Module6_Lab3_FMML20210660.ipynb

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  "metadata": {
    "colab": {
      "name": "Module6_Lab3_FMML20210611.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/SreenadhSingamaneni/IIITH-FMML20210660/blob/main/Module6_Lab3_FMML20210660.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5jMitcrlNMvL"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import random\n",
        "import math\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.style.use('ggplot')\n",
        "from matplotlib.pylab import rcParams\n",
        "rcParams['figure.figsize'] = 10, 8\n",
        "\n",
        "from sklearn import metrics\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn.linear_model import Ridge\n",
        "from sklearn.linear_model import Lasso\n",
        "from sklearn.model_selection import train_test_split\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('ggplot')\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "\n",
        "from sklearn.datasets import load_digits\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "import sklearn.metrics as metrics"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ErY9WV83Nb6I"
      },
      "source": [
        "# Regression Lab 3: Regularization, SVM Regression and Logistic Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "```\n",
        "Module Coordinator : Pranav Tadimeti\n",
        "```\n"
      ],
      "metadata": {
        "id": "ZC2pqZ4FahRz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Part A: Ridge and Lasso Regularization"
      ],
      "metadata": {
        "id": "K-LziY3RZrrr"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w4iI-n_-viY1"
      },
      "source": [
        "## Motivation behind regularization\n",
        "\n",
        "Most, if not all real world data is noisy, i.e. there are outliers in the data which throw the model off during training. Let's look at a noisy sine wave as an example. We'll try to fit polynomials of various degree to the curve."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SWO75ZhYaIQM"
      },
      "source": [
        "np.random.seed(10)  \n",
        "\n",
        "x = np.array([i*np.pi/180 for i in range(60,300,4)]).reshape((-1,1))\n",
        "y = np.sin(x) + np.random.normal(0,0.15,x.shape)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LmPJxVOQYPM2"
      },
      "source": [
        "def poly_regression(x,y,deg,show=True):\n",
        "\n",
        "  poly = PolynomialFeatures(degree=deg)\n",
        "\n",
        "  x_ = poly.fit_transform(x)\n",
        "  poly.fit(x_,y)\n",
        "\n",
        "  m1 = LinearRegression()\n",
        "  m1.fit(x_,y)\n",
        "  y_pred = m1.predict(x_)\n",
        "\n",
        "  \n",
        "  if show:\n",
        "    plt.plot(x,y_pred,color=\"red\")\n",
        "    plt.title(\"Visualization of actual data vs predicted outputs (polynomial regression deg={})\".format(deg))\n",
        "    plt.scatter(x,y,color=\"blue\")\n",
        "    plt.legend([\"predicted polynomial\",\"actual data points\"])\n",
        "    plt.show()\n",
        "\n",
        "    print(\"\\n Coefficients obtained\\n\")\n",
        "    print(m1.coef_)\n",
        "    print(\"\\n\")\n",
        "\n",
        "  return y_pred"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_0hW2UghnqEc"
      },
      "source": [
        "For now, let's not think about how we obtain these coefficients. We'll look into how they are obtained in a later module."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "AG3Ev4yXaMTw",
        "outputId": "4ee866cf-a479-4c74-cd9c-6a7a2bd2d30c"
      },
      "source": [
        "for deg in range(1,14,3):\n",
        "  y_pred = poly_regression(x,y,deg)"
      ],
      "execution_count": 4,
      "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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.         -0.61957457]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.          1.68692165 -0.53175186 -0.03567846  0.01391921]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -5.59523300e+01  6.89561793e+01 -4.46319059e+01\n",
            "   1.65148424e+01 -3.52813549e+00  4.04509832e-01 -1.92268762e-02]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -4.86124812e+02  7.26132188e+02 -5.95880098e+02\n",
            "   2.93255129e+02 -8.74561572e+01  1.45461061e+01 -8.06062525e-01\n",
            "  -1.38205866e-01  2.62232264e-02 -1.32095913e-03]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -1.77942599e+04  4.45882359e+04 -6.66100409e+04\n",
            "   6.61553398e+04 -4.61171897e+04  2.32177849e+04 -8.55126155e+03\n",
            "   2.30570202e+03 -4.49925397e+02  6.18240901e+01 -5.67111742e+00\n",
            "   3.11610280e-01 -7.75456391e-03]]\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3oyZPl2fmLVC"
      },
      "source": [
        "This is exactly the same issue as we had seen previously in lab 1! The higher degree polynomials **overfit** the training data, by trying to capture noise in it. Though the model may do well on this set, if we try to fit the learnt curve to another noisy sine wave, it would result in a lower accuracy. Luckily, there's a way around this."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ppZxACBmp8q"
      },
      "source": [
        "**Q:** What trend do you observe with respect to the coefficient values as degree grows?\n",
        "\n",
        "\\\n",
        "\n",
        "**A:** The magnitudes of the coefficients go up drastically with degree!\n",
        "\n",
        "\\\n",
        "\n",
        "Now, why does that happen? Intuitively, we can think about what the polynomial is trying to fit here. In the above example, the polynomial is trying to fit to a noisy sine wave. To approximate the large oscillations we see, the coefficients need to have large magnitudes. We can also see that this only happens with higher degree polynomials, since lower degree polynomials cannot even approximate these oscillations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "74rKw9wzyELF"
      },
      "source": [
        "## Ridge Regression\n",
        "\n",
        "Ridge regression works by adding a term to the loss function which is proportional to the sum of the squared coefficients of the model.\n",
        "\n",
        "$L_r = \\sum_{i=1}^{N} (y - y_p) ^2 + \\alpha |w|^2$,\n",
        "\n",
        "where $\\sum_{i=1}^{N} (y - y_p) ^2$ is the typical mean-squared error loss and $\\alpha |w|^2$ is the regularization term, $w$ being the coefficient of the term. We can see that it penalizes the squared value of the coefficients."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pvdklTCyfnYI"
      },
      "source": [
        "def ridge_regression(x,y,deg,alpha):\n",
        "\n",
        "  poly = PolynomialFeatures(degree=deg)\n",
        "  x_ = poly.fit_transform(x)\n",
        "  \n",
        "  r = Ridge(alpha,normalize=True)\n",
        "  r.fit(x_,y)\n",
        "\n",
        "  y_pred_ridge = r.predict(x_)\n",
        "\n",
        "  plt.title(\"Ridge Regressed polynomial deg={}, alpha={}\".format(deg,alpha))\n",
        "  plt.scatter(x,y,color=\"blue\")\n",
        "  plt.plot(x,y_pred_ridge,color=\"red\")\n",
        "  plt.legend([\"actual data\",\"predicted data\"])\n",
        "  plt.show()\n",
        "\n",
        "  print(\"\\n Coefficients obtained\\n\")\n",
        "  print(r.coef_)\n",
        "  print(\"\\n\")"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "iyoUQt6Dk1fJ",
        "outputId": "b7d2e56c-b067-42c0-fa5b-b849a6c491b1"
      },
      "source": [
        "alpha = 0.1908 #@param {type:\"slider\", min:0, max:1, step:0.0001}\n",
        "\n",
        "for deg in range(1,14,3):\n",
        "  ridge_regression(x,y,deg,alpha=alpha)"
      ],
      "execution_count": 6,
      "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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.         -0.52030112]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -2.58022614e-01 -3.06542422e-02 -3.26452482e-03\n",
