/582DUpLm+d/EJTc1fH8ox6nqaICioqCUlHfvkHpaHc7Z5Drq9szTQj/AGqB73dh3m8BU81sIEHJaCawuGvhiRS2uC6Maq93Tr8PP4T//d/mXkCpHkD9+gXDPlx/fVD/TyQ67AHUWf/9uMZpSlWkIqpMFZxcX0iXaUK4ErjB3bdlOmN3f87MHgaWAvXAi8DcrocoUrjivDAqMdVJ7Lk62Pu/O+gFlFizJpg4ZAgcfzz8+78HRwBTpnS5B1BH/ffj2JNNJqG+Pqhf1df3rrGfMpXrC+k6TAhmdjDw/4Bn3P3+rs7c3b8DfKebsUme2x2Hdu6OyC6MamiA5ctbdgFdty6YVloK5eW8dtppHHLJJTBxYuQ9gNLFsSeb673jfJHLC+k63GLc/XXgsCzFIgWktw/tnBdqa2Hx4ubG/5lnYEvY62TUKPjEJ4LyT3k5jBsHZqxNJjlk8uTYQ4tjTzbXe8eioSukm3J98qtX2ro1yLSp+v9zz1G1s4wkFVSMGkbigguaE8CBB+Y62lj2ZFPzSw07rW0qu5QQcqxQyy46vI/Av/7VfBewhQvhxRebewBNnkzVWd9j5qOXU9dQRMk6Y/5FhbWNdIeOPHNLCSGHCmnjb524esvhfVYT8ttvt6z/r1oVvN+vXzAG0PXXN90FjCFDSN4BdQ/vXkdhOvLMLSWEHCqUjb+9xFXoo0jGmpDd4dVXmxv/ykpI7wE0bRp89rNB+efoo4Ok0MrueBS2O/7mfKKEkEOFsvEXSuLqqkh/V6oHUHoCSPUA2nvvoOG/6qrgCGDixOAKrE70lqOwrtgdf3M+UUJIk+16fqFs/IWSuLqqR7+rthZeeCEYBO7360hWD6ei9i/BIHCjRwc9gKZPDxLB2LHdvtKqp0dhnW3T+XgOq9CPPAuZEkIoV/X8Qtj4CyVxpWTayHXldxVt3w5PPNF8BPDcc1BbGwwCZ8EgcCUlNzL/t+tJfGqfaH9QN3W2TRfSOSzJDiWEUG8ti0QlnxNXegKArjVy7f6uDz9s0QNo2osvBoPsFBUFYwBdfjmUl5Nc/G/UfW9AsN00QPLlfUh8Kvrf2B2dbdPa5qU1JYRQby2L9Hat93Ivuqibjdxbb7W8C9jLLwfv9+8Pxx7LmxdeyOjPfQ6mTg1OCocq9oGS/wwqSH36BHf4iktXyzudbdPa5qU1JYRQoZVF8kE+1J9b7+VCBo2cO7zySssuoG++GUwbOjQYA2jWrKD+P2UK9OvHmmSS0W3MLJEI7uh1+eVBDFddBUccEf366E55p7NtWtu8tKaEkCafyyL5Jl/qz633cmfNCh4tGrmGBli2rGUPoA8/DGaw997Byd+vfz14PuKIjHoApVu/PsgxqTt8xVF66W55p7NtWtu8pFNCkG7Jl/pzm3u5O3eSqH8BFlTCLQth0aJgWAiAMWPgk58M9v6nT4dDD+3xWMvdKb1EXf4RiYISgnRLPjVQicO3ktiyCP60EK6rhOefD4r6ABMmwIUXNncBHTky+uV3sfQSR/lHJApKCNItOW2gUj2AUiWg9B5AkyfDFVcEjf+0afGe5U3TldJLXOUfkZ5SQpBu60oD1aMT0G+91dz4L1wI//hH8H7//kGvnxtvDI4Apk6FLN8QvTvy6ehKJJ0Swm4g172B2iuRpOIaOnRoc6PoHjT46T2A3normDZsWNAD6KKLggRw1FFtjgGU71T+kXylhNDL5UNvoLZKJJCKy+nb5wgmv/obEm/PC0pBqR5A++wTlH6uuSZ47kYPoLj0NMmq/CP5SAmhl8uH3kAtSyROxfBlJL+zkbod02mgCBog+V/LSIyphlNPbe4BdMghXeoBlK0joXxIsiJxUELo5XJer96yhcTmRcw/bw3JvxkV7zxI4suVwFRKwjGAioucioe/Bmfd0e3FxNFItx4SIyUfkqxIHGJNCGY2HLgHOBxw4BJ3r4pzmYUkG3u0Wa9Xr1vXsgdQdTU0NpIoKiJx1FFw3nQov4bE8ccz/9UB4TmEZSTO6tl9gKNupFsnmB/+sPk8Ry6SbK7PA8nuIe4jhJ8Af3H3c82sBBgY8/IKRjbLDrHWq998s2UPoFdeCd5P9QD61reCElAbPYBScSWTW3ocRtSNdOsEU109vGlatpOsSlSSLbElBDMbBkwHLgZw9zqgLq7lFZp8KTt0ac/TPRj0LX0QuLffDqYNGxb0+//855t7AJWU9HyZGYq6kW6dYMrKNn1kedn698qXbUV6P3P3eGZsVgbMBVYBRwJLgCvdfVurz80GZgOUlpYeNW/evFjiiVJNTQ2De9jffeXKoVx99ZHs2mUUFzs/+tEyJkzo+Z5yus7ibI6hD8XFjR+JwRoaeOOJraz8m3Hijsc56c3fULJ5MwC1I0aw+Ygj2HzkkWw64gi2jRmTUQ+gtpY5atS7PV6fcVi5cijV1cMpK9uU0xi7sq1EsW1mg+KM1owZM5a4+5Qez8jdY3kAU4B64Njw758At3b0nbFjx3pUFi1yv/324DlqCxYsiGQ+mcbY3d/SWZy33+5eVOQOwfPt361z/9vf3G+91f3kk33RgBN9ANu8iF0+wLb7olNvdf/FL9xffdW9sbFrwbS3zNujW59xSK37n/50SV7E0dk2kM/rMp3ijBaw2CNot+M8h7AWWOvuz4V/PwxcH+PymhRKzTWTskOcv6ViSg0lRQOoa4QS30XFd0+mqn4XSSqoOKiU5MTzqHuhPw2Nfajr05fktG+RuKSHy6z4aK0/NexQvklf9337HsnkyR9d99k62avrFiQbYksI7v6+mb1tZuPc/RVgJkH5KHaFXHNt3cBE+lvWrWtxBXBi2TLmNx5Dss+JVBz2AZR9hpkPf4m6hj6UvGfceR2ULI+2N01btf7UhWr5Jn3du9tH1n2h7HiIZCruXkZfAR4Mexi9AXw+5uUBedD3vpvaamC6/Vvc6f/++/CrXzX3Akr1ABowIOj1c9NNJMrLSUydCoMGcccdUPfb5uSzfn08vWkKZW83fd337es5vx5BXU8lbrEmBHevJjiXkFVxdAts7yKlKLXVwNxwQ4a/JdUDKK0L6NS1a4Npw4cHPYAuuSToAtpOD6C2kk+2G+98avTSt6OhQ5eRSLS8ViKbOx46GpFs6LVXKve0Ievoxu3pFylFqb0Gps3fUl8fDPuc6gJaWRns0gPstx+Ul7N633059NJL4fDDgxv+diLXg67lY6PX0bUS2VxfhVwGlcJRsAkhzj3Jzm7cnn6RUpQ6bGB27Ahu/JI6AqiqgpqaYNrBB8MZZzTfBObgg8GMd5JJDp04scsx5Mv9kQuh0cvW+irUMqgUloJMCHHvSbZumKDji5Tai7E7Caupgdm8GR5f1JwAXnghCMAs2OO/6KKg8S8vh/3379Lvy6eyTLq4G718/d2ZyPXRm+weCjIhxL0n2dmN22trO76ArFsJ64MPWl4BvHx5cBewvn1hyhS48sqg8T/+eBgxotu/LR/LMilxNnr5/LszVSgn46VwFWRCiHtPsr2GKfXcWTfJ9hJW0x7qCU5ivzVU3fcyycd3UPHBvOBeABD0AEok4KabghLQscfCoEGR/bZ8L8vE1ejl++8WyQcFmRCycfjck9tDfiRhTW+k6sE1zPz8x6jb1YcSq+NOv52r+Al1lFDS53TmX34mic8eHNwTuJ0xgKLQ1WRayGWWdKrBi3SuIBJCW41Splf5xt2YtVmKmLKL+XetJvnIeipq/kTizHu4Y8Ns6riVBoqoo4RHDvsWda8OoKHRqLO+JA+4kMTUeGJM15Vk2hvKLCmqwYt0Lu8TQncbpWw1ZkEpwmloMOp2NpD83C9JvH8liW3bSEBw16+zzqJi/2mU/KgPdbuckpIiPv21UVRelZs91kyPfnpbmUU1eJGO5X1C6G6jFGdjVlRTA3/+MyxcSMWfN1DScCd1FAfjAZGEiy9u7gK6334AJID5p7XcQz3iiPzeY00vsxQVBfe6r6rqXqy9pfQk0pvlfULobu030prx+++3uABs2rJlwZXBffuSmDKF+RfeR7LoRCr+/QASn/hVu7NpvYfa3h5rvjSeqTLLAw/AfffBz38O99/f9aOt3lR6EunN8j4hdLf22+2asTusWdPyLmCrVwfTBg6ERII1F13EmFmzgh5AAweSIDgCiEK+NZ6pwefq69s/2uosgfW20pNIb5X3CQG6fwK59ffmzoVHHoFPfxpmzw7fbGyEVatajALKO+8E0/bYIxgDaPZsKC+nqu4okn/vy9ChS7l8Rsf3AO7uXn4+Np4dHW1lksDUw0ekMBREQuhMR41SqmHetAl+8AMA54kngCeeYPau/wluCL9hQ/Dh/fdvrv2Xl8OECU1jAFVVwcxPdDw2fibxdCYfG8+OjrYySWDq4SNSGPIuIXRnz7qjC8FmznTqap3gpm0WPpxHHnFmH7IKPvWpoPGfPh3GjAmGhuhkGW2NjZ9JPJnI18azvaO0TBOYeviI5L+8Sgg7dhR1a8+6ZaPkVBQvguv/SPKhUdTt+AIN9MWoB4qA4B7Sn/7BVLh2dcaxdTY2fvvxdH0vv5Aaz3xNYCLSdXmXEDras27z6OH990msrWT+qW+RfKaYivd/Q+LaKigupmLcxZT0baSusZGSfkV85StGdXXqHMLwLsXW2dj47X12d2gkCymBiUj78iohDBjQwLZtHZ28dOpqoaRvA/NP/gGJV37Z1AMoMXAgieOOgy+dAuW3wbHHkhg4kPkRduHsaGz89j4rIlIo8i4htNizPrYRXloJlZUk796Duh3n0UBf6uqc5FP1JE7+eNADaPp0mDQJios/Mk81zF2TL9dAiEj25VVCwJ1En+dIFFfCHQuDHkAbNwJQsdcZlBSdQ533oaSkiIqnvgXHd34XMMlcvl0DISLZlVcJYchrrwU3fwc49FA455ymLqCJMWOY/6xp7zVG+XgNhIhkT+wJwcyKgMXAO+5+ekefrRs2LLh6rLwc9t33I9NV/olXPl4DISLZk40jhCuBl4GhnX2wdu+94bzz4o+oi3aXuvru1jtKRFqKNSGY2UjgNOA24OtxLisubdXVezMdhYnsvsyDS3jjmbnZw8AdwBDgmrZKRmY2G5gNUFpaetS8efNii6c7HnzwQO69dwyNjUafPo1ccskazjprFYMHD45tmStXDqW6ejhlZZuYMKHzLq7tqampiTXOqBRCnIUQIyjOqBVKnDNmzFji7lN6PCN3j+UBnA78T/i6AvhTZ98ZO3as55tFi9wHDHAvKgqeFy1yX7BgQVaX111xxhmlQoizEGJ0V5xRK5Q4gcUeQbsdZ7/N44EzzWwN8BvgRDP7dYzLi0Wqrn7rrdnphtlWTx8RkWyI7RyCu98A3ABgZhUEJaPPxrW8OGWzrq6ePiKSK3l1HYKop4+I5E5WEoK7J4FkNpbVG6inj4jkwm4/9kNVFdxxR/AsIrI76xUlo+5eOKaxe0REmhV8QuhJo66xe0REmhV8yagn3TRTPXqKinrWo0dlJxHpDQr+CKEn3TSj6NGjspOI9BYFnxB62qj3tEePyk4i0lsUfEKA3HbT1IVkItJb9IqEkEu6kExEegslhAjoQjIR6Q0KvpeRiIhEQwlBREQAJQQREQkpIYiICKCEICIiISUEEREBlBBERCSkhCAiIoASgoiIhJQQREQEUEIQEZFQbAnBzD5mZgvMbJWZrTSzK+NaloiI9Fycg9vVA1e7+1IzGwIsMbMn3X1VjMsUEZFuiu0Iwd3fc/el4eutwMvAAXEtT0REesbcPf6FmI0GFgKHu/uWVtNmA7MBSktLj5o3b17s8fRUTU0NgwcPznUYnVKc0SmEGEFxRq1Q4pwxY8YSd5/S4xm5e6wPYDCwBDins8+OHTvWC8GCBQtyHUJGFGd0CiFGd8UZtUKJE1jsEbTXsfYyMrNi4BHgQXf/XZzLEhGRnomzl5EBvwBedvf/jGs5IiISjTiPEI4HPgecaGbV4ePUGJcnIiI9EFu3U3f/O2BxzV9ERKKlK5VFRARQQhARkZASgoiIAEoIIiISUkIQERFACUFEREJKCCIiAighiIhISAlBREQAJQQREQkpIYiICKCEICIiISUEEREBlBBERCSkhCAiIoASgoiIhJQQREQEUEIQEZGQEoKIiABKCCIiEoo1IZjZKWb2ipm9ZmbXx7ksERHpmdgSgpkVAf8NfBIYD1xgZuPjWp6IiPRMnEcIxwCvufsb7l4H/AY4K8bliYhID/SNcd4HAG+n/b0WOLb1h8xsNjA7/LPWzFbEGFNU9gL+lesgMqA4o1MIMYLijFqhxDkuipnEmRAy4u5zgbkAZrbY3afkOKROKc5oFUKchRAjKM6oFVKcUcwnzpLRO8DH0v4eGb4nIiJ5KM6E8AJwqJmNMbMS4HzgDzEuT0REeiC2kpG715vZFcBfgSLgXndf2cnX5sYVT8QUZ7QKIc5CiBEUZ9R2qzjN3aOYj4iIFDhdqSwiIoASgoiIhLKWEDobxsLM+pnZb8Ppz5nZ6LRpN4Tvv2Jmn8hhjF83s1VmttzM5pvZqLRpDWZWHT5iPXmeQZwXm9mHafFcljbtIjNbHT4uynGcP06L8VUz25Q2LZvr814zW9feNTAW+K/wdyw3s8lp07KyPjOI8cIwtpfMbJGZHZk2bU34fnVU3RN7EGeFmW1O+7f9dtq0rA11k0Gc16bFuCLcHkeE07K5Pj9mZgvCdmelmV3Zxmei2z7dPfYHwUnl14GDgBJgGTC+1We+DNwdvj4f+G34enz4+X7AmHA+RTmKcQYwMHz9pVSM4d81ebQuLwZ+2sZ3RwBvhM97hK/3yFWcrT7/FYKOB1ldn+GypgOTgRXtTD8VeBwwYCrwXA7WZ2cxHpdaNsFwMc+lTVsD7JUn67IC+FNPt5e442z12TOAp3O0PvcDJoevhwCvtvH/PbLtM1tHCJkMY3EWcH/4+mFgpplZ+P5v3L3W3f8JvBbOL+sxuvsCd98e/vkswbUV2daTIUE+ATzp7hvcfSPwJHBKnsR5AfBQTLF0yN0XAhs6+MhZwAMeeBYYbmb7kcX12VmM7r4ojAFyt21msi7bk9WhbroYZy63zffcfWn4eivwMsEoEOki2z6zlRDaGsai9Y9q+oy71wObgT0z/G62Ykx3KUFWTulvZovN7Fkz+1QM8aVkGuenw8PHh80sdYFgttZll5YVlt7GAE+nvZ2t9ZmJ9n5LNtdnV7TeNh14wsyWWDBUTK4lzGyZmT1uZhPC9/JyXZrZQIJG9JG0t3OyPi0oo08Cnms1KbLtM+dDVxQiM/ssMAU4Ie3tUe7+jpkdBDxtZi+5++u5iZA/Ag+5e62ZfZHgyOvEHMWSifOBh929Ie29fFqfBcPMZhAkhGlpb08L1+XewJNm9o9wDzkXlhL829aY2anAY8ChOYolE2cAz7h7+tFE1tenmQ0mSEpXufuWuJaTrSOETIaxaPqMmfUFhgHrM/xutmLEzE4CbgTOdPfa1Pvu/k74/AaQJMjkceg0TndfnxbbPcBRmX43m3GmOZ9Wh+RZXJ+ZaO+35NXwLGY2keDf+yx3X596P21drgMeJZ6Sa0bcfYu714Sv/wwUm9le5Nm6TNPRtpmV9WlmxQTJ4EF3/10bH4lu+8zSiZG+BCc0xtB8wmhCq89cTsuTyvPC1xNoeVL5DeI5qZxJjJMITnwd2ur9PYB+4eu9gNXEdEIswzj3S3t9NvCsN59k+mcY7x7h6xG5ijP83GEEJ+ksF+szbZmjaf9E6Gm0PGn3fLbXZwYxHkhwfu24Vu8PAoakvV4EnJLDdblv6t+aoCF9K1yvGW0v2YoznD6M4DzDoFytz3DdPADc2cFnIts+Y1vZbQR9KsEZ8teBG8P3vkuwpw3QH/i/4Ub9PHBQ2ndvDL/3CvDJHMb4FPABUB0+/hC+fxzwUrgRvwRcmuN1eQewMoxnAXBY2ncvCdfxa8Dncxln+PfNwPdafS/b6/Mh4D1gF0Gd9VJgDjAnnG4EN3t6PYxnSrbXZwYx3gNsTNs2F4fvHxSux2XhNnFjjtflFWnb5rOkJbC2tpdcxRl+5mKCDi3p38v2+pxGcM5iedq/7alxbZ8aukJERABdqSwiIiElBBERAZQQREQkpIQgIiKAEoKIiISUEEREBFBCEGlXOOzwv4Wv/4+Z3ZXrmETipLGMRNr3HeC74Zg1k4AzcxyPSKx0YZpIB8zsb8BgoMLdt4aD7d0IDHP3c3MbnUi0VDISaYeZHUFwg5I6D8aix4Px+i/NbWQi8VBCEGlDeIORBwluPlJjZnHdSEgkbyghiLQS3hTld8DV7v4ycCvB+QSRXk3nEES6wMz2BG4D/g24x93vyHFIIpFRQhAREUAlIxERCSkhiIgIoIQgIiIhJQQREQGUEEREJKSEICIigBKCiIiElBBERARQQhARkdD/B9s+hrMR2TqFAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Plot predicted linear function\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\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",
        "plt.title('Linear fit')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2b8d1554",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2b8d1554",
        "outputId": "e25ac0ee-8d03-4cac-c03d-cf7892103b09"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([4.21509616]), array([[2.77011339]]))"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "# Now use Linear Regression Algorithm\n",
        "# Will return the intercept and slope\n",
        "\n",
        "lin_reg = LinearRegression()\n",
        "lin_reg.fit(X, y)\n",
        "lin_reg.intercept_, lin_reg.coef_\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "78986699",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "78986699",
        "outputId": "70d071a1-e174-456e-9ee1-7cf9b8314d06"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [9.75532293]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "# Predict again y values for X=0 and 2.\n",
        "lin_reg.predict(X_new)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "518040f5",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "518040f5",
        "outputId": "79242ee9-ce33-4a6a-bb37-3f24bb26e29a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [2.77011339]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "# Old way: using Least Squares fit for finding intercept and slope\n",
        "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
        "theta_best_svd\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2ea78899",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2ea78899",
        "outputId": "116c896e-1c4e-4619-c617-bd135e786668"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [2.77011339]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "np.linalg.pinv(X_b) @ y"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4e3f5353",
      "metadata": {
        "id": "4e3f5353"
      },
      "source": [
        "## Gradient Descent Method"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "079b1e4a",
      "metadata": {
        "id": "079b1e4a"
      },
      "outputs": [],
      "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",
        "for epoch in range(n_epochs):\n",
        "    gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
        "    theta = theta - eta * gradients\n",
        ""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5ef47f9f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5ef47f9f",
        "outputId": "502ab077-cc0c-42ad-a2a8-6eb1792d75bd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [2.77011339]])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "# Trained model parameters\n",
        "theta\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "68d11cc5",
      "metadata": {
        "id": "68d11cc5"
      },
      "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": null,
      "id": "37d97ba8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "37d97ba8",
        "outputId": "ae8baa9d-1771-4e60-f961-83c7bdf1eb05"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "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",
        "        random_index = np.random.randint(m)\n",
        "        xi = X_b[random_index : random_index + 1]\n",
        "        yi = y[random_index : random_index + 1]\n",
        "        gradients = 2 * xi.T @ (xi @ theta - yi)  # for SGD, do not divide by m\n",
        "        eta = learning_schedule(epoch * m + iteration)\n",
        "        theta = theta - eta * gradients\n",
        "        theta_path_sgd.append(theta)  # extra code – to generate the figure\n",
        "\n",
        "# extra code – this section beautifies figure\n",
        "plt.plot(X, y, \"b.\")\n",
        "plt.xlabel(\"$x_1$\")\n",
        "plt.ylabel(\"$y$\", rotation=0)\n",
        "plt.title('Gradient Descent fit')\n",
        "plt.axis([0, 2, 0, 15])\n",
        "plt.grid()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "90d26203",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "90d26203",
