distribute_validation_regularization.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "ml1-arm64",
      "language": "python",
      "name": "ml1-arm64"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.1"
    },
    "colab": {
      "name": "distribute_validation_regularization.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/heysatya/ValidationRegularization/blob/main/distribute_validation_regularization.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hide": true,
        "id": "JgueoRnQ6GzI"
      },
      "source": [
        "# Validation and Regularization\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "hide": true,
        "id": "AWSGS-gh6GzZ"
      },
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import scipy as sp\n",
        "import matplotlib as mpl\n",
        "import matplotlib.cm as cm\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TL8TVEJc6RKv",
        "outputId": "a1a18741-185c-4f04-aa1f-bb1d4d38353a"
      },
      "source": [
        "!git init"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Initialized empty Git repository in /content/.git/\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aKvrVCcH6Ziv",
        "outputId": "94e661c4-4463-4892-db25-be6ba0873e29"
      },
      "source": [
        "!git pull https://github.com/heysatya/ValidationRegularization.git"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "remote: Enumerating objects: 60, done.\u001b[K\n",
            "remote: Counting objects:   1% (1/60)\u001b[K\rremote: Counting objects:   3% (2/60)\u001b[K\rremote: Counting objects:   5% (3/60)\u001b[K\rremote: Counting objects:   6% (4/60)\u001b[K\rremote: Counting objects:   8% (5/60)\u001b[K\rremote: Counting objects:  10% (6/60)\u001b[K\rremote: Counting objects:  11% (7/60)\u001b[K\rremote: Counting objects:  13% (8/60)\u001b[K\rremote: Counting objects:  15% (9/60)\u001b[K\rremote: Counting objects:  16% (10/60)\u001b[K\rremote: Counting objects:  18% (11/60)\u001b[K\rremote: Counting objects:  20% (12/60)\u001b[K\rremote: Counting objects:  21% (13/60)\u001b[K\rremote: Counting objects:  23% (14/60)\u001b[K\rremote: Counting objects:  25% (15/60)\u001b[K\rremote: Counting objects:  26% (16/60)\u001b[K\rremote: Counting objects:  28% (17/60)\u001b[K\rremote: Counting objects:  30% (18/60)\u001b[K\rremote: Counting objects:  31% (19/60)\u001b[K\rremote: Counting objects:  33% (20/60)\u001b[K\rremote: Counting objects:  35% (21/60)\u001b[K\rremote: Counting objects:  36% (22/60)\u001b[K\rremote: Counting objects:  38% (23/60)\u001b[K\rremote: Counting objects:  40% (24/60)\u001b[K\rremote: Counting objects:  41% (25/60)\u001b[K\rremote: Counting objects:  43% (26/60)\u001b[K\rremote: Counting objects:  45% (27/60)\u001b[K\rremote: Counting objects:  46% (28/60)\u001b[K\rremote: Counting objects:  48% (29/60)\u001b[K\rremote: Counting objects:  50% (30/60)\u001b[K\rremote: Counting objects:  51% (31/60)\u001b[K\rremote: Counting objects:  53% (32/60)\u001b[K\rremote: Counting objects:  55% (33/60)\u001b[K\rremote: Counting objects:  56% (34/60)\u001b[K\rremote: Counting objects:  58% (35/60)\u001b[K\rremote: Counting objects:  60% (36/60)\u001b[K\rremote: Counting objects:  61% (37/60)\u001b[K\rremote: Counting objects:  63% (38/60)\u001b[K\rremote: Counting objects:  65% (39/60)\u001b[K\rremote: Counting objects:  66% (40/60)\u001b[K\rremote: Counting objects:  68% (41/60)\u001b[K\rremote: Counting objects:  70% (42/60)\u001b[K\rremote: Counting objects:  71% (43/60)\u001b[K\rremote: Counting objects:  73% (44/60)\u001b[K\rremote: Counting objects:  75% (45/60)\u001b[K\rremote: Counting objects:  76% (46/60)\u001b[K\rremote: Counting objects:  78% (47/60)\u001b[K\rremote: Counting objects:  80% (48/60)\u001b[K\rremote: Counting objects:  81% (49/60)\u001b[K\rremote: Counting objects:  83% (50/60)\u001b[K\rremote: Counting objects:  85% (51/60)\u001b[K\rremote: Counting objects:  86% (52/60)\u001b[K\rremote: Counting objects:  88% (53/60)\u001b[K\rremote: Counting objects:  90% (54/60)\u001b[K\rremote: Counting objects:  91% (55/60)\u001b[K\rremote: Counting objects:  93% (56/60)\u001b[K\rremote: Counting objects:  95% (57/60)\u001b[K\rremote: Counting objects:  96% (58/60)\u001b[K\rremote: Counting objects:  98% (59/60)\u001b[K\rremote: Counting objects: 100% (60/60)\u001b[K\rremote: Counting objects: 100% (60/60), done.\u001b[K\n",