            "  -1.22827132e-04]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -2.49962889e-01 -3.32238191e-02 -4.44132490e-03\n",
            "  -4.74507640e-04 -1.75487401e-05  1.03568846e-05  4.47175753e-06]]\n",
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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MqNmYLRC3YC+I9Mc8YeZh1kh6lvd5W9tPBRE7aVey/Jpjng+yrM9lOU4DF5zLxU6ZYwaPH6y8nsCsvV9byfQvwwwiJbdS/AjcXtF7K4lC1Y5S6m3gUsMwrgx0XlxRSoVi1kxWG4bxSKDz4w/W0OfhhmG08dPxkzFPApf74/i1iTXo4phhGDcGOB/RmMFltGEYnjZRlnfcLpgn0DMMw9jvq+OKivm7T8QnrPsYBmF+SYowR5mMxHVndEAopa7FHL3zX8wRWQ9jXkm8G7hcVU/WiLxzMft1HgxwdqodpdTFmE0SGzGbREZgNi1dF8h8WXoAm3wZQERgVYsgghk4bsKsZkZiNlvca7jpXAyQUMwRRG0w2yT/B3Q1DOOXgOaqevoAs912GWaznvCMAdyL2TcSglkjHmQYxicBzRVgGMZqzP5DUUNU2+YsIYQQgSfriQghhKi0YG7OkiqSEEJUju35Ar0VzEGEv/6yv1xDfHw8qampfsxNzSDlZI+Ukz1STvZUZTklJCRUSTolpDlLCCFEpUkQEUIIUWkSRIQQQlRaUPeJCCGqjmEY5ObmUlxcjN113A4fPkxeXp6fc1b9+bqcDMMgJCSEyMhI25+Vv0gQEUIAkJubS3h4OGFh9k8LYWFhhIaG+jFXNYM/yqmwsJDc3FyioqJ8elxPSRCpZvbuDSU5OZZDh0Jp1qyIpKQsWrUqb/VhIewpLi72KICIwAoLCwuKWqB8Y6qRvXtDGTq0IXv2hJ/atnVrOMuWpUsgEV4LdLOI8FwwfGbSsV6NJCfHlgogAHv2hJOc7LwCrxBCVA0JItXIoUOu21QPH5Y2aVH7fPvtt2zevNmrY5xzzjkV7jNt2jRmzZpV7j6ffPIJ27ZVtIhpzSRBpBpp1sx1k1XTptKUJWqfjRs3smXLlkBnA5AgIqqJpKQsEhMLSm1LTCwgKSkrQDkSwrdGjx5Nnz596Nq1K4sWnV4F4IsvvqB379706NEDTdPYt28fCxcuZM6cOfTs2ZNNmzbx0EMP8eGHH556TUktIzs7G03T6N27N927d2fdunUV5uPVV1+lU6dODBw4kB07dpzavnjxYvr27UuPHj246667OHnyJJs3b+bTTz9l8uTJ9OzZk927d5fZLycnx4elFFykY70aadWqiGXL0klOjuXw4VCaNi1/dJarkVzx8VWcaVEt1Xv6acJ/+63C/ZRS2F1OoqBtWzKfe67cfaZNm0ZcXBwnT57k+uuvp2/fvhiGwWOPPcaqVato1aoVx44dIy4ujhEjRhATE8M999wDwNKlrte5ioiIYN68ecTGxpKens4NN9xAr1693HZK//zzz6xevZpPP/2UwsJC+vTpwyWXXALAddddx7BhwwB46aWXWLp0KaNHj6Znz5706NGDfv36AVCvXr1S+y1ZsoRRo0bZKqfqRoJINdOqVREzZmRUuJ+7kVzr1hnESj+8CFJvv/02a9euBcwJWHft2kVaWhrt27enVatWAMTFxXl0TMMwePHFF9m0aRNKKQ4dOsTRo0dp0qSJy/03bdpEnz59Tt1/0bNnz1PP/fHHHyQnJ5OZmUl2djadO3d2eQzn/bp27epRnquTGhdEfH0fRXW9L8PdSK6JE4uYNi1AmRLVRkU1hhJhYWEUFhb6JM1vv/2W//znP6xZs4aoqCiGDBni0X0QYWFhFBcXA+Y9LwUFZtPvqlWrSEtLY+3atYSHh3P11VdX+v6Khx9+mHnz5nHhhReyfPlyNm7caGu/TZs2VSq96qBG9Yns3RvK0JvjuDBlGjkbfyclJZqhQxuyd2/lRi+VXM2npESzcWOE18erTPpjxzZgyJBGjB3bwKN03Y3kOngw8OPKhXAlKyuL+vXrExUVxfbt29m6dSsAV155Jd999x179+4F4NixYwDExMRw4sSJU69v2bIlv/xirka9fv36U0EkKyuL+Ph4wsPD+eabb9i/f3+5+Wjfvj3r1q3j5MmTnDhxgk8//fTUcydOnKBp06YUFBSQkpJyanvdunXJzs6ucL+aqEYFkeTkWEL37uOfTOZHLmcLV9Bvz1u8Obmg4he7OV6g7svwNoC5G8nVvLms9SWCU5cuXSgqKqJz58688MILXHHFFQA0atSI5ORk7rzzTnr06MG9994LmM1Mn3zyyamO9WHDhrFx40Z69OjBli1biI6OBmDw4MH89NNPdO/enZUrV9KmTZty83HxxRdzww030LNnT4YPH85ll1126rnHHnuMfv36MXDgwFLHGTBgADNnzqRXr17s3r3b7X41UTCvsW54uihVly4GGzdGEEc6t7KE0bzNFfyXPBVBUf8+5AwdSn6nThBiL3YOGdKIjRsjymzv2DGPFSvSymz3ZdPX2LENSEmJLrN90KCcSveJJCYWWH0isohQRWrjYks5OTmnTrx2+bI5qybzVzm5+sysRalkZcPKKLn6PkZD3mAsbzCWy/gvk8+cw3UblhL9wQcUtmpFztCh5Nx8M8XNmtk6njNX92W468iePj2DRYtiPA4s3t5Y6G4k15lnxlHLzo1CCD/ySRDRNO1toB9wRNf1i1w8r4BXgb5ADjBK1/WtvkjbUVJSFlu3hpc6kR9LvIi8fz3LLfMnc/7vHzLk2DwuTk4mdto0crt3J+fWW8nr1g1czLDp6nju7stw1/Q1YkQjcnJO13zsznXlixsL7Y7kEkKIyvJVTeRdYAawwM3z1wHnWH9XAzOtf33K1dX38OHZjB/fwDrBj+Q5RtI54TcWd59Js0+WE7V+PYUJCeTceis5Q4dS3Lx5ucdzV5NwV3NwDCBgBpZnnqlHTIxRbu3EkwAmhBCB4rM+EU3TWgMfuqmJvAV8qev6UuvxH0AXXdcPlnNIj/tEXLVhl9u38PJRIj/9lOhFi4jcsAEjNJTcHj3IGT6cvC5dbPedlJeOKxERxeTlnT52YmKBy9pJSR+LnRsL7aqNbf2VURvLSfpE/Ef6RLzXAtjn8Hi/ta28IOIT5fYthIeT27cvuX37ErpnD9FLlhC9bBlR69ZRmJhIzvDhZu2kYcMK03FVc4iJKSI7u2z6jgEEyq+dSHOUECKYBVXHuqZpY4AxALquE+/BHB1hYWEu909MDMXV/UCtWjntHx8PV15J0ZQpGKtXE/LWW9R7/nlip06l+MYbKb77boyrrwY3UyXEx8O6dQYTJxZx8KCieXODO+4o4u67Q9i58/RrIiMNcnPLHuOrryJLbf/ppyg+/riAM8+0XQS2uCsnb+zaBRMnhp563xMnFvk831XNH+UU7A4fPlypRalkISt7/FFOERERAf+eVtWnfwA4w+FxS2tbKbquzwZmWw8NT5oT3DU/jBsXysaNZYe6jhuXTmqq6+ajQ4dupFmzgTyzeDNnfzaf6JUrCV+yhPyLLyb79ts52b8/uFiSMjaWMneDL15cukkqO1uxfn3Z1zoHlp07FRMmFPq8JuLrZprTo9JO17g2biyu9gtl1cbmrLy8PI+XcA3m5qxvv/2WWbNmsWDBAtavX8+2bdsYO3asy32PHz9OSkqKx/NbTZs2rdT8Xe6cc845/Pnnn26fr2z6eXl5Zb6nVnNWlamqILIaGKtp2jLMDvXjFfSH+IzdznHXQ3Q7smzZ+SROmEDUe+8RM38+cePHU/+558i+9VZyRo6k6IwznJMsk75jINi7N5Q//ggrlY5zH0mJ6rBOSHk3ZEpTnPCHoqIij4Ndr1696NWrl9vnMzMzWbBgQcAmSQx0+t7w1RDfpUAXIF7TtP3AM0A4gK7rs4CPMYf3bscc4nu7L9K1y07fQvknwyJyRo4kZ8QI6nz3HTFvv03dt96i7syZ5PbqRfYdd5DfsaPbpi7nvDgHNXe1E3+sE7JrF0yY0KBU3wtQ6ZskZaGs2mvv3lD+9a9YDh4M8cm8cvv27WPYsGFccskl/PLLL5x77rm89tprREVFcfXVV9O/f3+++uor7rvvPho0aMDUqVPJz88nMTGRl19+mZiYGL744gueeeYZoqKiuOqqq04de/ny5fz88888//zzHD16lMcff5w9e/YAMGXKFN5++2327NlDz549ufbaa3nqqaeYOXMma9asIT8/nz59+vDoo48C5jTxK1asID4+noSEhFMz/JYum73cf//95OTklApe2dnZ3H777Rw/fpzCwkKSkpLo3bs3L7zwQqn0x48f73K/YOSTIKLr+i0VPG8A9/siLX+xdTJUivwOHcjv0IGQv/4iZsECohctImrdOgouuIDs0aPJGTTIZVOXIzu1E38M5927N5Rhw8LZubPOqW2bNoWjlOLAgdNfBU/WbZeFsmondzfXetuMuWPHDqZNm0a7du0YP3488+fPP9VUFBcXx7p160hPT+fOO+9k+fLlREdH88YbbzB79mzuvfdeHnvsMXRd58wzz3TbxPTUU0/Rvn175s2bR1FREdnZ2TzxxBP88ccfp+bJ2rBhA7t27eKjjz7CMAxGjRrFd999R3R0tNtp4h09/fTTjBw5kptuuol333331HZ309I7p19YWOjR9PWBVKPmzvKGpyfD4oQEsh5/nMObN3PM6ghp8NhjNG3XjtgXXyTk0CHbaZfUTgYNyqFjxzwGDcrxS59CcnJsqU5+gL/+Ci8VQMCz+cFkoazayV/zyiUkJNCuXTvAnPPq+++/P/Vc//79AdiyZQvbtm1jwIAB9OzZkxUrVrB//362b99Oq1atOOuss1BKceONN7pM45tvvmHkyJEAhIaGUq9evTL7bNiwgQ0bNtCrVy969+7Njh072LVrV6lp4mNjY0tNE+9o8+bNDBw4EKBUPkqmpe/Rowc333zzqWnpndndLxjIsApLpW/ui4ri5NChnLz5ZrOpa+5c6s6YQd1ZszjZvz8nxoyh8KIyt86UURXDed3VtlzxdnqV6typLirmr2ZM5yttx8cl90MYhsG1117Lm2++WWrf//3vf16l7cgwDMaOHcuIESNKbZ8zZ47tY7iqNdidlt6X09f7m9RELF7XBqymrmPz5nHk66/JHjGCyLVradK7N42GDCHi00/BWusgUNzVtlypzPQqK1akMWNGhgSQWsBfzZgHDhzghx9+AOD9998/VStxdOWVV7J582Z27doFmDfc7dixgzZt2rBv3z5279596vWudOrUiQULzMk1ioqKyMzMLDOtfJcuXVi+fPmp6d0PHjxIampqudPEO2rXrh0ffPABYAaEEu6mpXdO39Pp6wNJgogDuyfDitb5KGrdmsxJkzj8ww8cf+opQvfsodGoUTTu1o3opUshN7cq3k4ZSUlZnHVW6RkKEhIKaNGi9BBNaY4SFfFXM+bZZ5/N/Pnz6dy5M8ePH+e2224rs0+jRo14+eWXuf/+++nRowf9+/dnx44dREZGkpyczMiRI+ndu7fb+yeee+45vv32W7p3706fPn3Ytm0bDRs2pF27dnTr1o1JkybRuXNnBg4cSP/+/enevTtjxozhxIkT5U4T75zGu+++S/fu3Tnk0LTtblp65/Q9nb4+kGrUVPBVMa7f3RTr5dZaCgqI+vBD6s6cSfivv1LUuDHZt99O9siRGB4u9emtrKx4JkwoLNX0BEhzlJPaeJ+Ip9OemKOz6nHoUIhPvjf79u3jtttu49///neljxGsavK0JxJEPOTVOh+GQZ2vv6buW28R+cUXFEdHk3PrrZwYM4biFi38lOPSauPJsTJqYzkFeu4sCSKeC4YgIs1ZHvKqQ1Ep8v/+d9IXLeLIZ5+Re911xLzzDk07dqTBQw8Rtm2bj3MrRPVxxhln1MgAUtNJEPGQrzoUCy+4gIzXXuPIt9+SfdttRH74IU26diXu9tsJ3+rzpVaqPW/Wmxf2BHGrhHAjGD4zac7yUKX6RGxQ6enEvPsudefNIyQjg7xrriHrgQfM5Xx9eINRdWym8VeZl6c6lpO3Tp48SXh4uEcTBQbz3FnBxB/lVFhYSEFBAVFONzdLn8hpQRlEwD/rfJRQ2dlEL1xI3dmzCT18mPzLL+fEAw+Q26tXucHE7vru3pSTL9eQ94S3681XRm0MIoZhkJubS3Fxse07oyMiIoL2/oVg4utyMgyDkJAQIiMjy3xWNXU9kRrFnzcGGjExZN9zD9mjRhG9YgV133yThqNHU9C2LR/4OLAAACAASURBVFnjxpHbt2+ZxbL8NQVFVafhjszPVTWUUmWuaitSG4NtZdTkcpI+kWAVGUnOiBEc+c9/OPbqq6jcXBrefTeNu3cn6v33oej0idtfU1A4qoo03JH5uYQIXhJEgl1YGCeHDOHIl1+Sbk3zEHf//TTp0oWo996DoqIquVIPZG1A5ucSInhJEKkuQkPJHTCAo59/Tvrs2RgREcQ9+CCNu3ZFK1hMCGWvyn15pR7I2kBVTVAphPCcdKxXV8XFRK5dS+zLLxP+++/sCDuXpwqfYTk3U0yo29FLlS2nQIyQCqRa932qJCkne6qynORmQ2FPSAi511/P0fXrSX/rLZq3CmEJw9gedTEvXbWEZUtSfXpyl9qAEMIVqYnUFMXFRK5ZQ+y0aYTv2EH+RReR9dhj5HXvXmpocK0vJ5uknOyRcrJHaiIi+IWEmH0m//43x155hZDMTBrddhvx/ftT55tvAp07IUQNJUGkpgkL4+RNN3Hkq6/ISE4m9OBB4jWNhrfcQvhPPwU6d0KIGqbWBpEaPxdTeDg5w4Zx+OuvOf7MM4T/8guN+/Yl7JZbCNu+PdC5E0LUELUyiJSMNEpJiWbjxghSUqIZOrRhzQskAJGRZI8Zw5GNG8kaPx61fj2Nu3al/qOPEnLwYKBzJ4So5mplEAnk3deBYsTGkvXIIxT83/+RPXo00e+9R5NOnYidMgWVmRno7AkhqqlaGURq9VxMjRuT+eyzHPnqK3L79iV2xgyaduhAzOzZ4DBBXI1v7hNC+EStDCIyFxMUnXEGGa+/zpF168i/9FLqP/ssTTp3JvKDD9i7J6T2NPcJIbxSK4OIzMV0WuFFF5G+ZAlpS5dixMbS8L77aHh9f1rs+b7UfjW9uU8IUTm1MojI3ddl5V17LUc/+YRj06cTd+IA39CJFQzhbE6P5KoVzX1CCI/U2vVE/LkmSLUVGsrJm2/mkS+G02bNLP7BS/RnNa/xIJP5J02b1gl0DoUQQaZW1kRE+cY9UczCxMc5hz9ZwEjGM50dIecwtc0MkKVQhRAOJIiIMkqa+zoMqs87Hd8gqet/CL+kDWf96x807t2bOl99FegslktGlglRdWptc5YoX+nmvjM5Yayk8OOPqTd5MvG33MLJPn3IfPppihITA5ZHV2u+AwFbxleI2kiCiLBHKXKvv57c7t2pO2cOdV99lSZdu3Li3ns5MXYshodrc5fHVXBwDgDu1nw/77xCtzeSSh+YEL4nzVnCM5GRnHjgAY589RUn+/Yl9pVXaHzttUSuXg0+WFbA7pQ07mYd2LrVdee/jCwTwj8kiIhKKU5IIGPGDFJTUjDi4mh477000jTCtm3z6rh2p6RxN+uAO7XpRlIhqpIEEeGV/Kuu4ujatWS88ALhv/1G4549qTdpEvt/P1mpzm27U9K4m3Xgiivy5UZSIaqQ9IkI74WGknPbbeT260fslCnUnTWLVnNWU6doGhu5GVC2O7ftTkmTlJTF1q3hZdZ8f/ZZczLJ5ORYDh8OpWlT130qQgjfkOVxa5mqKKfXbt3GTRse4Uq28hnduY83+ZNzGTQop8LObVcd5omJBS4DUEkHvD+ChXyf7JFysqcmL4/rk5qIpml9gFeBUGCurusvOj0/CvgXcMDaNEPX9bm+SFsEn6/yO/Avvudu3uIFnuAXLmYKE9hw8OEKX1tyj4qd4CCzDggReF4HEU3TQoE3gJ7AfmCzpmmrdV3/zWnX5bquj/U2PRH8mjUropgIZnIfqxjMNB5hIs/y1y+LiNgwibzOnct9vQQHIaoPX3SsXwVs13V9p67r+cAyYIAPjiuqKcdZkg/TjOEsZliTtcQ1NGh06600uP9+Qo4eDXAuhRC+4IvmrBbAPofH+4GrXex3o6Zp1wLbgId1Xd/nvIOmaWOAMQC6rhMfH287E2FhYR7tX1tVRTnFx8O6dQYTJxZx8KCieXODpyd2I7T5fymcOpWol14iasMGiqZMoXjUKFBV1nxrm3yf7JFysqcml1NVjc5aAyzVdT1P07S7gflAN+eddF2fDcy2HhqedERJB589VVVOsbEwbVrpbakngHvuIaxHD+onJRFxzz3kzZ9PxosvUtSmjd/z5An5Ptkj5WRPADrWq4wvmrMOAGc4PG7J6Q50AHRdT9N1vWTt1bnAlT5IV1RThW3akLZyJRn/+hfhv/1Gk549qfvyy5CfH+isCSE85Isgshk4R9O0MzVNqwMMBVY77qBpWnOHh/2B332QrqjOQkLIufVWjnz5Jbm9e1Nv6lQa9+1L+E8/BTpnQggPeB1EdF0vBMYC6zCDg67r+q+apj2naVp/a7cHNU37VdO0n4AHgVHepitqhuImTTg2axZp77xDyLFjxPfrR73Jk1EnT/o9bZkyXgjvyc2GtUwwl5PKzKTe5MnELF5MYevWZEydSn6HDn5Jq6KbGoO5nIKJlJM9NflmQ5k7SwQNo149jicnk7p8ORgG8UOGUP/JJ1HZ2T5Py+5Ej0KI8kkQEUEnv1Mnjn7+OSfuvJPo+fNp3L07db75xqdp2J3oUQhRPgkiIigZUVFkPvssaatWQVgY8ZpG/QkTUCdO+OT4did6FEKUT4KICGr5V13F0U8/5cSYMUQvXOizWonjXfUlZMp4ITwnQUQEPSMqisxnniEtJQXCw4nXNOo9/bRXI7hKJnocNCiHjh3zGDQoR9ZhF6ISZD0RUWXsrJ1envx27Ti6fj2xL7xA3XnziPziC4698goFV1bu3lWZ6FEI70kQEVXC1ZDarVvDmT49g0WLYmwHFiM6mszJk8nt3ZsG48cTP3AgJ+67j6xHHoE6rtdXF0L4jwQRUSXcDakdMaIROTmnW1XtroCY//e/c/Tzz6k/cSKxM2aYtZLXX6fwvPP8kn8hhGvSJyKqhLshtY4BBDy7V8OoV4+M6dNJnzePkIMHaXzddcTMmQPFxV7nVwhhjwQRUSXcDal1xdN7NXL79OHov/9NXqdO1J84kUa33EKI02wHMsWJEP4hQURUCVdDamNifHevRnHjxqTPn0/GSy8RvmULTXr0IHK1OQ9oSX9MSko0GzdGkJISzdChDSWQCOEDEkRElXA1pHbBgnTf3quhFDnDh3N0/XoKzzqLhvfeS4OHH+a155EpToTwE+lYF1XG1ZDaZcvSSU6O5fDhUJo29XzYrytFZ51FakoKsdOnU/f110mu8wPbWcpmriq1n0xxIoT3JIiIgPLbvRrh4WT94x/kde5MxPBxfMM1PMOzvMQ/KMYMHjLFiRDek+YsUaPlt2/P7vc/Y130QF7gST6jBwkckClOhPARCSKixmtxUSzxn73OjCtm0j7ke36vcymfjF0mU5wI4QMSRESt0CqxmMFr+pP1xVqi2jTl/MdGUu/ppyEvL9BZE6JakyAiapXCNm04umYNJ+64g7rz5hHfvz+hO3cGOltCVFsSRETtExlJ5nPPkfbOO4Tt30/jPn2Iev/9QOdKiGpJgoiotfJ69eLIp59S0LYtcfffT/2kJPBienkhaiMJIqJWK05IIG3FCrLGjiVm8WIa33ADodu3BzpbQlQbEkSECA8na8IE0hYuJOTQIRpfdx0hS5eeelrm3RLCPQkiQljyunXj6Pr1FFx0EWGjRlH/8cfZ92eBzLslRDkkiAjhoKR5q2j8eGIWLqTRwEGoPftL7SPzbglxmgQRIZyFhVE0ZQrpb79N06ydbOUK+rGm1C4y75YQJgkiQriR27s3Sd2/YRdnsob+TOFxQikEZN4tIUrIBIxCONi7N5Tk5FjS08No2LABw+8O55b/28D4vY/yOC/Rjs0ktVxAUpL8dIQACSJCnFKyeNXptUei2bo1nOkvZ7Bo0cuk/vI3Ht35IN/mX0Vm6lsUtLoioPkVIhhIc5YQluTkWJeLVy1aFMOMGRncvuF6jq/9gNDIMOIHDyZ6wQIwjADlVojgIEFECMuhQ647yx070QsvuoijH39M3t//ToMJE2jw8MNyl7uo1SSICGFp1szemu9GXBzp8+eTNX48UStXEj9oEKH797t8rRA1nQQRISxJSVn213wPCSHrkUdIf+cdwnbvJv6666jzzTdVlFMhgocEESEsrVoVsWxZOoMG5dC5czGDBuWwbFl6uYtX5fXsydGPPqI4Pp5Gt9xCzOzZ0k8iahUZnSWEg5I13+Pj40lNtbf2e9HZZ5O6Zg0NHn6Y+s8+S/jPP3P8X//CiIryc26FCDypiQjhA0bduhybPZvMf/yDqPffp9HAgYQeOBDobAnhdz6piWia1gd4FQgF5uq6/qLT8xHAAuBKIA24Wdf13b5IW4igoRQnHnzQXJ9k7Fjir7uOY3PmkH/11YHOmRB+43VNRNO0UOAN4DqgLXCLpmltnXa7Azim63ob4GXgJW/TFSJY5fXoQeqHH2LUr08jTSN64cJAZ0kIv/FFc9ZVwHZd13fqup4PLAMGOO0zAJhv/X8l0F3TNOWDtIUISoVt2nD0ww/N+0kef5z6jz8O+fmBzpYQPueL5qwWwD6Hx/sB5/r7qX10XS/UNO040AhIddxJ07QxwBhrP+Lj421nIiwszKP9ayspJ3t8Uk7x8fDRRxQ99RQx06YRtXs3hcuWmdtrCPk+2VOTyymoRmfpuj4bmG09NFJTU8vbvRRzNI39/WsrKSd7KiqnkokaDx0KpVmzIpKSstwPBR4/nqjWrWnw6KOEdOhA+jvvUHj++X7KedWS75M9VVlOCQkJVZJOCV80Zx0AznB43NLa5nIfTdPCgPqYHexCVDslEzV6strhycGDSV25EpWbS3z//kSsX1+FORbCf3wRRDYD52iadqamaXWAocBqp31WA7dZ/x8C/FvXdbkjS1RL7iZqrGi1w4IrruDoRx9RePbZNBw9mrpvvik3Jopqz+sgout6ITAWWAf8bm7Sf9U07TlN0/pbu80DGmmath0YDzzubbpCBIqdiRrdKU5IIG3VKnL79aPe88/T4KGHIC8PMGs4Y8c2YMiQRowd20DWcRfVgk/6RHRd/xj42Gnb0w7/zwVu8kVaQgSa3Yka3TGiojg2cyYF551HvalTCd2zh1+efYeh955bqoazdWt4hdOuCBFocse6EB7yaKJGd5TixMMPkz5zJnV++YWWQ/oRs2dbqV3sNJEJEWgSRITwkONEjR075tmaqNGd3P79SV25krCCXL6lI735pNTzdprIhAikoBriK0R1UTJRox0VDQcuuPxynum2gfvXaXzE9TzEK8zgAcB+E5kQgSJBRAg/Krtuu+u+jjsm1ufW375gyr5RvM6DnMs2XmmV7FkTmRABIM1ZQviR3eHArVoV8baez8KBi1jafBwPMIMfWt5AYsPjVZldITwmNREhfMi56WrPHtc/MVd9Ha1aFfHaG1lAEhnzm9LgqacoHDSItHffpbhFCz/nXIjKkSAihI+4arqKianccOCc226jKDGRuLvvpvENN5D+7rsUXHKJT/MrhC9Ic5YQPuKq6So7O5To6OJS2+wOB87r0oXUDz7ACAuj0eDBMlWKCEoSRITwEXd3sp9/fkGlhwMXnn8+qR9+SOG559LwjjuIefttX2ZZCK9Jc5YQPuLuTvbERPvDgV0pbtKEtJUraTB2LPWfeorQPXvIfPppCJV7SETgSU1ECB/xyZ3sbhjR0RybM4cTd95J3blziRszBnXypNfHFcJbEkSE8BFf3snuUmgomc8+y/HnniNy3ToaDRlCyNGjvjm2EJUkzVlC+JAnd7JXVvYdd1B4xhnE3Xcf8f37k7ZwIUVt2vg1TSHckZqIENVQXq9epK1cicrJofGAAdT5/vtAZ0nUUhJEhKimCi67jNTVqylu2JBGQ4cSuWZNoLMkaiEJIkJUY0WJiRz94AMKLr6YhvfcQ8ysWbJaoqhSEkSECABfrmJoNGxI6rJlnLz+eupPmkS9p5+GIpn9V1QN6VgXoorZndnXI1FRHJs1i6LnnqPunDmEHjrEsddeg6goH+VaCNekJiJEFbM7s6/HQkLInDiR4888Q+TatcQPHYpKT/fumEJUQIKIEFXM3fQormb2rUyzV/aYMRybOZPwX34hfuBAQvfu9TrPQrgjzVlCVDF306M4z+zrTbNX7g03kNakCQ1Hjya+f3/SFyyQWYCFX0hNRIgqZnd6FG+bvfKvvpqfZ64mLTuKmOuHMPemzV514AvhigQRIaqY3elR3DV77dljr4lr795QBj7enstyNrKtuA0Tvh3Cin4fSiARPiXNWUIEgJ3pUdw1e/3f/4WzdWvEqcfumrhO12QSuJavWMVgpqXdyeI7JtJq/Z2glNfvQwipiQgRpFw1e8XEFJGTU/pn666Jy7Emk0U9+vIxixjGsN8mUv+JJ+ReEuETUhMRIkiVNHslJ8dy+HAoTZuaa7Zv3Vq2OcrVyC7nmkwBdRjJAqLPacrgBdMJOXyYY2+8IfeSCK9ITUSIIFbS7LViRRozZmSQmFjocj9Xa7a7qsm0SiwiYUESxydNInL9evNekmPH/JJ3UTtIEBGiGvFk4avyOvCzR4/m2KxZhP/8s3kvyf79VfUWRA0jzVlCVCOumriSkrLc3jdSXgd+br9+pDVqdOpekrSFCym88EJ/Zl/UQBJEhKhmfLnwVX6HDqSmpNBo2DDib7yR9Llzye/UySfHFrWDNGcJUcsVnn8+R1evpighgUbDhxP5wQeBzpKoRiSICCEobtGC1FWryL/iChredx8xs2cHOkuimpAgIoQAwGjQgLQlSzjZty/1n32Wes8+C8XFgc6WCHISRIQQp0VGcmzWLE7cfjt1Z8+mwQMPQH5+oHMlgph0rAshSgsNJXPSJIqbN6feCy8QevQo6fPmYcR6ud6JqJG8CiKapjUElgOtgd2Aput6mTuXNE0rAn6xHu7Vdb2/N+kKIfxMKU7cfz9FTZvS4JFHiB88mLSFCylu1izQORNBxtvmrMeBz3VdPwf43Hrsykld1y+z/iSACFFNnBwyhPQFCwjds4f4/v0J+/PPQGdJBBlvg8gAYL71//nAQC+PJ4SopMqsgmhHXufOpL33Hio/n/iBA6mzebNPjitqBm/7RJrqun7Q+v8hoKmb/SI1TfsBKARe1HX9fVc7aZo2BhgDoOs68fHxtjMSFhbm0f61lZSTPdWtnHbtgmHDwtm58/T07j/9FMXHHxdw5pk+SKBrV4q++orwG26g0dChFC5YgDFgQLUrp0CpyeWkDMModwdN0z4DXDWEPgnM13W9gcO+x3Rdj3NxjBa6rh/QNO0s4N9Ad13Xd1SQN+Ovv/6q8A2UiI+PJzU11fb+tZWUkz3VrZzGjm1ASkp0me2DBuXYurt9795QkpNjOXQolGbN3E+lEpKeTsORIwn/8UeOT55M9KOPVqtyCpSq/D4lJCQAVNliMRXWRHRd7+HuOU3TDmua1lzX9YOapjUHjrg5xgHr352apn0JXA5UFESEEDa5WwXR1RTxzjxZy724YUPSVqwg7t57afDkkxQdOwbjxkGI3C1QW3n7ya8GbrP+fxtQZr4ETdPiNE2LsP4fD1wD/OZlukIIB+5WQXQ1RbwzT9dyN6KiSJ87l+wRIwidOpUGDz4IeXmeZ1rUCN4GkReBnpqm/Qn0sB6jadrfNE2ba+1zAfCDpmk/AV9g9olIEBHChzyZIt5ZpWoxYWEcnzKFwkmTiE5JodHw4ajMTI/yLGqGCvtEAkj6RPxAysme6lhOJf0adqaId+RNf0p8fDzZs2bR4JFHKDznHNIWLKDYbJMXDmp1n4gQonqo7BTxSUlZbN0aXqpJy24tBsx7SYqaNKHhXXfR+IYbSFuwQNYlqUWkN0yIWq68FRDtyr/2WlJTUgCIHzyYiA0b/JXdoOev+3WClTRn1TJSTvZIOdnjXE4hf/1Fo5EjCfvzTzKSkzl5880BzF3VczXSLTGxgHXrDGJja2ZzltREhBA+U5yQQGpKCnnXXEPc+PHETp0KwXuh6nPuRrpNnFhzayMSRIQQPmXExpI+fz7ZQ4cS+/LLtWoIsLuRbgcPVlnFoMpJx7oQwvfCwzk+dSpFrVpRLzmZ0AMHSJ87F6Nhw0DnzK/c3a/TvHnNrY1JTUQI4R9KcWLcONLffJM6P/5I4/79Cd25M9C58it39+tMnGh/kEJ1I0FECOFXuQMGkLZ8Oer4cRrfcAN1Nm0KdJb8xt1IN59MghmkpDlLCOF3+e3akbpmDQ1HjqTR0KFkTJ3KyRtvDHS2/KKy9+tUV1ITEaKWCdR9DEWtW5P6wQfkX3klcQ8+SOyLL0JxcZWkLfxHaiJC1CKezNjrD0ZcHGlLllD/n/8k9vXXCdu+nYxXX8WIifF72sI/pCYiRC3i6Yy9flGnDsdfeonjEycSuW4d8YMGEXLgQNWlL3xKgogQtYg36474lFJk33UX6fPnE7pnD42vv57wLVuqNg/CJySICFGLeLLuSFX0neR160bq6tUYUVHEDxlC1PLlPk9D+JcEESFqEbvrjpT0naSkRLNxYwQpKdEMHdrQL4Gk8LzzOPrRR+RfdRVx48dT7+mnoaCg4heKoCBBRIhaxO6MvVXdd2I0bEja4sWcuOsu6s6bR6NbbiEkLc0vaQnfktFZQtQydu5jCEjfSVgYmRMnUnDRRTRISiK+b1/S582j8KKL/Jem8JrURIQQZXizZru3Tg4ZQmpKCqqoiMYDBhCl635PU1SeBBEhRBnerNnuCwWXXsrRTz4h/4oriHv4YeonJUFubpWkLTwjQUQIUYYvVjv0VnF8PGlLl5I1diwxixcTP2gQofv2VVn6vrRrFzV2tUNZ2bCWkXKyR8rJnqoqp4j164kbNw5CQjj22mvkde/u9zR9Ze/eUIYNa8LOnafXFElMLPBbUJaVDYUQwkler14cXbuWohYtaDRyJPUmTYL8/EBny5bk5NhSAQQCMEuAH0kQEUJUC0WtW3P0gw/IHjmSurNmmc1bu3cHOlsVCppZAvxEgogQovqIiuL4lCmkz5lD2K5dNO7dm6hVqwKdq3IFcqRbVZAgIoTwSlVNLe+Yzp0f38qP735OQdu2xD3wAA3GjUNl+W/kmDfvMSkpi7POKt33XJUj3fxNOtZrGSkne6Sc7MnKiqd3b1Xq7nZfdBrv3RtKcnIshw6F0qxZEcOHZzN+fIOy6Sw6woUp06n7yisUNW9OxrRp5P/97169J1d5cZ4+39P3mJUVz4QJhRw+HErTpkUkJWX5baRbVXesSxCpZaSc7JFycs355F5QEMGHH5a9Kh80KKfSq/u5OmnHxBSRne0+nfAtW4h76CHCdu4ke9QoMp98EiM6utLpO77H7GzF+vVRbtO2oyq/T1UdRGTaEyGELa5O7pGRri9C3XUaO5+gXV2Ru5q3y1UAcUyn4MorObp+PbEvvkjduXOJ+PJLMl5+mfyrrrL9/kry5/weIyJcr75YUzrGvSV9IkIIW1yd3HNzXV/wupta3s7MwO5GM1WUjhEVReazz5K6ciUUF9No8GDqP/EE6vhx28dz9R7z8lyfJmtKx7i3JIgIIWxxd3J3vlJ312lsd2Zgd6OZoqPtpZPfoQNHP/uM7NtvJ3rhQpp07kzU+++DjaZ7b99jbSTNWUIIW9yd3Dt3ziMmxqiw09ju/RJJSVls3RpepiN7+vQMFi2KsdU5bcTEkDlpEidvuon6EyYQd//9RC9dSsYLL1B09tl+e4+1kXSs1zJSTvZIOZXlqr/grLMMFi8+4vKEareDulevk8TEGKX6ScCsufjkpF1URPTChdSd8hJGTi7Lmz3AJ5ePZ+w/Q8sc0xcjsVxx9X2y0z9UGTI66zQJIn4g5WSPlJNrJSe+kpP7lClhxMaWLSdXJ+OEhAKUUhw4EFbuNn/MK7V3bygP3JTP