        "outputId": "6d303d98-9426-4cc2-d42f-74025a595d65"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21076011],\n",
              "       [2.74856079]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "# Found parameters: Intercept & Slope\n",
        "theta\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b2a1bdd6",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b2a1bdd6",
        "outputId": "cf4511a1-231d-49b7-8e0b-4db1930935db"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "# Now use the SDGRegressor Algorithm\n",
        "\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": null,
      "id": "44eb1105",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "44eb1105",
        "outputId": "5cb87f28-fcba-4819-fc95-9f20c469f941"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([4.21278812]), array([2.77270267]))"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "# Returned parameters: Intercept and Slope\n",
        "\n",
        "sgd_reg.intercept_, sgd_reg.coef_"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "993c4f06",
      "metadata": {
        "id": "993c4f06"
      },
      "source": [
        "## Polynomial Regression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "06e97e91",
      "metadata": {
        "id": "06e97e91"
      },
      "outputs": [],
      "source": [
        "# Generate a collection of data around y = 2 + X + (1/2) X**2\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"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2804452a",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "2804452a",
        "outputId": "7faa9a5a-ef54-40d8-a854-5045323727e2"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Generate plot for collection of points\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.title('Random set of points')\n",
        "plt.axis([-3, 3, 0, 10])\n",
        "plt.grid()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3ab81cf5",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3ab81cf5",
        "outputId": "4d59cee7-8672-4f81-8101-e532229f0cd7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.75275929])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "# Use the Polynomial Regression Algorithm\n",
        "\n",
        "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
        "X_poly = poly_features.fit_transform(X)\n",
        "X[0]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "80e7e328",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "80e7e328",
        "outputId": "1e6501cd-8835-4e7f-cba5-6ba5bee0eb96"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.75275929,  0.56664654])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "X_poly[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "adecf4d3",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "adecf4d3",
        "outputId": "3c513132-b4d0-4420-c76a-8b4275c69b19"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "lin_reg = LinearRegression()\n",
        "lin_reg.fit(X_poly, y)\n",
        "lin_reg.intercept_, lin_reg.coef_\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "00105c9b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "00105c9b",
        "outputId": "9a805e92-04c8-46f3-b4a3-56ad89b9adeb"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Plot quadratic prediction fit\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.title('Quadratic regression fit')\n",
        "plt.legend(loc=\"upper left\")\n",
        "plt.axis([-3, 3, 0, 10])\n",
        "plt.grid()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9dac69f8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "9dac69f8",
        "outputId": "7b785997-3632-41fe-b391-e9bf7fb9d9fd"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Make polynomial plot and compare different fits\n",
        "\n",
        "plt.figure(figsize=(6, 4))\n",
        "\n",
        "for style, width, degree in ((\"r-+\", 2, 1), (\"b--\", 2, 2), (\"g-\", 1, 100)):\n",
        "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
        "\n",
        "    std_scaler = StandardScaler()\n",
        "    lin_reg = LinearRegression()\n",
        "\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.title('Different polynomial regression fits')\n",
        "plt.axis([-3, 3, 0, 10])\n",
        "plt.grid()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2f970f57",
      "metadata": {
        "id": "2f970f57"
      },
      "source": [
        "# Regularized Linear Models\n",
        "\n",
        "## Ridge Regression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e6696abb",
      "metadata": {
        "id": "e6696abb"
      },
      "outputs": [],
      "source": [
        "# Generate random noise about y = 1 + (1/2) X\n",
        "np.random.seed(42)\n",
        "m = 20\n",
        "X = 3 * np.random.rand(m, 1)\n",
        "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
        "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2fa73724",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "2fa73724",
        "outputId": "3ab772a0-dd70-4cb2-a6b5-70dc438b4fbb"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# 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.title('Random set of points')\n",
        "plt.axis([0, 3, 0, 3.5])\n",
        "plt.grid()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6eb91adc",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6eb91adc",
        "outputId": "c6f1d8b7-797c-44ae-a0c6-73538c6f1007"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.55325833]])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "# Ridge Regression Algorithm\n",
        "\n",
        "ridge_reg = Ridge(alpha=0.1, solver=\"cholesky\")\n",
        "ridge_reg.fit(X, y)\n",
        "ridge_reg.predict([[1.5]])\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b6134658",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "b6134658",
        "outputId": "019a8dcf-06ad-4440-8586-782b40b397f2"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 648x252 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Plot for different values of alpha\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.title('Ridge linear regression fit')\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",