            "remote: Compressing objects: 100% (59/59), done.\u001b[K\n",
            "remote: Total 60 (delta 1), reused 60 (delta 1), pack-reused 0\u001b[K\n",
            "Unpacking objects: 100% (60/60), done.\n",
            "From https://github.com/heysatya/ValidationRegularization\n",
            " * branch            HEAD       -> FETCH_HEAD\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "hide": true,
        "id": "KGcVaxMS6Gza"
      },
      "source": [
        "def make_simple_plot():\n",
        "    fig, axes=plt.subplots(figsize=(12,5), nrows=1, ncols=2);\n",
        "    axes[0].set_ylabel(\"$y$\")\n",
        "    axes[0].set_xlabel(\"$x$\")\n",
        "    axes[1].set_xlabel(\"$x$\")\n",
        "    axes[1].set_yticklabels([])\n",
        "    axes[0].set_ylim([-2,2])\n",
        "    axes[1].set_ylim([-2,2])\n",
        "    plt.tight_layout();\n",
        "    return axes\n",
        "def make_plot():\n",
        "    fig, axes=plt.subplots(figsize=(20,8), nrows=1, ncols=2);\n",
        "    axes[0].set_ylabel(\"$p_R$\")\n",
        "    axes[0].set_xlabel(\"$x$\")\n",
        "    axes[1].set_xlabel(\"$x$\")\n",
        "    axes[1].set_yticklabels([])\n",
        "    axes[0].set_ylim([0,1])\n",
        "    axes[1].set_ylim([0,1])\n",
        "    axes[0].set_xlim([0,1])\n",
        "    axes[1].set_xlim([0,1])\n",
        "    plt.tight_layout();\n",
        "    return axes"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IuLdn5qA6Gzb"
      },
      "source": [
        "## PART 1: Reading in and sampling from the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "F13mCWuM6Gzc",
        "outputId": "651d5ffa-50d1-410e-e360-fc9f9b84f02f"
      },
      "source": [
        "df=pd.read_csv(\"data/noisypopulation.csv\")\n",
        "df.head()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>f</th>\n",
              "      <th>x</th>\n",
              "      <th>y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.047790</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.011307</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.051199</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.010000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.054799</td>\n",
              "      <td>0.02</td>\n",
              "      <td>0.007237</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.058596</td>\n",
              "      <td>0.03</td>\n",
              "      <td>0.000056</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.062597</td>\n",
              "      <td>0.04</td>\n",
              "      <td>0.010000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          f     x         y\n",
              "0  0.047790  0.00  0.011307\n",
              "1  0.051199  0.01  0.010000\n",
              "2  0.054799  0.02  0.007237\n",
              "3  0.058596  0.03  0.000056\n",
              "4  0.062597  0.04  0.010000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cMWuSKEK6Gzc"
      },
      "source": [
        "f=df.f.values\n",
        "x=df.x.values\n",
        "y = df.y.values"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-v1m26KK6Gzd",
        "outputId": "bfee87f0-4254-4437-8c72-850e9bdcb415"
      },
      "source": [
        "df.shape"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(200, 3)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L-qA5L_26Gze"
      },
      "source": [
        "From 200 points on this curve, we'll make a random choice of 60 points. We do it by choosing the indexes randomly, and then using these indexes as a way of getting the appropriate samples"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vdP7Gtla6Gze",
        "outputId": "3a209c8f-d5e6-4220-ebd4-f212ecc72aba"
      },
      "source": [
        "indexes=np.sort(np.random.choice(x.shape[0], size=60, replace=False))\n",