2P3/ZAQLyaABb8Y9Ts+UmznjnPAy+9oJYJ4EAefvk7tgVVLb8iawSBA5TYKIH0g52SPlZI+7cho7tgEpKWWH2JbUOkpO0L4YPmuHY34u4Sde5HGu4xOORp1B2JRHODl4MITa79D3tMbiXE7uyic6upicnNNd1ZUJqDIBoxCi2nPX/3HiRAgzZmSwYkUaM2ZkkJXl+hTk6+Gzjvn5mUvpy1q68TlpIY2Je+ghGnfrRvSSJbbXLPF2+WB35eMYQDw9ZqBIEBFC+Jzd+aK8nVfK3XQkzttjY8ve6/EF3Xiy5wbSZ83CiIykwWOP0bR9e+q++irq2LFy0/V2UkV379ubYwaKV6OzNE27CZgIXABcpev6D2726wO8CoQCc3Vdf9GbdIUQwc3dCCvnYbF293PFVZPS1q3hTJ+eUWaKlISEAlq0KCzT9/LYP7LJbXUDuf36Ueebb6g7axb1kpOp+/rrnBwyhJwbb6Tgb38DVbp1yNvg5+p9l9yVfw7bSOAvNtDFo2MGild9IpqmXQAUA28Bj7oKIpqmhQLbgJ7AfmAzcIuu679VcHjpE/EDKSd7pJzsKa+cPO2g9nQklrt+hZYtC9i/P7zMduf+GHfphP3+O3XfeouoNWtQubkUJiZyctAgcgYNoqhNm1N59qZPxPl9t4zP5pGzdIpmLqND3gZ+4wIu5FcSEwuDvk/EJx3rmqZ9ifsg0gGYqOt6b+vxBABd16dUcFgJIn4g5WSPlJM9gSynIUMasXFjRJnt9eoVk5lZtqW+Y8c8VqxIs318lZVF5Nq1RKWkEPH116jiYgratiWvY0fyO3RgZ0J7Xpjd2lbwc1lOBQWE//YbUatWEb1yJSEZGeS2SGRl/dvRo28j7Iwm1WJ0VlXcbNgCcFwYeT9wtasdNU0bA4wB0HWd+Ph424mEhYV5tH9tJeVkj5STPYEsp8TEUDZuLLs9Lg4yM8tub9XKw7zGx8N998F991Fw8CAhy5cT+vHHxCxaRN25c2kIrGzbFqN9e4wzz4T/a4lxoiVGy5aQkABFRZCTAydPErZjB40zMlC//orassX8+/lnVF4eRng4xQMGUDB6/kP2HgAABIpJREFUNCFdu6KFhKCdfjeeF0wVqzCIaJr2GdDMxVNP6rr+gS8zo+v6bGC29dDw5ApHrhztkXKyR8rJnkCW07hxoWzc6PpeC1fTxo8bl05qaiX7F8LDYfhw8y8vj/Cffybiu++os2kTdVatIjSj4uHIJXWj4pgYCi65hIJRo8i/9FLyr7mG4pLglp5eufw5sGoiVabCIKLreg8v0zgAnOHwuKW1TQghKq1VqyKWLUt32Z/ibrtPRERQ0K4dBe3awQMPAKCyswk9eJCQv/4i9OBBQg8fhrAwiqOiIDKSuo0bk1lYSOHZZ1N41lke3ZMS7KqiOWszcI6maWdiBo+hwK1VkK4QooZr1arI5U2J7rb7ixETQ2GbNmB1vDuLjo8nt4bWbL26T0TTtEGapu0HOgAfaZq2ztqeoGnaxwC6rhcCY4F1wO/mJv1X77IthBDeq6qlfWsymfaklpFyskfKyZ7qXE7+mmzRlZq8sqHcsS6EqJW8nbpEmCSICCFqJW+nLhEmCSJCiFrJ26lLhEmCiBCiVkpKyiIxsaDUNln21nOyPK4Qolby+/0ktYQEESFErVXV95PURNKcJYQQotIkiAghhKg0CSJCCCEqTYKIEEKISpMgIoQQotKCeu6sQGdACCGqKZk7C7MQbP9pmrbF09fUxj8pJyknKadaUU5VJpiDiBBCiCAnQUQIIUSl1aQgMrviXQRSTnZJOdkj5WRPjS2nYO5YF0IIEeRqUk1ECCFEFZMgIoQQotKq/Sy+mqa9DfQDjui6flGg8xOsNE07A1gANMW8B2e2ruuvBjZXwUfTtEjgKyAC8/exUtf1ZwKbq+CkaVoo8ANwQNf1foHOTzDSNG03kAUUAYW6rv8tsDnyvZpQE3kX6BPoTFQDhcAjuq63BdoD92ua1jbAeQpGeUA3XdcvBS4D+mia1j7AeQpW44DfA52JaqCrruuX1cQAAjUgiOi6/hWQHuh8BDtd1w/qur7V+n8W5o+/RWBzFXx0XTd0XT9hPQy3/mT0iRNN01oC1wNzA50XEVjVvjlLeE7TtNbA5cCmAGclKFnNNFuANsAbuq5LOZX1CpAExAY6I0HOANZrmmYAb+m6XuOG+lb7mojwjKZpdYH3gId0Xc8MdH6Cka7rRbquXwa0BK7SNE362hxomlbSB7kl0HmpBjrpun4FcB1mE/K1gc6Qr0kQqUU0TQvHDCCLdV1fFej8BDtd1zOAL5A+N2fXAP2tTuNlQDdN0xYFNkvBSdf1A9a/R4AU4KrA5sj3pDmrltA0TQHzgN91XZ8e6PwEK03TGgMFuq5naJoWBfQEXgpwtoKKrusTgAkAmqZ1AR7VdX14QDMVhDRNiwFCdF3Psv7fC3guwNnyuWofRDRNWwp0AeI1TdsPPKPr+rzA5iooXQOMAH7RNO1Ha9sTuq5/HMA8BaPmwHyrXyQE0HVd/zDAeRLVU1MgRdM0MM+1S3Rd/ySwWfI9mfZECCFEpUmfiBBCiEqTICKEEKLSJIgIIYSoNAkiQgghKk2CiBBCiEqTICKEEKLSJIgIIYSotP8HNKl4MaAYJywAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -2.29408641e-01 -3.23577946e-02 -4.80081730e-03\n",
            "  -6.50293746e-04 -7.24699525e-05 -4.25748466e-06  9.00209223e-07\n",
            "   4.71216499e-07  1.41511617e-07  3.58110395e-08]]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[[ 0.00000000e+00 -2.17327395e-01 -3.09365488e-02 -4.70684716e-03\n",
            "  -6.75888906e-04 -8.72371643e-05 -9.17294017e-06 -4.63740129e-07\n",
            "   1.26857573e-07  5.95070758e-08  1.70446336e-08  4.15540984e-09\n",
            "   9.33965834e-10  1.99842776e-10]]\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mgPGs0n1zcZD"
      },
      "source": [
        "## Lasso Regression\n",
        "\n",
        "Lasso regression is similar to ridge regression, except it penalizes the absolute value of the weights.\n",
        "\n",
        "$L_l = \\sum_{i=1}^{N} (y - y_p) ^2 + \\alpha |w|$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yzhaPWYIqJY6"
      },
      "source": [
        "def lasso_regression(x,y,deg,alpha):\n",
        "\n",
        "  poly = PolynomialFeatures(degree=deg)\n",
        "  x_ = poly.fit_transform(x)\n",
        "  \n",
        "  l = Lasso(alpha,normalize=True)\n",
        "  l.fit(x_,y)\n",
        "\n",
        "  y_pred_lasso = l.predict(x_)\n",
        "\n",
        "  plt.title(\"Lasso Regressed polynomial deg={}, alpha={}\".format(deg,alpha))\n",
        "  plt.scatter(x,y,color=\"blue\")\n",
        "  plt.plot(x,y_pred_lasso,color=\"red\")\n",
        "  plt.legend([\"actual data\",\"predicted data\"])\n",
        "  plt.show()\n",
        "\n",
        "  print(\"\\n Coefficients obtained\\n\")\n",
        "  print(l.coef_)\n",
        "  print(\"\\n\")"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "JNgh_cQ8qUHM",
        "outputId": "30af0aff-3810-4e0c-fbc0-493234233af1"
      },
      "source": [
        "alpha = 0.002 #@param {type:\"slider\", min:0, max:0.01, step:0.001}\n",
        "\n",
        "for deg in range(1,14,3):\n",
        "  lasso_regression(x,y,deg,alpha=alpha)"
      ],
      "execution_count": 8,
      "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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[ 0.         -0.60676107]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[ 0.        -0.5779558 -0.0046448 -0.         0.       ]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[ 0.00000000e+00 -4.20298161e-02 -1.20999306e-01 -0.00000000e+00\n",
            " -0.00000000e+00  0.00000000e+00  0.00000000e+00  1.12901130e-05]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[ 0.00000000e+00 -0.00000000e+00 -1.23420451e-01 -0.00000000e+00\n",
            " -0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
            "  0.00000000e+00  0.00000000e+00  8.61643410e-08]\n",
            "\n",
            "\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"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Coefficients obtained\n",
            "\n",
            "[ 0.00000000e+00 -5.51898836e-02 -1.08910005e-01 -0.00000000e+00\n",
            " -0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
            "  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
            "  0.00000000e+00  5.80196758e-10]\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mfCcE1UmrEvk"
      },
      "source": [
        "### Feature selection\n",
        "\n",
        "Sometimes, data may contain features that are not relevant to the model; they do not contribute to the model's predictions. Naturally, we would want to get rid of such features in our data. **Feature selection** is a process by which we understand which features are actually relevant to the model and remove the unrelated features from our data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LwydhHOCqgVJ"
      },
      "source": [
        "The advantage of lasso regularization over ridge regularization is that it does a better job of feature selection. In ridge regression, the coefficient can approach zero, but never truly reaches zero. Hence, the model cannot perform feature selection.\n",
        "\n",
        "In lasso regression, since we are penalizing the absolute value of the coefficient, the feature can have a zero coefficient, which is the same as feature selection. In the above example, we can clearly see the feature selection process in action, with higher degree polynomials have zero-valued coefficients for some of the terms."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2uJlAzuTunuO"
      },
      "source": [
        "## Applying regularization to the crime dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "sNQJBcEAutAu",
        "outputId": "d9142240-291c-409f-954d-b31815b478a1"
      },
      "source": [
        "src = 'http://archive.ics.uci.edu/ml/machine-learning-databases/communities/communities.data'\n",
        "crime = pd.read_csv(src, header=None, na_values=['?'])\n",
        "\n",
        "crime.head()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   0     1        2                    3    4     5     6     7     8     9    \\\n",
              "0    8   NaN      NaN         Lakewoodcity    1  0.19  0.33  0.02  0.90  0.12   \n",
              "1   53   NaN      NaN          Tukwilacity    1  0.00  0.16  0.12  0.74  0.45   \n",
              "2   24   NaN      NaN         Aberdeentown    1  0.00  0.42  0.49  0.56  0.17   \n",