        "plt.title('Ridge polynomial regression fit')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "61c7ab73",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "61c7ab73",
        "outputId": "52a9be21-fd78-4045-d822-d423f1a43522"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.55302613])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "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]])\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "06185887",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "06185887",
        "outputId": "d2e2806b-3408-4b7e-ca54-64058febf8b3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.55321535]])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "# 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]])\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "37a3af00",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "37a3af00",
        "outputId": "e5c3e53e-5ee9-45db-8e37-2fe7964d6419"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.97944909]), array([[0.38251084]]))"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "ridge_reg.intercept_, ridge_reg.coef_\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e4b1b30a",
      "metadata": {
        "id": "e4b1b30a"
      },
      "source": [
        "## Lasso Regression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ae959cdd",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ae959cdd",
        "outputId": "b38b60bb-08ce-470c-c0d5-28c905315c22"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.53788174])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "lasso_reg = Lasso(alpha=0.1)\n",
        "lasso_reg.fit(X, y)\n",
        "lasso_reg.predict([[1.5]])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1dd40ee8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "1dd40ee8",
        "outputId": "625dae7f-c484-479d-e7ac-4172e1423820"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 648x252 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "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.title('Lasso linear regression fit')\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",
        "plt.title('Lasso polynomial regression fit')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4bcc1e7b",
      "metadata": {
        "id": "4bcc1e7b"
      },
      "source": [
        "## Elastic Net"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8815fa73",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8815fa73",
        "outputId": "d05674a8-83e8-47ef-9494-29e9b32f4f7e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.54333232])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "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",
      "id": "e595fb80",
      "metadata": {
        "id": "e595fb80"
      },
      "source": [
        "## Logistic Regression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "cc42bbfe",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "id": "cc42bbfe",
        "outputId": "1bbe70d4-bdef-48d8-e3d9-71fe67a1d98f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x216 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAADgCAYAAAAuXT6RAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAAsTAAALEwEAmpwYAAAxCUlEQVR4nO3deXxU5fn38c+VBIjKEha1KiqIilj3BWu1daxUobVo1QrU3Vra/rD94dJWaqVVumDlaaVPtdaF8qhVsIoWrGKlGlxYBJQlCMMuYScJJxCyTnI/f9yTSQKBjBA4M8n3/Xqd15nrLDPXHA655pxzn/uYcw4RERFJfRlhJyAiIiLJUdEWERFJEyraIiIiaUJFW0REJE2oaIuIiKQJFW0REZE0oaItksLM7Akze2Af1jvOzErMLHMf1v2NmRWY2abPu+7+2NfvKtKamO7TFmkeZrYGuMM5Ny1dP9vMjgOiwPHOuS3NkdsePudWfL4XH6jPEGmJdKQtIvUdBxQeyIItIvtORVvkADOzdmb2qJltiA+Pmlm7evN/ZmYb4/PuMDNnZifG5403s9/EX3czs9fNLDCzIjN738wyzOw5fLGdEj8l/jMz6xF/n6z4ul3M7O/xz9hmZq81kmc/4G3g6Pj7jDeziJmt22W5NfFlMbNfm9lLZvasme0ws8Vmdl69ZY81s0lmttXMCs3sL2bWB3gCuDD+OcGu3zUef9/MVsS/62QzO7rePGdmPzSz5fHt8ZiZ2f7+W4mkOhVtkQPvfuBLwFnAmUBf4JcAZtYfuBvoB5wIRPbyPvcA64DDgSOBXwDOOXcTsBb4lnOuvXPuD42s+xxwKPBF4AjgT7suED+1PgDYEH+fW5P8fgOBCUAOMBn4S/y7ZQKvA58BPYBjgAnOuSXAD4GZ8c/J2fUNzexrwO+B64Gj4u8xYZfFrgTOB86IL3dFkvmKpC0VbZED7wbgIefcFufcVuBB4Kb4vOuBvzvnFjvnSoFf7+V9qvAF7HjnXJVz7n2XRKMUMzsKX4x/6JzbFl93+v58oV184Jx7wzlXjf9xcGZ8el/gaOCnzrmdzrly59wHSb7nDcA459zHzrkKYAT+yLxHvWVGO+cC59xa4F38jyKRFk1FW+TAOxp/pFjrs/i02nn59ebVf72rR4AVwH/MbJWZ3Zfk5x8LFDnntiW5/OdVv5V5KZAdPy1/LPCZcy62D+/ZYJs550qAQvzR+p4+t/0+fI5IWlHRFjnwNgDH14uPi08D2Ah0rzfv2D29iXNuh3PuHufcCfhT0neb2WW1s/fy+flAFzPL+byJAzvxp9WBxCnvw5NcNx84rva6+i6aOkPQYJuZ2WFAV2B9kp8t0iKpaIs0rzZmll1vyAJeBH5pZoebWTdgJPB8fPmXgNvMrI+ZHQrs8T5lM7vSzE6MN7gqBqqBmvjszcAJja3nnNsIvAk8bmadzayNmX01ye+zDH/k/E0za4O/Ft+uiXVqfYT/UTLazA6Lb4+L6uXb3cza7mHdF/Hb5ax4o73fAbOdc2uS/GyRFklFW6R5vQGU1Rt+DfwGmAssBBYBH8en4Zx7E/gz/prsCmBW/H0qGnnvk4BpQAkwE3jcOfdufN7v8T8MAjO7t5F1b8JfE18KbAGGJ/NlnHPFwP8AT+OPcnfiG8Mls2418C18A7u18fUGxWe/AywGNplZQSPrTsP/gHkFX/h7AYOT+VyRlkydq4ikkPjtUHlAu328FiwiLZiOtEVCZmbfjt/L3Rl4GJiigi0ijVHRFgnfD/CnrFfir1P/KNx0RCRV6fS4iIhImtCRtoiISJpQ0RYREUkTjXV6EKqcnBx34oknhp1GWti5cyeHHXZY2GmkPG2n5ESjUaqrqzn11FPDTiXlaZ9KjrZT8ubNm1fgnGuy46KUK9pHHnkkc+fODTuNtJCbm0skEgk7jZSn7ZScSCRCEAT6/5cE7VPJ0XZKnpl91vRSOj0uIiKSNlS0RURE0oSKtoiISJpIuWvajamqqmLdunWUl5eHnUpK6dSpE0uWLAnt87Ozs+nevTtt2rQJLQcRkdYkLYr2unXr6NChAz169MA/4EgAduzYQYcOHUL5bOcchYWFrFu3jp49e4aSg4hIa5MWp8fLy8vp2rWrCnYKMTO6du2qsx8iIgdRWhRtQAU7BenfRETk4Eqboi0iItLaNVm0zWycmW0xs7w9zDcz+7OZrTCzhWZ2Tr15t5jZ8vhwS3MmLiIi0tokc6Q9Hui/l/kDgJPiw1DgrwBm1gX4FXAB0Bf4Vfx5wXKQ3H777RxxxBGcdtppYaciIiLNoMmi7Zx7DyjayyJXAc86bxaQY2ZHAVcAbzvnipxz24C32XvxByA/P5/x48cD/lavSCRCSUkJANXV1USjUYqKfDqxWIxoNMq2bdsSy0ejUYIgaBAXFxcDUFlZSTQaZfv27QBUVFQQjUbZsWMH4Bu8RaPRxOeVlZURjUbZuXMnAKWlpUSjUUpLSwHfr240GqWsrAyAkpISotFoonHWjh07iEajVFRUALB9+3ai0SiVlZUAFBcXE41GqaqqAiAIggbxtm3biEajxGIxAIqKihL9Q9d/v5qaGgAKCgqIRqOJbXn11VfzxBNPJOItW7awbNmyRLx582aWL1+eiDdt2sSKFSsS8caNG1m5cmUi3rBhA6tWrUrE69evp6CgIBGPGDGCoUOHJuJ7772XYcOGJeLhw4czfPjwRDxs2DDuvffeRDx06FBGjBiRiG+77TZGjhyZiG+88UZGjRqViAcPHszo0aMT8bXXXsuYMWMS8cCBAxk7dmwiHjBgAI8//ngi7tevH0899VQijkQiu+17zz//POD/7SORCBMnTgT8v10kEmHSpEmA3/aRSIQpU6YAfltGIhGmTp0K+P06Eokwbdo0AFatWkUkEmH69OmA7/c7EokwY8YMAPLy8ohEIsyZMweA+fPnE4lEmD9/PgBz5swhEomQl+dPgM2YMYNIJJL4958+fTqRSCTx7zVt2jQikQj5+fkATJ06lUgkwqZNmwCYMmUK8+fPT+xrkyZNIhKJJP7vTJw4kUgkktj3n3/+eSKRSGJfHT9+fIPuKp966in69euXiB9//HEGDBiQiMeOHcvAgQMT8ZgxY7j22msT8ejRoxk8eHAiHjVqFDfeeGMiHjlyJLfddlsiPtj73kMPPaR9rxn3vUgkkvhbkkr7XnU1/OpXv2PQoO8RBFBQAHff/Qeuv/5u1qyBFStg6NA/ct11v2bBApg3D264YSzXXDOG99