        "indexes"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  3,   7,  10,  12,  13,  14,  24,  27,  31,  34,  45,  46,  48,\n",
              "        59,  66,  69,  71,  72,  75,  78,  79,  83,  84,  87,  93,  99,\n",
              "       106, 108, 111, 114, 117, 120, 123, 124, 127, 138, 139, 141, 144,\n",
              "       147, 148, 158, 159, 163, 165, 166, 167, 169, 171, 173, 179, 180,\n",
              "       181, 184, 189, 191, 193, 195, 196, 197])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pg5WaVF86Gzf"
      },
      "source": [
        "samplex = x[indexes]\n",
        "samplef = f[indexes]\n",
        "sampley = y[indexes]"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "figure_type": "m",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        },
        "id": "iFIbg25S6Gzf",
        "outputId": "a43f2942-dc6d-40b1-eb73-5a6a8a230e6c"
      },
      "source": [
        "plt.figure(figsize=(12,8))\n",
        "plt.plot(x,f, 'k-', alpha=0.6, label=\"f\");\n",
        "plt.plot(x[indexes], y[indexes], 's', alpha=0.3, ms=10, label=\"in-sample y (observed)\");\n",
        "plt.plot(x, y, '.', alpha=0.8, label=\"population y\");\n",
        "plt.xlabel('$x$');\n",
        "plt.ylabel('$y$')\n",
        "plt.legend(loc=4);"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jjr0fMhk6Gzg"
      },
      "source": [
        "sample_df=pd.DataFrame(dict(x=x[indexes],f=f[indexes],y=y[indexes]))"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IjcYK8ub6Gzg"
      },
      "source": [
        "## Part 2: Fit on training set and predict on test set\n",
        "\n",
        "We will do the split of testing and training for you in order to illustrate how this can be done.\n",
        "\n",
        "### Train-test split"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F2esLsrw6Gzh",
        "outputId": "b58a88b5-6dd9-4e11-f9c1-fb612753629d"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "datasize=sample_df.shape[0]\n",
        "print(datasize)\n",
        "#split dataset using the index, as we have x,f, and y that we want to split.\n",
        "itrain,itest = train_test_split(np.arange(60),train_size=0.8)\n",
        "print(itrain.shape)\n",
        "xtrain= sample_df.x[itrain].values\n",
        "ftrain = sample_df.f[itrain].values\n",
        "ytrain = sample_df.y[itrain].values\n",
        "xtest= sample_df.x[itest].values\n",
        "ftest = sample_df.f[itest].values\n",
        "ytest = sample_df.y[itest].values"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "60\n",
            "(48,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o-IWO9i46Gzh",
        "outputId": "93af73ae-c066-461f-a10e-6388b872064a"
      },
      "source": [
        "sample_df.x[itrain].values"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.74      , 0.7344196 , 0.78965524, 0.74166004, 0.5833461 ,\n",
              "       0.82850909, 0.71210742, 0.43754875, 0.62271266, 0.81523718,\n",
              "       0.67438375, 0.8478414 , 0.70159191, 0.93      , 0.68028873,\n",
              "       0.69278797, 0.96      , 0.70533267, 0.58      , 0.6       ,\n",
              "       0.78      , 0.1       , 0.14      , 0.12      , 0.83724472,\n",
              "       0.81      , 0.75158452, 0.66984294, 0.66721109, 0.82      ,\n",
              "       0.46      , 0.61      , 0.64832591, 0.53      , 0.9       ,\n",
              "       0.95      , 0.74865483, 0.84      , 0.56      , 0.61360216,\n",
              "       0.79526318, 0.27      , 0.87      , 0.31      , 0.6045978 ,\n",
              "       0.24      , 0.07      , 0.75177773])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NtOEPF6K6Gzi"
      },
      "source": [
        "We'll need to create polynomial features, ie add 1, x, x^2 and so on."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XXitJjy_6Gzi"
      },
      "source": [
        "### The `scikit-learn` interface\n",
        "\n",
        "Scikit-learn is the main python machine learning library. It consists of many learners which can learn models from data, as well as a lot of utility functions such as `train_test_split`. It can be used in python by the incantation `import sklearn`.\n",