              "3   34   5.0  81440.0  Willingborotownship    1  0.04  0.77  1.00  0.08  0.12   \n",
              "4   42  95.0   6096.0    Bethlehemtownship    1  0.01  0.55  0.02  0.95  0.09   \n",
              "\n",
              "   ...   118   119   120   121   122  123  124   125   126   127  \n",
              "0  ...  0.12  0.26  0.20  0.06  0.04  0.9  0.5  0.32  0.14  0.20  \n",
              "1  ...  0.02  0.12  0.45   NaN   NaN  NaN  NaN  0.00   NaN  0.67  \n",
              "2  ...  0.01  0.21  0.02   NaN   NaN  NaN  NaN  0.00   NaN  0.43  \n",
              "3  ...  0.02  0.39  0.28   NaN   NaN  NaN  NaN  0.00   NaN  0.12  \n",
              "4  ...  0.04  0.09  0.02   NaN   NaN  NaN  NaN  0.00   NaN  0.03  \n",
              "\n",
              "[5 rows x 128 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-4296c5eb-ab34-479a-8ee7-3273c2d8133f\">\n",
              "    <div class=\"colab-df-container\">\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>...</th>\n",
              "      <th>118</th>\n",
              "      <th>119</th>\n",
              "      <th>120</th>\n",
              "      <th>121</th>\n",
              "      <th>122</th>\n",
              "      <th>123</th>\n",
              "      <th>124</th>\n",
              "      <th>125</th>\n",
              "      <th>126</th>\n",
              "      <th>127</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>8</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Lakewoodcity</td>\n",
              "      <td>1</td>\n",
              "      <td>0.19</td>\n",
              "      <td>0.33</td>\n",
              "      <td>0.02</td>\n",
              "      <td>0.90</td>\n",
              "      <td>0.12</td>\n",
              "      <td>...</td>\n",
              "      <td>0.12</td>\n",
              "      <td>0.26</td>\n",
              "      <td>0.20</td>\n",
              "      <td>0.06</td>\n",
              "      <td>0.04</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.32</td>\n",
              "      <td>0.14</td>\n",
              "      <td>0.20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>53</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Tukwilacity</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.16</td>\n",
              "      <td>0.12</td>\n",
              "      <td>0.74</td>\n",
              "      <td>0.45</td>\n",
              "      <td>...</td>\n",
              "      <td>0.02</td>\n",
              "      <td>0.12</td>\n",
              "      <td>0.45</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.00</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.67</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>24</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Aberdeentown</td>\n",
              "      <td>1</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.42</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.56</td>\n",
              "      <td>0.17</td>\n",
              "      <td>...</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.21</td>\n",
              "      <td>0.02</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.00</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.43</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>34</td>\n",
              "      <td>5.0</td>\n",
              "      <td>81440.0</td>\n",
              "      <td>Willingborotownship</td>\n",
              "      <td>1</td>\n",
              "      <td>0.04</td>\n",
              "      <td>0.77</td>\n",
              "      <td>1.00</td>\n",
              "      <td>0.08</td>\n",
              "      <td>0.12</td>\n",
              "      <td>...</td>\n",
              "      <td>0.02</td>\n",
              "      <td>0.39</td>\n",
              "      <td>0.28</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.00</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>42</td>\n",
              "      <td>95.0</td>\n",
              "      <td>6096.0</td>\n",
              "      <td>Bethlehemtownship</td>\n",
              "      <td>1</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.55</td>\n",
              "      <td>0.02</td>\n",
              "      <td>0.95</td>\n",
              "      <td>0.09</td>\n",
              "      <td>...</td>\n",
              "      <td>0.04</td>\n",
              "      <td>0.09</td>\n",
              "      <td>0.02</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.00</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.03</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 128 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-4296c5eb-ab34-479a-8ee7-3273c2d8133f')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-4296c5eb-ab34-479a-8ee7-3273c2d8133f button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-4296c5eb-ab34-479a-8ee7-3273c2d8133f');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wcHCxEzFvAo4",
        "outputId": "3a93e89e-9a16-46f8-a887-f037576f3018"
      },
      "source": [
        "crime.drop([0, 1, 2, 3, 4], axis=1, inplace=True)\n",
        "crime.dropna(inplace=True)\n",
        "\n",
        "# checking for any null values\n",
        "crime.isnull().any().any()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "equG48iavjkn"
      },
      "source": [
        "def lin_regression(x,y,show=True):\n",
        "\n",
        "  # learning the coefficient and intercept\n",
        "\n",
        "  x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2)\n",
        "\n",
        "  m1 = LinearRegression()\n",
        "  m1.fit(x_train,y_train)\n",
        "\n",
        "  y_pred = m1.predict(x_test)\n",
        "  metrics.mean_squared_error(y_pred,y_test)\n",
        "\n",
        "  # plotting data and predictions\n",
        "\n",
        "  if show:\n",
        "\n",
        "    print(\"The coefficients are: \\n {} \\n\\n The intercept is: {}\\n\".format(m1.coef_,m1.intercept_))\n",
        "    print(\"The RMSE for linear regression is: {}\".format(math.sqrt(metrics.mean_squared_error(y_pred,y_test))))"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BI7DcptkvRXU",
        "outputId": "a055ad46-f8b2-42cd-9f1b-b1712a5d3baa"
      },
      "source": [
        "x_crime = crime.drop(127,axis=1)\n",
        "y_crime = crime[127]\n",
        "\n",
        "lin_regression(x_crime,y_crime)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The coefficients are: \n",
            " [-3.62199499e+00  1.79147875e+00  1.23989416e-01  6.10868138e-01\n",
            " -9.74240317e-02  5.46270872e-03 -8.40520330e-01 -1.95759662e+00\n",
            "  1.39731317e+00  9.54198648e-01  4.02060226e+00 -2.30858822e-01\n",
            " -5.10594166e-01 -2.94370481e-01 -3.60748140e-01 -8.34422289e-01\n",
            " -1.13705864e+00  3.21289051e-01  1.04297377e-02  1.34499080e+00\n",
            " -1.42507894e+00  5.58868500e-01 -3.56355865e-01 -1.07216082e-01\n",
            " -1.73896378e-01 -5.29481787e-02  2.12058345e-01 -4.27160630e-01\n",
            "  1.08881974e+00 -2.64935584e-01 -9.26037495e-01 -6.93050187e-02\n",
            "  2.64739839e-01  9.85791437e-01 -1.07959236e-01  2.97940967e-01\n",
            "  5.45702125e-01  1.73641628e-01 -1.99286092e-01 -2.84909052e-01\n",
            "  2.43156926e-02 -6.13403791e-01  3.48799633e-01 -6.13089866e-01\n",
            " -7.52098447e-01 -6.25872383e-02  2.50065633e-01 -4.63277459e-02\n",
            " -3.89760741e-03 -5.53359644e-02 -5.98457315e-02 -2.28122223e-01\n",
            "  4.10293743e-01 -6.30234536e-01  9.46276358e-03  4.74980895e-01\n",
            " -2.71729939e-01 -4.21464410e-01  1.45486931e+00 -1.50189290e+00\n",
            " -5.63103330e-02  6.04002636e-01  1.26400173e+00 -2.17193308e+00\n",
            " -4.18696137e-01  1.02570144e-01 -8.70558069e-01 -1.20636552e+00\n",
            "  7.88440307e-01  5.74155325e-01 -7.40702877e-04  7.37018162e-02\n",
            "  1.99339710e-01  1.43874435e+00  4.83902164e-03  3.85577907e-02\n",
            "  2.33718747e-02  1.43212903e-01 -4.64830370e-01  1.03698060e-01\n",
            " -1.10975119e+00  6.96458376e-01 -4.30096714e-01 -6.05139102e-01\n",