+H3Fy45prH+Pa3/8qbb8Lrr8M3vvE3rrpqPK+8Ai+9BJdd9hQDB04gWc1xy9cxQH69eF182p6m78bMhuKP0mnTpg1Lly4lNzeXWCxGEATEYjF27NhBTU0NsViMsrIyduzYQXV1dSLOyspqEGdmZhKLxRJxRkYGVVVVxGIxSktLMTMqKysTMfgiXhs75xLxzp07qampoby8PBFXV1dTVlaWiGs/JxaLUVJSQlVVFaWlpYm4srKyQdymTZsGy2dlZTV4v8zMzAbzd40zMjIS26OkpAQzS+RX+yPk7LPPZunSpdTU1LBjxw7Ky8uprq5OzK+oqNgtrr/+rnHt9qof19TUkJubC8DatWspLi5OxPn5+VRUVCTidevWASTi9evX065du0S8YcMGdu7cmYg3bdpEdXV1It68eTNt27ZNxFu2bGHVqlWJeOvWraxcuTIRFxYWsnz5cnr16kVubi5FRUUsW7YsMb/2R1FtHATBbvvekiVLyM3Npby8nCAIWLx4Mbm5uZSUlBAEAXl5eXTp0oXi4mKCIGDRokV06NCBoqIigiBg4cKFZGdns2XLFoIgYMGCBWRlZbFhwwaCIOCTTz7BOcfatWsJgoCPP/6YyspKVq9eTRAEzJs3j507d7JixYpEv+C1eQZBwJw5cygoKCAvL48gCJg9ezYbN25k/vz5BEHArFmzWLt2LQsWLCAIAmbOnMnKlStZuHAhQRAwY8YMunTpwqJFi4jFYontXft+77//Pu3bt2fx4sUEQcB7771HdnY2S5YsIQgCpk+fTlZWViKf2m1Z+2O6Nl62bBlFRUWJePny5RQWFibilStXsnXr1kS8atUqtmzZkohXr17N5s2bE/GaNWsaLH+w971YLJbUvlcbt9Z9r2PHjokDqb3te0EQ8OGHH9KpUyfy8vLYtq2Yt96aQVZWJz74YAMbN3bjyScX4NwhzJpVw5o15/HLX0aJxdqwYEFXli27mttuW01FRSbRaG/Wrv0hAwZspLIyg88+u4iCgjM477wiqqoy2Lx5ICUl/enZcyfV1UYQ3EpFxc107lxJLGaUlw+nujqDl15yOGfALwBfYL2fAfDPf9bGdwPwyiu18f8C8OqrtbH/8fjaa7XxDwCYPLk2/n58PIRkmHOu6YXMegCvO+d2O89qZq8Do51zH8Tj/wI/ByJAtnPuN/HpDwBlzrkxu75Hfb1793b1jxYBlixZQp8+fZL5Pq1KMvdpr1mzhiuvvDLxq7i5pcO/jR5akJzaB4bUHlHJnmmfapxzUFICRUWwbRvk5s7n+OPPIgiguLhu2L7dDzt21I1LSuqG+MnL0JlBmzaQleXHmZl1cVZWXZyZWRfv+rqxISNj9/GLL9o859x5TeXUHEfa64Fj68Xd49PW4wt3/em5zfB5KaesrIz+/fvzzjvvkJmZybp16/jwww8ZNGgQlZWV9OvXj3feeYesrLToy0ZEBPBFuKgINm+GTZv8eMsW2Lq1bigogMJCPxQVQfysddxZ+/zZhx1WNxx6aMPhkEPqxtnZdePsbGjXruHr+kPbtnXj2qFNm7rxrkNm5v5uweS9+GJyyzVHFZkM3GlmE/CNzoqdcxvN7C3gd/Uan10OjNjTm6SzcePGcc0115AZ/xf+73//y6effsqgQYNo27Ytl112GRMnTuSGG24IOVMRES8Wg40bYe1ayM/34/Xr/bBhQ93QsAg37dBDoUsX6NwZzAJ69MghJwdycqBTJ+jYsW7cocPuw2GH+SKcoRuSG9Vk0TazF/FHzN3MbB2+RXgbAOfcE8AbwDeAFUApcFt8XpGZjQLmxN/qIefc3hq0pbwFCxbw4x//mIKCApYuXYpzjgceeIBp06bxwgsvAPDBBx9w9913k5OTw1tvvcWkSZO4+uqrGTFihIq2iBxUQQDLl/sGUytXwurVdUN+vm9o1ZROneDII+ELX/DjI4+Eww+vG7p180OXLn7Izq5bNzd3vi4jNLMmi7Zzbq9Xx52/KD5sD/PGAeP2LbXUUl5ezqBBg3j22Wfp27cvDzzwAOXl5dx///08+eST9OjRA4CLL76Y888/nzFjxiRutaqurk60xKzvK1/5SqJRV31jxoxp0PpxXw0ZMoTc3FwKCgro3r07Dz74IN/73vf2+31FJHXU1MCaNbBkCXz6qR8vXeqLdb2bOxp11FFw7LF+OO446N4djjkGjj7aD0cd5Y+cJXWk3UXWA9VzZlPt8aZNm8Y555xD3759ATjjjDOYOnUqhYWF5OTkNFg2Go1yyimnJOLMzEzatm27W8Ox999/v9nyb8yLyV4kEZG0sH07fPIJLFxYN+TlQfwGmN0ceiiceCKcdBL06gU9e9YNxx/vr+9Kekm7oh2WvLw8Tj/99ET88ccfc84553DIIYc0eGhGQUEBnTp12q3RWUVFBdn1zxuR3JF2qvXvnczdBiKy/0pLYe5c+Ogjf//vvHn+6LkxRx0Fp54KffrUDb17++kp9idE9lPaFe2wakbXrl155513AH/P6aRJk5gxYwadO3emurqa8vJysrOzWbNmDUcffXSDdQsLC+nWrdtuz51O5kh7b0XyYDyac9u2bXTurI7sRA60devgvfdgxgyYNQsWLPCNxepr2xZOPx3OPtuPzzjDj7t2DSdnOfjSrmiHZciQIUyePJnTTjuNbt268eKLL9I1/j/l8ssv54MPPqBfv36ccsopFBQUcNppp/Hkk0/y5S9/mXfffZdvfvObIX+DfXPXXXclemoSkeaTnw/vvAPTp/uhXmeDgG89fdZZcMEFcN55cO658MUv+sItrZeKdpLat2+f6CZwV8OGDeNPf/oT/fr1o3379nz00UcN5r/wwgsNujz8vG6//XZef/11jjjiiAPWSUpjpk6dytKlS3nkkUf46U9/etA+V6QlKinx3Vq+/Tb85z++sVh9HTvCxRfDRRfBhRfC+edD+/ahpCopTEW7GZxzzjlceumlVFdXJ+7VrlVZWcnVV1/NySefvM/vf+utt3LnnXdy880373W53Nxcxo8f/7mPjBctWtSg32Xw955369aNG2+8kTvvvPPzpiwi+FbdU6b4ITe34T3PHTtCJAKXXOLHZ555cDvzkPSkot1Mbr/99kant23btsli25SvfvWrrFmzZr/eA3z/zcOHD2f9+vVkZGTw3HPP0bt3b04//XRef/313ZZ//fXXOfPMM/f7c0VaC+dg0SLfL/Vrr/mW3bUyMuBLX4LLL/dD376+1y2Rz0NFu5Woqqrijjvu4Mknn6RXr1688cYbjB49mr///e97XKdbt248/fTTdOvWLeX7FxcJi3O+OL/0ki/W9R+d0KEDXHEFDBwIAwb4TkhE9oeKdgtwwQUXUFFRQUlJCUVFRZx11lkAPPzww1xxxRUAvPbaayxevDjxCLpYLMZXvvKVvb7vwIEDGzzCTkTqbNgA//gHPPtswyPqbt3gmmvg2mv9aW81HJPmpKLdAsyePRvY+zXtBQsW8Nvf/lY9oonsh/JymDQJ/vSnM/j4Y98bGfjuO6+7Dr7zHV+o9WwgOVDUJXsrcdRRR/HWW29RE/8rs2jRInWUIpKkaBTuucd383nDDTB3bhcyM/0R9Wuv+Qdv/O1v0K+fCrYcWCraaWDIkCFceOGFRKNRunfvzjPPPPO53+P222+npqaGPn36cNZZZ/Hwww+nXG9rIqmkuhpefRUuvRROOQX++Ef/+Mkzz4Sf/GQZGzfCK6/AVVfpFLgcPPpNmAaS7UM8Eons8Yk6hxxyCC+//HIzZiXSMhUXw7hx8Oc/+1u2wPfhPWQIDB3q75+ePn0DXbvu+22cIvtKRVtEBP8c6f/zf+Dpp6H2kQAnnAA/+Qnceqt/RKVI2FS0RaRVW7kSHn4Yxo+v6/wkEoHhw+HKK9XhiaQWFW0RaZWWLoVRo2DCBN8K3My3/r7vPjjnnLCzE2mciraItCqrV8ODD8Jzz/linZUFt9wCP/+5f5ylSCpLm6LtnFNr5xSjW8YknaxfD7/5jb9mHYv5Yv3978OIEXD88WFnJ5KctCja2dnZFBYW0rVrVxXuFOGco7CwkOzs7LBTEdmrkhL4wx9gzBgoK/N9gN98M/zqV76hmUg6SYui3b17d9atW8fWrVvDTiWllJeXh1o0s7Oz6d69e2ifL7I31dXw//4f3H8/bNrkp11zjb+Ofeqp4eYmsq/Somi3adOGnj17hp1GysnNzeXss88OOw2RlPPee/5WrQULfNy3r+8c5aKLws1LZH+pRzQRaTE2bYKbbvLPqF6wAI47Dl54AWbOVMGWliEtjrRFRPYmFoPHHoORI2H7dsjO9g3MfvpTOOSQsLMTaT4q2iKS1ubOhTvuqDsVfuWVMHasGplJy6TT4yKSlkpL4Wc/gwsu8AW7Rw+YPBmmTFHBlpYrqaJtZv3NLGpmK8zsvkbm/8nM5seHZWYW1JtXXW/e5GbMXURaqXffhTPOgEce8fHdd0NeHnzrW+HmJXKgNXl63MwygceArwPrgDlmNtk592ntMs65u+ot/2OgfpPmMufcWc2WsYi0Wjt3+uvUf/2rj087DZ55xrcOF2kNkjnS7guscM6tcs5VAhOAq/ay/BAguWdJiogkaeZMOOssX7DbtPFdkc6bp4ItrUsyDdGOAfLrxeuACxpb0MyOB3oC79SbnG1mc4EYMNo591oj6w0FhgIcfvjh5ObmJpN7q1dSUqJtlQRtp+QEQUB1dXXKbauqKmP8+B5MmHAcNTXGCSeUMGLEEk48cSczZoSTk/ap5Gg7Nb/mbj0+GHjZOVddb9rxzrn1ZnYC8I6ZLXLOray/knPuSeBJgN69e7tIJNLMabVMubm5aFs1TdspOTk5OQRBkFLbaulSGDIE5s/3T+H6+c/hwQfb067d+aHmpX0qOdpOzS+Z0+PrgWPrxd3j0xozmF1OjTvn1sfHq4BcGl7vFhHZjXMwbhyce64v2Cec4Hs5Gz0a2rULOzuR8CRTtOcAJ5lZTzNriy/Mu7UCN7NTgM7AzHrTOptZu/jrbsBFwKe7risiUqu4GL77Xfje9/xtXTfcAJ98AhdfHHZmIuFr8vS4cy5mZncCbwGZwDjn3GIzewiY65yrLeCDgQmu4fMa+wB/M7Ma/A+E0fVbnYuI1DdnDgwa5J95fdhhvtHZTTeFnZVI6kjqmrZz7g3gjV2mjdwl/nUj680ATt+P/ESkFXDOF+jhw6GqCs45ByZMgJNOCjszkdSiHtFEJFQlJf4U+LBhvmDfeSfMmKGCLdIY9T0uIqH59FO47jpYssSfDn/6aRg8OOysRFKXiraIhOKVV+CWW3wvZ6eeCi+/DH36hJ2VSGrT6XEROaiqq+GXv/RH2Dt3+vuwZ89WwRZJho60ReSgCQJ//fqNNyAjwz/w4667fMcpItI0FW0ROSiWLIGrroLly6FLF5g4Efr1CzsrkfSi0+MicsBNnQpf+pIv2GeeCXPnqmCL7AsVbRE5YJyDsWPhm9+E7dv9dewPP4SePcPOTCQ9qWiLyAFRVQU//KHvMKWmBkaO9KfEDzss7MxE0peuaYtIsysqgmuvhdxcyM6Gv/9d91+LNAcVbRFpVitX+tPh0Sh84Qvwr39B375hZyXSMqhoi0izmTkTBg6EggI4/XT497/h2GObXk9EkqNr2iLSLP75T7j0Ul+wr7gCPvhABVukualoi8h+cc53knL99VBRAUOHwpQp0LFj2JmJtDwq2iKyz6qr4Sc/gZ/9zMd/+AM88QS0aRNuXiItla5pi8g+KSvzXZK++iq0bQvPPguDBoWdlUjLpqItIp9bQYFvcDZzJuTkwGuvwSWXhJ2VSMunoi0in8uaNb6h2bJlvqHZm2/CF78YdlYirYOuaYtI0hYsgAsv9AX7jDNg1iwVbJGDSUVbRJLy7rvw1a/Cpk3+1q733oOjjw47K5HWRUVbRJr00kvQv79/6Mf11/tT4p06hZ2VSOujoi0ie/WXv/h+wysr/e1dL74I7dqFnZVI66SiLSKNcg5++Uv48Y/969//Hh59FDL0V0MkNGo9LiK7icXgRz+Cp5+GzEw/vvXWsLMSERVtEWmgrAy++11/73V2tr+e/a1vhZ2ViECSp8fNrL+ZRc1shZnd18j8W81sq5nNjw931Jt3i5ktjw+3NGfyItK8qqs70L+/L9g5OTBtmgq2SCpp8kjbzDKBx4CvA+uAOWY22Tn36S6LTnTO3bnLul2AXwHnAQ6YF193W7NkLyLNpqKiCytW/J7ycn8r11tvwWmnhZ2ViNSXzJF2X2CFc26Vc64SmABcleT7XwG87Zwrihfqt4H+e1shPz+f