        "\n",
        "The library has a very well defined interface. This makes the library a joy to use, and surely contributes to its popularity. As the [scikit-learn API paper](http://arxiv.org/pdf/1309.0238v1.pdf) [Buitinck, Lars, et al. \"API design for machine learning software: experiences from the scikit-learn project.\" arXiv preprint arXiv:1309.0238 (2013).] says:\n",
        "\n",
        ">All objects within scikit-learn share a uniform common basic API consisting of three complementary interfaces: **an estimator interface for building and ﬁtting models, a predictor interface for making predictions and a transformer interface for converting data**. The estimator interface is at the core of the library. It deﬁnes instantiation mechanisms of objects and exposes a `fit` method for learning a model from training data. All supervised and unsupervised learning algorithms (e.g., for classiﬁcation, regression or clustering) are oﬀered as objects implementing this interface. Machine learning tasks like feature extraction, feature selection or dimensionality reduction are also provided as estimators.\n",
        "\n",
        "We'll use the \"estimator\" interface here, specifically the estimator `PolynomialFeatures`. The API paper again:\n",
        "\n",
        ">Since it is common to modify or ﬁlter data before feeding it to a learning algorithm, some estimators in the library implement a transformer interface which deﬁnes a transform method. It takes as input some new data X and yields as output a transformed version of X. Preprocessing, feature selection, feature extraction and dimensionality reduction algorithms are all provided as transformers within the library.\n",
        "\n",
        "To start with we have one **feature** `x` to predict `y`, what we will do is the transformation:\n",
        "\n",
        "$$ x \\rightarrow 1, x, x^2, x^3, ..., x^d $$\n",
        "\n",
        "for some power $d$. Our job then is to **fit** for the coefficients of these features in the polynomial\n",
        "\n",
        "$$ a_0 + a_1 x + a_2 x^2 + ... + a_d x^d. $$\n",
        "\n",
        "In other words, we have transformed a function of one feature, into a (rather simple) **linear** function of many features. To do this we first construct the estimator as `PolynomialFeatures(d)`, and then transform these features into a d-dimensional space using the method `fit_transform`.\n",
        "\n",
        "![fit_transform](https://github.com/heysatya/ValidationRegularization/blob/main/images/sklearntrans.jpg?raw=1)\n",
        "\n",
        "Here is an example. The reason for using `[[1],[2],[3]]` as opposed to `[1,2,3]` is that scikit-learn expects data to be stored in a two-dimensional array or matrix with size `[n_samples, n_features]`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F_YNCNAN6Gzk",
        "outputId": "1ff40e6d-89a1-42d4-f066-601ff1a2c63c"
      },
      "source": [
        "np.array([1,2,3]).reshape(-1,1)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2],\n",
              "       [3]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VwFTjYAF6Gzk"
      },
      "source": [
        "To transform `[1,2,3]` into [[1],[2],[3]] we need to do a reshape.\n",
        "\n",
        "![reshape](https://github.com/heysatya/ValidationRegularization/blob/main/images/reshape.jpg?raw=1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V_6gq7hH6Gzk",
        "outputId": "66dbaec7-f1fd-4bdf-8608-2a6577f8a019"
      },
      "source": [
        "xtest.reshape(-1,1)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.63712089],\n",
              "       [0.70520676],\n",
              "       [0.59516207],\n",
              "       [0.91546575],\n",
              "       [0.97      ],\n",
              "       [0.34      ],\n",
              "       [0.13      ],\n",
              "       [0.58610946],\n",
              "       [0.80255796],\n",
              "       [0.80965752],\n",
              "       [0.44      ],\n",
              "       [0.03      ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uvtc4D5F6Gzl"