            " -2.01253922e-01  2.25903520e+00 -5.33304402e-01 -2.58449121e-01\n",
            " -6.65294297e-02  2.09126663e-02  2.54573751e-01  2.51961129e-01\n",
            " -2.27106938e-01  1.30433199e-01 -1.69590515e-02  1.13677580e-01\n",
            " -7.09000901e-01 -2.55378890e+01 -1.03480807e+00  1.18819693e+00\n",
            " -4.95037898e-01  4.81738671e-01  4.31548602e-02  2.43277146e+01\n",
            " -2.78618593e-01  7.74274208e-02  3.96846769e-01  5.51952313e-01\n",
            "  2.65593228e-01 -5.31345438e-01 -6.30437673e-01  4.38094044e-02\n",
            " -1.47999981e-02  3.07592703e-01  1.45161145e-01 -1.06716001e-01\n",
            "  1.51444450e-01  3.56829473e-01 -1.88252772e-01 -1.34623457e-02\n",
            "  5.63123614e-04 -1.79543243e-01] \n",
            "\n",
            " The intercept is: 2.2338823427498413\n",
            "\n",
            "The RMSE for linear regression is: 0.23637155467905246\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HiGqKKLTyq1s"
      },
      "source": [
        "x_train,x_test,y_train,y_test = train_test_split(x_crime,y_crime,test_size=0.3)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ex34CY-lwKd2",
        "outputId": "8830590e-23d9-4d9c-de9f-3e07335839ea"
      },
      "source": [
        "r = Ridge(alpha=0.2,normalize=True)\n",
        "r.fit(x_train,y_train)\n",
        "y_pred_ridge = r.predict(x_test)\n",
        "\n",
        "print(\"The coefficients are: \\n {}\".format(r.coef_))\n",
        "print(\"The RMSE for ridge regression is: {}\".format(math.sqrt(metrics.mean_squared_error(y_pred_ridge,y_test))))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The coefficients are: \n",
            " [-2.14993215e-02  9.19697792e-03  6.69239639e-02 -7.89276663e-02\n",
            " -4.00958843e-02  5.27138501e-02  8.70724802e-02 -5.04556264e-02\n",
            " -1.73856120e-02  1.27398173e-02 -1.68677199e-02  2.81670260e-02\n",
            "  3.50013688e-02 -5.53307559e-02 -1.22999127e-01 -2.06335009e-01\n",
            " -6.08591334e-03  2.83091303e-02 -6.96912935e-02  5.56784758e-02\n",
            "  1.27257640e-02  4.42992630e-02 -7.81230106e-02 -9.17945161e-02\n",
            " -1.12034119e-03 -1.05942206e-01  3.79288179e-02 -2.81537326e-02\n",
            " -1.09849933e-02 -1.13014261e-01 -6.68247113e-02 -1.45309214e-02\n",
            "  1.05472623e-01 -2.39119375e-02 -1.02066356e-01  5.51127896e-02\n",
            "  4.28467782e-02 -2.50320985e-02 -2.20989060e-02  1.53288152e-02\n",
            " -7.80327458e-03 -6.10669979e-03  4.48234043e-02 -1.21773075e-01\n",
            " -1.14003315e-01 -1.02372720e-01 -4.91536072e-02 -4.67721158e-02\n",
            "  4.02243587e-02  3.96058642e-02  9.94606883e-02 -1.04348600e-01\n",
            " -4.54285567e-02 -2.34634950e-02  4.55805438e-02  3.99131075e-02\n",
            "  3.10722627e-03  1.27028549e-02  2.08337084e-02  1.11039660e-02\n",
            " -1.54208795e-02 -2.03907692e-03  2.53489743e-02  1.56960801e-03\n",
            "  9.96132647e-03  8.15442380e-02 -4.23702473e-02  2.38031864e-02\n",
            "  2.68431623e-02  1.54920582e-01 -6.66127043e-02  2.39758424e-02\n",
            " -4.00269663e-02  1.75686955e-02  1.66437560e-02  2.67006836e-02\n",
            " -4.22617442e-02 -5.95214501e-02 -6.46590884e-02 -2.04012057e-02\n",
            " -3.03655153e-02 -2.58046032e-02 -8.04147615e-02  2.22241852e-02\n",
            " -4.97605621e-03  4.52990425e-02 -1.09243159e-01 -1.17680207e-01\n",
            " -1.01123124e-01  6.70201124e-02  1.22406141e-01  2.12402491e-02\n",
            " -1.08739867e-01  6.77976486e-02  1.32933728e-02  6.53143449e-03\n",
            " -1.13058269e-02 -3.46116309e-02  2.66158183e-02 -2.46081158e-03\n",
            " -1.92101584e-02  6.48348434e-02  8.55580954e-02 -3.46116309e-02\n",
            " -9.39768729e-02 -4.17519895e-02 -1.76883405e-02  2.31706209e-02\n",
            "  8.83263470e-02 -2.10897012e-02  2.25932555e-02  1.24356814e-02\n",
            " -1.03729945e-02  4.62847648e-02 -9.88933575e-05 -4.38474622e-02\n",
            "  4.47840303e-02  4.31123832e-02 -4.99956760e-03  2.36773112e-02\n",
            " -2.20165197e-02  6.61996755e-02]\n",
            "The RMSE for ridge regression is: 0.18021470410721144\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wfp6mDKczJCM",
        "outputId": "03dac163-6e06-49f3-bf43-24775f3fb756"
      },
      "source": [
        "l = Lasso(alpha=0.002,normalize=True)\n",
        "l.fit(x_train,y_train)\n",
        "y_pred_lasso = l.predict(x_test)\n",
        "\n",
        "print(\"The coefficients are: \\n {}\".format(l.coef_))\n",
        "print(\"The RMSE for lasso regression is: {}\".format(math.sqrt(metrics.mean_squared_error(y_pred_lasso,y_test))))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The coefficients are: \n",
            " [ 0.          0.          0.         -0.19809017 -0.          0.\n",
            "  0.          0.          0.         -0.          0.          0.\n",
            " -0.         -0.         -0.         -0.13915446 -0.          0.\n",
            " -0.         -0.         -0.         -0.         -0.         -0.\n",
            " -0.         -0.         -0.          0.          0.00135136  0.\n",
            "  0.         -0.          0.         -0.         -0.          0.\n",
            "  0.         -0.          0.          0.          0.          0.\n",
            "  0.         -0.22718377 -0.30725928 -0.         -0.         -0.\n",
            " -0.          0.          0.          0.          0.          0.\n",
            "  0.          0.          0.          0.          0.          0.\n",
            " -0.          0.          0.          0.          0.          0.\n",
            "  0.         -0.          0.          0.         -0.          0.01243139\n",
            " -0.         -0.          0.01037356  0.          0.          0.\n",
            "  0.         -0.         -0.         -0.         -0.         -0.\n",
            " -0.         -0.          0.         -0.         -0.          0.\n",
            "  0.1460367   0.         -0.         -0.          0.         -0.\n",
            "  0.          0.         -0.          0.          0.          0.\n",
            "  0.          0.         -0.         -0.          0.          0.\n",
            "  0.          0.          0.          0.         -0.          0.\n",
            "  0.          0.          0.01610201  0.         -0.          0.\n",
            " -0.          0.        ]\n",
            "The RMSE for lasso regression is: 0.17429288717648245\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Part B: SVM Regression"
      ],
      "metadata": {
        "id": "GwnLKC2YZyjH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "AJhW5TpOeJeS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We know that the SVM algorithm works by finding a dividing hyperplane between the two classes in some feature space. How do we apply that concept to the task of regression?\n",
        "\n",
        "The key insight is that we can define a parameter $ϵ$ which defines a \"tube\" around the hyperplane (in the diagram, the green line is the hyperplane and the two red lines determine the tube around it. Each red line is $ϵ$ units away from the hyperplane. We then define a \"slack\" term $ξ$ which measures the distance between the decision boundary (red line) and outliers (points outside the tube). In the code below, the variable `C` represents the slack term.\n",
        "\n",
        "We can thus define an optimization problem of minimizing the $ξ$ value while trying to fit as many points in the tube as possible."
      ],
      "metadata": {
        "id": "1oPzro2jeMYF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.svm import SVR\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "import sklearn.datasets as datasets\n",
        "\n",
        "\n",
        "import plotly.graph_objects as go\n",
        "import plotly.express as px\n",
        "\n",
        "\n",
        "data = datasets.load_iris()\n",