8ePHA1BVVUUkEuH5558HoLS0lEgkwsSJEwEoLi4mEokwadIkAAoKCohEIkyZMgWATZs2EYlEmDp1auK9I5EI06ZNA2DVqlVEIhGmT58OQDQaJRKJMGPGDADy8vKIRCLMmTMHgPnz5xOJRJg/fz4Ac+bMIRKJkJeXB8CMGTOIRCJEo1EApk+fTiQSYdWqVQBMmzaNSCRCfn4+AFOnTiUSibBp0yYApkyZQiQSoaCgAIBJkyYRiUQoLi4GYOLEiUQiEUpLSwF4++23iUQiVFVVATB+/HgikUhiWz711FP069cvET/++OMMGDAgEY8dO5aBAwcm4jFjxnDttdcm4tGjRzN48OBEPGrUKG688cZEPHLkSG677bZEPGLECIYOHZqI7733XoYNG5aIhw8fzvDhwxPxsGHDuPfeexPx0KFDGTFiRCK+7bbbGDlyZCK+8cYbGTVqVCIePHgwo0ePTsTXXnstY8aMScQDBw5k7NixiXjAgAE8/vjjibhfv3489dRTiTgSibTafe9vf/svs2f/kfLy3px8MjzwwJvceeee973nn3++Ve97Dz30kPa9kP7utfR9rynJXNM+BsivF68DLmhkuWvN7KvAMuAu51z+HtY9ZtcVzWwoMBSgTZs2LF26lNzcXGKxGEEQsGTJEnJzcykvLycIAhYvXkxubi4lJSUEQUBeXh5dunShuLiYIAhYtGgRHTp0oKioiCAIWLhwIdnZ2WzZsoUgCFiwYAFZWVls2LCBIAj45JNPcM6xdu1agiDg448/prKyktWrVxMEAfPmzWPnzp2sWLGCIAiYO3cuQRCwdOlSgiBgzpw5FBQUkJeXRxAEzJ49m40bNzJ//nyCIGDWrFmsXbuWBQsWEAQBM2fOZOXKlSxcuJAgCJgxYwZdunRh0aJFBEHAhx9+SKdOnRLv9/7779O+fXsWL15MEAS89957ZGdnJ7bH9OnTycrKSuSTm5sL+P+M27ZtS8TLli2jqKgoES9fvpzCwsJEvHLlSrZu3ZqIV61axZYtWxLx6tWr2bx5cyJes2ZNg+XXrl1LcXFxIs7Pz6eioiIRr1u3DiARr1+/nnbt2iXiDRs2sHPnzkS8adMmqqurE/HmzZtp27ZtIt6yZQurVq1KxFu3bmXlypWJuLCwkOXLl9OrVy9yc3MpKipi2bJlifnbtm0jGo0m4tp/09a27xUWHsc993wJ5w4jO3sRDz+8nYUL5+x131uyZEmr3vdisVhS+15t3Fr3vY4dOxKNRpv1715L3feSZc65vS9gdh3Q3zl3Rzy+Cbig/qlwM+sKlDjnKszsB8Ag59zXzOxeINs595v4cg8AZc65Mbt/kte7d29X+4tN9i43N7fBL0xpnLbTnr37Llx1FezYATk5c+ne/ScsWjQj7LRSnvap5Gg7Jc/M5jnnzmtquWROj68Hjq0Xd49PS3DOFTrnKuLh08C5ya4rIuF4+WXfy9mOHf6RmqefPoLMzNKw0xKRvUimaM8BTjKznmbWFhgMTK6/gJkdVS8cCCyJv34LuNzMOptZZ+Dy+DQRCdETT/juSCsrYdgw+Mc/ICOjKuy0RKQJTV7Tds7FzOxOfLHNBMY55xab2UPAXOfcZOAnZjYQiAFFwK3xdYvMbBS+8AM85JwrOgDfQ0SS4Bw89BD8+tc+HjUK7r8fzEJNS0SSlFTnKs65N4A3dpk2st7rEUCjzd+cc+OAcfuRo4g0g+pq33f444/7rkifeAK+//2wsxKRz0M9oom0AuXlcOON8Mor/mEfL74I3/522FmJyOeloi3SwgWBbyH+3nv+cZr/+hdccknYWYnIvlDRFmnB1q/3LcTz8nwvZ1Onwumnh52ViOwrFW2RFmrJEl+w166FU07x3ZIed1zYWYnI/tCTcUVaoA8+gIsu8gX7wgt9rIItkv5UtEVamJdfhn79YNs2GDjQP6mra9ewsxKR5qCiLdKCPPqo7zSlogJ+9COYNAkOPTTsrESkuahoi7QANTVw991w112+A5Xf/x4eewwyM8POTESakxqiiaS50lJ/D/arr0KbNjBunI9FpOVR0RZJY5s3++vWH33k78GeNAm+9rWwsxKRA0VFWyRNffopfOMb8Nln0KMH/PvfcOqpYWclIgeSrmmLpKFp0+DLX/YFu29fmDVLBVukNVDRFkkzjz/uO00pLoZrr4V334Ujjww7KxE5GFS0RdJELAZ33umff11dDffdBy+9pFu6RFoTXdMWSQPbtvn7r6dNg7Zt4emn4aabws5KRA42FW2RFLd0qX9K17JlcMQR/tauL3857KxEJAw6PS6SwiZP9g3Nli3zT+f66CMVbJHWTEVbJAXV1MBDD/kj7B074LrrYMYMOP74sDMTkTDp9LhIitmxA26+GV57Dczgd7+Dn//cvxaR1k1FWySF5OX5o+poFHJy4IUXYMCAsLMSkVSh0+MiKeK55/z162gUTjvNX79WwRaR+lS0RUJWXg4//KE/JV5W5sezZ8NJJ4WdmYikGp0eFwnR8uUweDB8/DG0awf/9//CHXfo+rWINE5FWyQkzz0H//M/UFICPXvCyy/DOeeEnZWIpDKdHhc5yGpbh998sy/Y11/vj7RVsEWkKUkVbTPrb2ZRM1thZvc1Mv9uM/vUzBaa2X/N7Ph686rNbH58mNycyYukm7lzfXF+7jk45BDfHemECb6luIhIU5o8PW5mmcBjwNeBdcAcM5vsnPu03mKfAOc550rN7EfAH4BB8XllzrmzmjdtkfRSVQW//S385jf+YR9nnOGLdZ8+YWcmIukkmSPtvsAK59wq51wlMAG4qv4Czrl3nXOl8XAW0L150xRJX0uWwIUXwoMP+oI9fLhvHa6CLSKfVzIN0Y4B8uvF64AL9rL894A368XZZjYXiAGjnXOv7bqCmQ0FhgIcfvjh5ObmJpGWlJSUaFslIaztVF0Nr77anaee6kllZSZHHlnOz3++lLPPDpg166Cn06QgCKiurtY+lQT930uOtlPza9bW42Z2I3AecEm9ycc759ab2QnAO2a2yDm3sv56zrkngScBevfu7SKRSHOm1WLl5uaibdW0MLbTp5/6W7dmzvTxbbfBo49m07HjWQc1j88jJyeHIAi0TyVB//eSo+3U/JI5Pb4eOLZe3D0+rQEz6wfcDwx0zlXUTnfOrY+PVwG5wNn7ka9ISqushFGj4OyzfcE+6ij4179g3Djo2DHs7EQk3SVTtOcAJ5lZTzNrCwwGGrQCN7Ozgb/hC/aWetM7m1m7+OtuwEVA/QZsIi3GrFlw7rkwcqQv3t//vj/iHjgw7MxEpKVo8vS4cy5mZncCbwGZwDjn3GIzewiY65ybDDwCtAf+ab4rp7XOuYFAH+BvZlaD/4EwepdW5yJpr6AARozwt28B9OoFTz0Fl14abl4i0vIkdU3bOfcG8MYu00bWe91vD+vNAE7fnwRFUlV1NTzzjC/YRUXQpg3ccw888AAcemjY2YlIS6RuTEX2wYcfwl13wZw5Pu7XD/7yF+jdO9y8RKRlUzemIp/DqlXwne/AxRf7gn3MMfDSS/Cf/6hgi8iBpyNtkSRs2wa/+x38+c++kdkhh8BPf+qH9u3Dzk5EWgsVbZG9KCmBsWNhzBgIAj/tllt8d6Td1e+fiBxkKtoijSgrgyeegN//HrZu9dMuvRQeecTf1iUiEgYVbZF6du70t2s98ghs2OCnfelL/mEfX/tauLmJiKhoi+BPfT/2GDz6qL/vGuCss/xp8G98A3z3AyIi4VLRllZt7VpfrJ94ArZv99MuuADuvx+++U3I0P0VIpJCVLSlVZo50x9Vv/KK7yQF4LLL4Be/8NeudWQtIqlIRVtajdJSf0/1X/8KH33kp2VlwZAhvqOU888PNz8RkaaoaEuLt3r1YbzyCjz3HBQX+2mdO8MPfgDDhunWLRFJHyra0iIVFsLEifDsszB7dt0h9AUXwNChMHiw+gcXkfSjoi0tRlkZvPmmP6L+97+hqspPP/TQGLfcksXQob5FuIhIulLRlrRWVgZTp8I//wlTpvgezMC3+u7fH26+GTp3nkH//l8NN1ERkWagoi1pp7AQ3njDF+k336wr1OB7KxsyBL77XTjqKD8tN7cmnERFRJqZirakPOdg0SJ/RP366/6xmDX16vC558L118N118EJJ4SXp4jIgaaiLSlpwwZ45x3/yMv//Ac2b66b16aN71L0W9/yQ8+e4eUpInIwqWhLSli7FqZPrxtWrGg4/5hj4Otf912KXnEFdOwYTp4iImFS0ZaDrqwMPvnE90o2cybMmgXr1zdcpn17+MpX4PLL/dCnj3opExFR0ZYDqqQE8vJg3ry6YfHiuq5Da+XkwMUXwyWX+OHss31vZSIiUkd/FqVZVFTA8uWwZIkvygsX+mHlyt2XzciA006DCy+sG04+WQ/nEBFpioq2JK2mxp/GXr7cDytW1BXqlSt3P3oG32isTx9/5HzuuX4480w47LCDn7+ISLpT0ZaEqirfajs/3zcMy8+H1avrhs8+g8rKxtfNyIBevXyBPvVUX5jPOMMfQbdte3C/h4hIS6Wi3QqUlcGWLf62qc2bYdMmP96wwR851443b254/3NjjjgCTjoJTjzRj086CU45xRfn7OyD831ERForFe004RyUl8P27bBtmx9mz+7Chg3+dWEhFBXVjbdurRt27kzuM8x8L2LHHgvHHefHPXr4+6B79vSv27c/kN9SRET2JqmibWb9gbFAJvC0c270LvPbAc8C5wKFwCDn3Jr4vBHA94Bq4CfOubeaLfsUVF3tG2WVlfmhtLTh69JSX0RrxyUldeOSEtixo+GwfbsfiovrHoBR54ykcmrTxh8hf+ELcOSRdcMxx8DRR9cNX/iCTmWLiKSyJou2mWUCjwFfB9YBc8xssnPu03qLfQ/Y5pw70cwGAw8Dg8zsVGAw8EXgaGCamZ3snGukyZJXVZWRaNRUU+PHu77edYjFdn8di+15qKqqG+9pqKxsOFRUNHxdXu7H9V+XlzdWWJtP27bQqZO/PapzZ6ipKaJXry507gxdu0KXLnXjww+vGzp00D3OIiItQTJH2n2BFc65VQBmNgG4CqhftK8Cfh1//TLwFzOz+PQJzrkKYLWZrYi/38w9fdjq1Ydx4omf92ukkhoyMirjQwWZmRVkZFTEX5fvNs7MLCUjo5zMzLJEnJVVSmZm3ZCVtZOsrJ1kZDT8RRAEAZs25bBpU0hfNU0EQUBOTk7YaaS8+fPnE4vFiEQiYaeS8rRPJUfbqfklU7SPAfLrxeuAC/a0jHMuZmbFQNf49Fm7rHvMrh9gZkOBoT46nbZt8wGHWTVQg1nNLuPq3cb+dXW917XTYw2mm8Xi02IN4oZDVXyojSsxqyQjo6revIp4XDuvArOK+PJJbNUk1J492FOL7erqaoIgaJ4Pa8G0nZITi8VwzmlbJUH7VHK0nZpfSjREc849CTwJ0Lt3bxeNHhtyRukhNzdXR0VJ0HZKTiQSIQgC5s+fH3YqKU/7VHK0nZJnSR7tJdMH1XqgfhXtHp/W6DJmlgV0wjdIS2ZdERERSUIyRXsOcJKZ9TSztviGZZN3WWYycEv89XXAO845F58+2MzamVlP4CTgo+ZJXUREpHVp8vR4/Br1ncBb+Fu+xjnnFpvZQ8Bc59xk4BnguXhDsyJ8YSe+3Ev4RmsxYNjeWo6LiIjIniV1Tds59wbwxi7TRtZ7XQ58Zw/r/hb47X7kKCIiIiR3elxERERSgIq2iIhImlDRFhERSRMq2iIiImlCRVtERCRNqGiLiIikCRVtERGRNKGiLSIikibM9zaaOsxsBxANO4800Q0oCDuJNKDtlDxtq+RoOyVH2yl5vZ1zHZpaKCWe8rWLqHPuvLCTSAdmNlfbqmnaTsnTtkqOtlNytJ2SZ2Zzk1lOp8dFRETShIq2iIhImkjFov1k2AmkEW2r5Gg7JU/bKjnaTsnRdkpeUtsq5RqiiYiISONS8UhbREREGpGyRdvMfmxmS81ssZn9Iex8Up2Z3WNmzsy6hZ1LKjKzR+L700Ize9XMcsLOKZWYWX8zi5rZCjO7L+x8UpWZHWtm75rZp/G/Tf8bdk6pzMwyzewTM3s97FxSlZnlmNnL8b9PS8zswr0tn5JF28wuBa4CznTOfREYE3JKKc3MjgUuB9aGnUsKexs4zTl3BrAMGBFyPinDzDKBx4ABwKnAEDM7NdysUlYMuMc5dyrwJWCYttVe/S+wJOwkUtxYYKpz7hTgTJrYXilZtIEfAaOdcxUAzrktIeeT6v4E/AxQA4U9cM79xzkXi4ezgO5h5pNi+gIrnHOrnHOVwAT8j2bZhXNuo3Pu4/jrHfg/sMeEm1VqMrPuwDeBp8POJVWZWSfgq8AzAM65SudcsLd1UrVonwx8xcxmm9l0Mzs/7IRSlZldBax3zi0IO5c0cjvwZthJpJBjgPx68TpUiJpkZj2As4HZIaeSqh7FH0zUhJxHKusJbAX+Hr+M8LSZHba3FULrEc3MpgFfaGTW/fi8uuBPP50PvGRmJ7hW2tS9iW31C/yp8VZvb9vJOfev+DL3409x/uNg5iYti5m1B14BhjvntoedT6oxsyuBLc65eWYWCTmdVJYFnAP82Dk328zGAvcBD+xthVA45/rtaZ6Z/QiYFC/SH5lZDb4P260HK79UsqdtZWan43+pLTAz8Kd8Pzazvs65TQcxxZSwt30KwMxuBa4ELmutPwD3YD1wbL24e3yaNMLM2uAL9j+cc5PCzidFXQQMNLNvANlARzN73jl3Y8h5pZp1wDrnXO3ZmpfxRXuPUvX0+GvApQBmdjLQFnU6vxvn3CLn3BHOuR7OuR74HeCc1liwm2Jm/fGn6gY650rDzifFzAFOMrOeZtYWGAxMDjmnlGT+1/EzwBLn3B/DzidVOedGOOe6x/8uDQbeUcHeXfxvdb6Z9Y5Pugz4dG/rpOIDQwDGAePMLA+oBG7RkZHsp78A7YC342clZjnnfhhuSqnBORczszuBt4BMYJxzbnHIaaWqi4CbgEVmNj8+7RfOuTfCS0nS3I+Bf8R/MK8CbtvbwuoRTUREJE2k6ulxERER2YWKtoiISJpQ0RYREUkTKtoiIiJpQkVbREQkTahoi0jtk4b+J+w8RGTvVLRFBCAHUNEWSXEq2iICMBroZWbzzeyRsJMRkcapcxURqX1i1evOudPCzkVE9kxH2iIiImlCRVtERCRNqGiLCMAOoEPYSYjI3qloiwjOuULgQzPLU0M0kdSlhmgiIiJpQkfaIiIiaUJFW0REJE2oaIuIiKQJFW0REZE0oaItIiKSJlS0RURE0oSKtoiISJpQ0RYREUkT/x8yUKNzStI1tAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Estimating Probabilities\n",
        "# Logistic Function Plot\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.title('Logistic function')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Metrics for Regression\n"
      ],
      "metadata": {
        "id": "MlrS3Wh6BrpI"
      },
      "id": "MlrS3Wh6BrpI"
    },
    {
      "cell_type": "code",
      "source": [
        "# example of increase in mean squared error\n",
        "\n",
        "from matplotlib import pyplot\n",
        "from sklearn.metrics import mean_squared_error\n",
        "# real value\n",
        "expected = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
        "# predicted value\n",
        "predicted = [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]\n",
        "# calculate errors\n",
        "errors = list()\n",
        "for i in range(len(expected)):\n",
        "\t# calculate error\n",
        "\terr = (expected[i] - predicted[i])**2\n",
        "\t# store error\n",
        "\terrors.append(err)\n",
        "\t# report error\n",
        "\tprint('>%.1f, %.1f = %.3f' % (expected[i], predicted[i], err))\n",
        "# plot errors\n",
        "pyplot.plot(errors)\n",
        "pyplot.xticks(ticks=[i for i in range(len(errors))], labels=predicted)\n",
        "pyplot.xlabel('Predicted Value')\n",
        "pyplot.ylabel('Mean Squared Error')\n",
        "pyplot.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "SQzaBfEOBvoF",
        "outputId": "e4b81d5f-a6c2-4577-9971-aa00b0156d00"
      },
      "id": "SQzaBfEOBvoF",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ">1.0, 1.0 = 0.000\n",
            ">1.0, 0.9 = 0.010\n",
            ">1.0, 0.8 = 0.040\n",
            ">1.0, 0.7 = 0.090\n",
            ">1.0, 0.6 = 0.160\n",
            ">1.0, 0.5 = 0.250\n",
            ">1.0, 0.4 = 0.360\n",
            ">1.0, 0.3 = 0.490\n",
            ">1.0, 0.2 = 0.640\n",
            ">1.0, 0.1 = 0.810\n",
            ">1.0, 0.0 = 1.000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# example of calculate the root mean squared error\n",
        "\n",
        "from sklearn.metrics import mean_squared_error\n",
        "# real value\n",
        "expected = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
        "# predicted value\n",
        "predicted = [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]\n",
        "# calculate errors\n",
        "errors = mean_squared_error(expected, predicted, squared=False)\n",
        "# report error\n",
        "print(errors)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eya0jNxaCOTb",
        "outputId": "50c7991b-a09f-4b3b-dcfc-4d144370c0f5"
      },
      "id": "eya0jNxaCOTb",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.5916079783099616\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# plot of the increase of mean absolute error with prediction error\n",
        "\n",
        "from matplotlib import pyplot\n",
        "from sklearn.metrics import mean_squared_error\n",
        "# real value\n",
        "expected = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
        "# predicted value\n",
        "predicted = [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]\n",
        "# calculate errors\n",
        "errors = list()\n",
        "for i in range(len(expected)):\n",
        "\t# calculate error\n",
        "\terr = abs((expected[i] - predicted[i]))\n",
        "\t# store error\n",
        "\terrors.append(err)\n",
        "\t# report error\n",
        "\tprint('>%.1f, %.1f = %.3f' % (expected[i], predicted[i], err))\n",
        "# plot errors\n",
        "pyplot.plot(errors)\n",
        "pyplot.xticks(ticks=[i for i in range(len(errors))], labels=predicted)\n",
        "pyplot.xlabel('Predicted Value')\n",
        "pyplot.ylabel('Mean Absolute Error')\n",
        "pyplot.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "a90Juv2-CoKy",
        "outputId": "0a7c5a87-eeb8-43a7-ee7a-c9002b01b39c"
      },
      "id": "a90Juv2-CoKy",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ">1.0, 1.0 = 0.000\n",
            ">1.0, 0.9 = 0.100\n",
            ">1.0, 0.8 = 0.200\n",
            ">1.0, 0.7 = 0.300\n",
            ">1.0, 0.6 = 0.400\n",
            ">1.0, 0.5 = 0.500\n",
            ">1.0, 0.4 = 0.600\n",
            ">1.0, 0.3 = 0.700\n",
            ">1.0, 0.2 = 0.800\n",
            ">1.0, 0.1 = 0.900\n",
            ">1.0, 0.0 = 1.000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# example of calculate the mean absolute error\n",
        "from sklearn.metrics import mean_absolute_error\n",
        "# real value\n",
        "expected = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
        "# predicted value\n",
        "predicted = [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]\n",
        "# calculate errors\n",
        "errors = mean_absolute_error(expected, predicted)\n",
        "# report error\n",
        "print(errors)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G-Fl0A9SDAXn",
        "outputId": "5b922c7e-aaa7-4490-fdf2-9b291e68da38"
      },
      "id": "G-Fl0A9SDAXn",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import r2_score\n",
        "\n",
        "y_true = [3, -0.5, 2, 7]\n",