        "df = pd.DataFrame(data=data.data, columns=data.feature_names)\n",
        "\n",
        "scaler=MinMaxScaler()\n",
        "for col in df.columns[:-1]:\n",
        "  df[col]=scaler.fit_transform(df[[col]])"
      ],
      "metadata": {
        "id": "nabO0otxf88R"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X=df[df.columns[2]].values.reshape(-1,1)\n",
        "y=df[df.columns[-1]].values\n",
        "\n",
        "model1 = LinearRegression()\n",
        "lr = model1.fit(X, y)\n",
        "\n",
        "epsilon = 0.5\n",
        "model2 = SVR(kernel='rbf', C=1, epsilon=epsilon)\n",
        "svr = model2.fit(X, y)"
      ],
      "metadata": {
        "id": "X1FocQCkf80d"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_range = np.linspace(X.min(), X.max(), 100)\n",
        "\n",
        "y_lr = model1.predict(x_range.reshape(-1, 1))\n",
        "y_svr = model2.predict(x_range.reshape(-1, 1))"
      ],
      "metadata": {
        "id": "nb6hYpxogXeB"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig = px.scatter(df, x=df[df.columns[2]], y=df[df.columns[-1]], \n",
        "                 opacity=0.8, color_discrete_sequence=['black'])\n",
        "\n",
        "fig.add_traces(go.Scatter(x=x_range, y=y_lr, name='Linear Regression', line=dict(color='limegreen')))\n",
        "fig.add_traces(go.Scatter(x=x_range, y=y_svr, name='Support Vector Regression', line=dict(color='red')))\n",
        "fig.add_traces(go.Scatter(x=x_range, y=y_svr+epsilon, name='+epsilon', line=dict(color='red', dash='dot')))\n",
        "fig.add_traces(go.Scatter(x=x_range, y=y_svr-epsilon, name='-epsilon', line=dict(color='red', dash='dot')))\n",
        "\n",
        "fig.update_layout(dict(plot_bgcolor = 'white'))\n",
        "\n",
        "\n",
        "fig.update_xaxes(showgrid=True, gridwidth=1, gridcolor='lightgrey', \n",
        "                 zeroline=True, zerolinewidth=1, zerolinecolor='lightgrey', \n",
        "                 showline=True, linewidth=1, linecolor='black')\n",
        "\n",
        "fig.update_yaxes(showgrid=True, gridwidth=1, gridcolor='lightgrey', \n",
        "                 zeroline=True, zerolinewidth=1, zerolinecolor='lightgrey', \n",
        "                 showline=True, linewidth=1, linecolor='black')\n",
        "\n",
        "fig.update_traces(marker=dict(size=3))\n",
        "\n",
        "fig.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "75DdATqfgcqB",
        "outputId": "f92fb303-6a58-45c0-ffe8-922c4ce95c6e"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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    {
      "cell_type": "markdown",
      "source": [
        "## Part C: Logistic Regression"
      ],
      "metadata": {
        "id": "TLFiEY7OZ2ei"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QEao5S0ki2jT"
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      "source": [
        "Just as we have linear and polynomial regression for predicting numerical values, we have another type of regression for predicting class labels of data, namely **logistic regression**. \n",
        "\n",
        "The reason its called logistic regression is because it makes use of the logistic function to generate output values. The logistic function is defined as:\n",
        "\n",
        "$g(z) = \\frac{1}{1 + e^{-z}}$\n",
        "\n",
        "\\\n",
        "\n",
        "The reason we use the logistic function is because its range is bounded between 0 and 1. Anything else comes to mind when talking about values between 0 and 1? Probabilities! And we saw in lab 3 how deeply related probability and classification are.\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1db86qd4W_4erTMC9no5P4ylWze6c2j7V\" width=\"500\" height=\"350\" align=\"middle\"/>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_44CGMRN_UtH"
      },
      "source": [
        "## Why use logistic function? Why not use linear regression? \n",
        "\n",
        "Let's see why we can't use linear regression for classification tasks with the help of an example."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
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        "id": "JWNOyCr__d0A",
        "outputId": "e25a406a-29a3-4791-c7c7-e947e7f9b912"
      },
      "source": [
        "x = np.array([i for i in range(10,30)])\n",
        "y = np.concatenate([np.ones(10), np.zeros(10)])\n",
        "\n",
        "fig = plt.figure(figsize=(10,5))\n",
        "xlabel = 'Age'\n",
        "ylabel = 'Purchased'\n",
        "plt.xlabel(xlabel)\n",
        "plt.ylabel(ylabel)\n",
        "plt.grid(color='k', linestyle=':', linewidth=1)\n",
        "_ = plt.plot(x, y, 'xb')"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6mTwm4lDKoMV"
      },
      "source": [
        "Suppose we have some product, and we collected data on the relationship between the age of a customer, and whether they purchased the item or not. Customers aged between 10 and 19 made the purchase (purchased=1), whereas those customers above the age of 19 did not (purchased=0).\n",
        "\n",
        "\\\n",
        "\n",
        "Now, let's try and fit linear regression and logistic regression models to this data, and test it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9iup50dU_oQG"
      },
      "source": [
        "def linear_regression(x,y):\n",
        "\n",
        "  lin_regression = LinearRegression()\n",
        "  lin_regression.fit(pd.DataFrame(x), y)\n",
        "\n",
        "  lin_y_pred_1 = lin_regression.predict(pd.DataFrame(x))\n",
        "\n",
        "  line_point_5 = x * 0 + .5\n",
        "\n",
        "  fig = plt.figure(figsize=(10,5))\n",
        "  xlabel = 'Age'\n",
        "  ylabel = 'Purchased'\n",
        "  plt.xlabel(xlabel)\n",
        "  plt.ylabel(ylabel)\n",
        "  plt.grid(color='k', linestyle=':', linewidth=1)\n",
        "  plt.plot(x, y, 'xb')\n",
        "  plt.plot(x, lin_y_pred_1, '-r')\n",
        "  plt.plot(x, line_point_5,'-g')\n",
        "  plt.legend([\"Data Points\",\"Linear Regression Model\",\"Decision Boundary\"])\n",
        "  plt.show()\n",
        "\n",
        "  return lin_regression"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "0abeDE8aHrwq",
        "outputId": "d220f81f-8d91-4ef4-ed4b-40aca3d2c2ee"
      },
      "source": [
        "lin_regression = linear_regression(x,y)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ub5AkghRIlJk"
      },
      "source": [
        "The green line is called the decision boundary, which is basically the line that divides the two classes on the cartesian plane."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4DBWBxAHHi0B",
        "outputId": "a1712d5e-8a6c-4f42-bbd8-e317179b8b1e"
      },
      "source": [
        "test_x = np.array([i for i in range(10,35,5)])\n",
        "test_y_pred = lin_regression.predict(pd.DataFrame(test_x))\n",
        "test_y_pred"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.21428571,  0.83834586,  0.46240602,  0.08646617, -0.28947368])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nx6BdyEEIu8r"
      },
      "source": [
        "Since linear regression predictions are not probabilities, values greater than 0.5 are considered to belong to positive purchase class."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AMK9K0Ls_9sX"
      },
      "source": [
        "def logistic_regression(x,y):\n",
        "\n",
        "  log_regression = LogisticRegression()\n",
        "\n",
        "  log_regression.fit(pd.DataFrame(x), y)\n",
        "\n",
        "  y_pred = log_regression.predict_proba(pd.DataFrame(x))\n",
        "  log_y_pred_1 = [item[1] for item in y_pred]\n",
        "\n",
        "  line_point_5 = x * 0 + .5\n",
        "\n",
        "  fig = plt.figure(figsize=(10,5))\n",
        "  xlabel = 'Age'\n",
        "  ylabel = 'Purchased'\n",
        "  plt.xlabel(xlabel)\n",
        "  plt.ylabel(ylabel)\n",
        "  plt.grid(color='k', linestyle=':', linewidth=1)\n",
        "  plt.plot(x, y, 'xb')\n",
        "  plt.plot(x, log_y_pred_1, '-r')\n",
        "  plt.plot(x, line_point_5,'-g')\n",
        "  plt.legend([\"Data Points\",\"Logistic Regression Model\",\"Decision Boundary\"])\n",
        "  plt.show()\n",
        "\n",
        "  return log_regression"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "WB6voRBlHUSf",
        "outputId": "1403d760-01d5-4d60-defa-2f9878d5122a"
      },
      "source": [
        "log_regression = logistic_regression(x,y)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2Cgpr78MT-Z"
      },
      "source": [
        "**Q:** What do you observe from the two graphs? Hint: think in terms of the decision boundary....\n",
        "\n",
        "**A:** According to the linear regression model, any age greater than 19 would belong to class 0 (no purchase), and any age less than or equal to 19 would belong to class 1 (purchase made). The logistic regression curve follows the same trend. We can think of the age 19 as a turning point of sorts."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XBRy-dhZLQVh"
      },
      "source": [
        "Now, say we've collected more data the next day, and add the new data to the existing data we had from day 1. We find that customers aged between 60 and 70 did not make a purchase, which is aligned with our earlier data as well."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "25ME4nIUA5e1"
      },
      "source": [
        "x = np.append(x, np.array([i for i in range(60,70)]))\n",
        "y = np.append(y, np.zeros(10))"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "COwTJ5XCBQCN",
        "outputId": "b53fd0ac-f8f1-4b1a-f6b4-c1991687d791"
      },
      "source": [
        "lin_regression = linear_regression(x,y)\n",
        "log_regression = logistic_regression(x,y)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eJKRz7FtIDnk",
        "outputId": "be37b989-7985-4c24-f08b-7302291bc5c8"
      },
      "source": [
        "test_x = np.array([i for i in range(18,26)])\n",
        "\n",
        "test_y_pred_lin = lin_regression.predict(pd.DataFrame(test_x))\n",
        "print(\"Linear Regression Predictions:\")\n",
        "print(test_y_pred_lin)\n",
        "\n",
        "test_y_pred_log = log_regression.predict_proba(pd.DataFrame(test_x))[:,1]\n",
        "print(\"Logistic Regression Predictions:\")\n",
        "print(test_y_pred_log)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Linear Regression Predictions:\n",
            "[0.56495292 0.55091537 0.53687781 0.52284026 0.50880271 0.49476516\n",
            " 0.48072761 0.46669006]\n",
            "Logistic Regression Predictions:\n",
            "[0.85713668 0.64502441 0.35497751 0.14286435 0.04805457 0.01505849\n",
            " 0.00460907 0.00140042]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mr-07NmOKQEC"
      },
      "source": [
        "We can now see where linear regression fails. The model tries to fit as many points as it can. By doing so, the turning point which was earlier 19 has now increased to 23, which is clearly wrong for the values 20, 21 and 22, which can be seen from the predictions on the test data.\n",
        "\n",
        "\\\n",
        "\n",
        "On the other hand, the logistic regression model predicts the classes correctly, and perfectly models the relationship between the data. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cO5SyZVNNp5Q"
      },
      "source": [
        "What we can conclude from these observations are that a probabilistic model is required for classification problems. Lab 3 covered the intuition behind MLE, cross-entropy and classification, and so now you should be able to appreaciate the motivation behind logistic regression."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y6iLySzwlPTm"
      },
      "source": [
        "## Applying logistic regression to MNIST digit Dataset\n",
        "\n",
        "Let's see logistic regression in action with the MNIST digits dataset. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "cc5dxfJi80nC",
        "outputId": "511e752d-18e7-4115-dd14-34c69d080601"
      },
      "source": [
        "# initializing and visualizing MNIST data\n",
        "\n",
        "digits = load_digits()\n",
        "\n",
        "plt.figure(figsize=(20,4))\n",
        "for index, (image, label) in enumerate(zip(digits.data[0:5], digits.target[0:5])):\n",
        " plt.subplot(1, 5, index + 1)\n",
        " plt.imshow(np.reshape(image, (8,8)), cmap=plt.cm.gray)\n",
        " plt.title('Training: %i\\n' % label, fontsize = 20)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x288 with 5 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "02h6gzviOn9o"
      },
      "source": [
        "x_train, x_test, y_train, y_test = train_test_split(digits.data, digits.target, test_size=0.2, random_state=0)\n",
        "log_reg = LogisticRegression()\n",
        "log_reg = log_reg.fit(x_train,y_train)"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "s5Hpqr1HO1lT",
        "outputId": "c74456cc-496d-4637-a8d8-8b0d7b09748b"
      },
      "source": [
        "y_pred = log_reg.predict(x_test)\n",
        "\n",
        "print(\"PREDICTIONS:\\n\")\n",
        "print(y_pred[:10])\n",
        "print(\"\\n\")\n",
        "\n",
        "plt.figure(figsize=(20,10))\n",
        "plt.title(\"Test image data\")\n",
        "\n",
        "for index, (image, label) in enumerate(zip(x_test[0:10], y_test[0:10])):\n",
        " plt.subplot(2, 5, index + 1)\n",
        " plt.imshow(np.reshape(image, (8,8)), cmap=plt.cm.gray)\n",
        " plt.title('Training: %i\\n' % label, fontsize = 20)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "PREDICTIONS:\n",
            "\n",
            "[2 8 2 6 6 7 1 9 8 5]\n",
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x720 with 10 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9IXb2AbpPzNf",
        "outputId": "b9283cdb-52ee-4983-a80a-11f98dbffcf9"
      },
      "source": [
        "# Accuracy\n",
        "\n",
        "acc = log_reg.score(x_test,y_test)\n",
        "print(\"Accuracy obtained on test set: {}\".format(round(acc*100,3)))"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy obtained on test set: 96.667\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ecHbLkhVQUSe",
        "outputId": "75991883-35b5-4011-adfc-99657d60c872"
      },
      "source": [
        "# Visualizing confusion matrix\n",
        "\n",
        "cm = metrics.confusion_matrix(y_test, y_pred)\n",
        "\n",
        "plt.figure(figsize=(9,9))\n",
        "sns.heatmap(cm, annot=True, fmt=\".3f\", linewidths=.5, square = True, cmap = 'Reds_r');\n",
        "plt.ylabel('Actual label');\n",
        "plt.xlabel('Predicted label');\n",
        "all_sample_title = 'Accuracy Score: {0}'.format(round(acc*100,3))\n",
        "plt.title(all_sample_title, size = 15);"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 648x648 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Exercises\n",
        "\n",
        "### Regularization:\n",
        "1. Play with the values of alpha in both regularization techniques, and try to predict the outcomes.\n",
        "2. Try the regularizations on different datasets to see the effect in various ways.\n",
        "\n",
        "### SVM regression:\n",
        "1. Play around with the value of `epsilon` and plot the different regression curves obtained.\n",
        "2. Change `C` and analyze the different plots obtained.\n",
        "\n",
        "### Logistic regression:\n",
        "1. Run logistic regression on different datasets and assess the results."
      ],
      "metadata": {
        "id": "jUprV2KwkB7P"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j5m6ZY-v0JTK"
      },
      "source": [
        "## References\n",
        "\n",
        "1. https://harish-reddy.medium.com/regularization-in-python-699cfbad8622\n",
        "2. https://towardsdatascience.com/logistic-regression-using-python-sklearn-numpy-mnist-handwriting-recognition-matplotlib-a6b31e2b166a"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cOtXOnOQ0Qyv"
      },
      "source": [
        "## Further Explorations\n",
        "\n",
        "1. https://en.wikipedia.org/wiki/Elastic_net_regularization"
      ]
    }
  ]
}