        "y_pred = [2.5, 0.0, 2, 8]\n",
        "print('1. ', r2_score(y_true, y_pred))\n",
        "\n",
        "y_true = [[0.5, 1], [-1, 1], [7, -6]]\n",
        "y_pred = [[0, 2], [-1, 2], [8, -5]]\n",
        "print('2. ',r2_score(y_true, y_pred,\n",
        "         multioutput='variance_weighted'))\n",
        "\n",
        "y_true = [1, 2, 3]\n",
        "y_pred = [1, 2, 3]\n",
        "print('3. ', r2_score(y_true, y_pred))\n",
        "\n",
        "y_true = [1, 2, 3]\n",
        "y_pred = [2, 2, 2]\n",
        "print('4. ', r2_score(y_true, y_pred))\n",
        "\n",
        "y_true = [1, 2, 3]\n",
        "y_pred = [3, 2, 1]\n",
        "print('5. ', r2_score(y_true, y_pred))\n",
        "\n",
        "y_true = [-2, -2, -2]\n",
        "y_pred = [-2, -2, -2]\n",
        "print('6. ', r2_score(y_true, y_pred))\n",
        "\n",
        "\n",
        "y_true = [-2, -2, -2]\n",
        "y_pred = [-2, -2, -2 + 1e-8]\n",
        "print('7. ', r2_score(y_true, y_pred))\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uzOtTAEzDXq7",
        "outputId": "2407de75-cc7f-4a38-8a60-739a36a5c07f"
      },
      "id": "uzOtTAEzDXq7",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.  0.9486081370449679\n",
            "2.  0.9382566585956417\n",
            "3.  1.0\n",
            "4.  0.0\n",
            "5.  -3.0\n",
            "6.  1.0\n",
            "7.  0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_absolute_error\n",
        "\n",
        "y_true = [3, -0.5, 2, 7]\n",
        "y_pred = [2.5, 0.0, 2, 8]\n",
        "print('1. ', mean_absolute_error(y_true, y_pred))\n",
        "\n",
        "y_true = [[0.5, 1], [-1, 1], [7, -6]]\n",
        "y_pred = [[0, 2], [-1, 2], [8, -5]]\n",
        "print('2. ',mean_absolute_error(y_true, y_pred))\n",
        "\n",
        "print('3. ', mean_absolute_error(y_true, y_pred, multioutput='raw_values'))\n",
        "\n",
        "print('4. ', mean_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7]))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B0Yt9F-CETQr",
        "outputId": "3ebedc2a-7bb8-4f49-b805-16a24c11781c"
      },
      "id": "B0Yt9F-CETQr",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.  0.5\n",
            "2.  0.75\n",
            "3.  [0.5 1. ]\n",
            "4.  0.85\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "y_true = [3, -0.5, 2, 7]\n",
        "y_pred = [2.5, 0.0, 2, 8]\n",
        "print('1. ', mean_squared_error(y_true, y_pred))\n",
        "\n",
        "y_true = [3, -0.5, 2, 7]\n",
        "y_pred = [2.5, 0.0, 2, 8]\n",
        "print('2. ',mean_squared_error(y_true, y_pred, squared=False))\n",
        "\n",
        "y_true = [[0.5, 1],[-1, 1],[7, -6]]\n",
        "y_pred = [[0, 2],[-1, 2],[8, -5]]\n",
        "print('3. ', mean_squared_error(y_true, y_pred))\n",
        "\n",
        "print('4. ', mean_squared_error(y_true, y_pred, squared=False))\n",
        "\n",
        "print('5. ',mean_squared_error(y_true, y_pred, multioutput='raw_values'))\n",
        "\n",
        "print('6. ', mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7]))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "scS8gpNsGAmT",
        "outputId": "b840b8b1-d9b3-4260-d901-be0f7806be60"
      },
      "id": "scS8gpNsGAmT",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.  0.375\n",
            "2.  0.6123724356957945\n",
            "3.  0.7083333333333334\n",
            "4.  0.8227486121839513\n",
            "5.  [0.41666667 1.        ]\n",
            "6.  0.825\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_absolute_percentage_error\n",
        "\n",
        "y_true = [3, -0.5, 2, 7]\n",
        "y_pred = [2.5, 0.0, 2, 8]\n",
        "print('1. ',mean_absolute_percentage_error(y_true, y_pred))\n",
        "\n",
        "y_true = [[0.5, 1], [-1, 1], [7, -6]]\n",
        "y_pred = [[0, 2], [-1, 2], [8, -5]]\n",
        "print('2. ', mean_absolute_percentage_error(y_true, y_pred))\n",
        "\n",
        "print('3. ', mean_absolute_percentage_error(y_true, y_pred, multioutput=[0.3, 0.7]))\n",
        "\n",
        "# the value when some element of the y_true is zero is arbitrarily high because\n",
        "# of the division by epsilon\n",
        "y_true = [1., 0., 2.4, 7.]\n",
        "y_pred = [1.2, 0.1, 2.4, 8.]\n",
        "print('4. ', mean_absolute_percentage_error(y_true, y_pred))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f012HOO2GjkU",
        "outputId": "7a6837cc-aa87-46ce-e870-e21da7d455e5"
      },
      "id": "f012HOO2GjkU",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.  0.3273809523809524\n",
            "2.  0.5515873015873016\n",
            "3.  0.6198412698412699\n",
            "4.  112589990684262.48\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import median_absolute_error\n",
        "\n",
        "y_true = [3, -0.5, 2, 7]\n",
        "y_pred = [2.5, 0.0, 2, 8]\n",
        "print('1. ', median_absolute_error(y_true, y_pred))\n",
        "\n",
        "y_true = [[0.5, 1], [-1, 1], [7, -6]]\n",
        "y_pred = [[0, 2], [-1, 2], [8, -5]]\n",
        "print('2. ', median_absolute_error(y_true, y_pred))\n",
        "\n",
        "print('3. ', median_absolute_error(y_true, y_pred, multioutput='raw_values'))\n",
        "\n",
        "print('4. ', median_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7]))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CsFEfXNbHJuF",
        "outputId": "b15bfc32-df74-4f5d-8982-517a3946b260"
      },
      "id": "CsFEfXNbHJuF",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.  0.5\n",
            "2.  0.75\n",
            "3.  [0.5 1. ]\n",
            "4.  0.85\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import max_error\n",
        "\n",
        "y_true = [3, 2, 7, 1]\n",
        "y_pred = [5, 2, 7, 1]\n",
        "max_error(y_true, y_pred)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VKuEljlOHkW_",
        "outputId": "2b70ab98-a898-4160-d3e5-76963581b166"
      },
      "id": "VKuEljlOHkW_",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "WtmqN_5YIcIZ"
      },
      "id": "WtmqN_5YIcIZ",
      "execution_count": null,
      "outputs": []
    }
  ],
  "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": "3.10.9"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}