      },
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.metrics import mean_squared_error"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 471
        },
        "id": "wlFYoAwq6Gzl",
        "outputId": "ac794cce-c51b-484f-c881-4bfc7ec903e2"
      },
      "source": [
        "PolynomialFeatures(3).fit_transform(xtest)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-20-63babab40c30>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPolynomialFeatures\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit_transform\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxtest\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sklearn/base.py\u001b[0m in \u001b[0;36mfit_transform\u001b[0;34m(self, X, y, **fit_params)\u001b[0m\n\u001b[1;32m    569\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    570\u001b[0m             \u001b[0;31m# fit method of arity 1 (unsupervised transformation)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 571\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mfit_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtransform\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    572\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    573\u001b[0m             \u001b[0;31m# fit method of arity 2 (supervised transformation)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sklearn/preprocessing/_data.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, X, y)\u001b[0m\n\u001b[1;32m   1506\u001b[0m         \u001b[0mself\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0minstance\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1507\u001b[0m         \"\"\"\n\u001b[0;32m-> 1508\u001b[0;31m         \u001b[0mn_samples\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_features\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1509\u001b[0m         combinations = self._combinations(n_features, self.degree,\n\u001b[1;32m   1510\u001b[0m                                           \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minteraction_only\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_array\u001b[0;34m(array, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, warn_on_dtype, estimator)\u001b[0m\n\u001b[1;32m    554\u001b[0m                     \u001b[0;34m\"Reshape your data either using array.reshape(-1, 1) if \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    555\u001b[0m                     \u001b[0;34m\"your data has a single feature or array.reshape(1, -1) \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 556\u001b[0;31m                     \"if it contains a single sample.\".format(array))\n\u001b[0m\u001b[1;32m    557\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    558\u001b[0m         \u001b[0;31m# in the future np.flexible dtypes will be handled like object dtypes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: Expected 2D array, got 1D array instead:\narray=[0.63712089 0.70520676 0.59516207 0.91546575 0.97       0.34\n 0.13       0.58610946 0.80255796 0.80965752 0.44       0.03      ].\nReshape your data either using array.reshape(-1, 1) if your data has a single feature or array.reshape(1, -1) if it contains a single sample."
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KmXgdXnV6Gzm",
        "outputId": "22f889fe-7466-4c31-c67d-eab850a9bfaa"
      },
      "source": [
        "PolynomialFeatures(3).fit_transform(xtest.reshape(-1,1))"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.00000000e+00, 6.37120888e-01, 4.05923025e-01, 2.58622038e-01],\n",
              "       [1.00000000e+00, 7.05206764e-01, 4.97316580e-01, 3.50711016e-01],\n",
              "       [1.00000000e+00, 5.95162068e-01, 3.54217887e-01, 2.10817050e-01],\n",
              "       [1.00000000e+00, 9.15465747e-01, 8.38077534e-01, 7.67231276e-01],\n",
              "       [1.00000000e+00, 9.70000000e-01, 9.40900000e-01, 9.12673000e-01],\n",
              "       [1.00000000e+00, 3.40000000e-01, 1.15600000e-01, 3.93040000e-02],\n",
              "       [1.00000000e+00, 1.30000000e-01, 1.69000000e-02, 2.19700000e-03],\n",
              "       [1.00000000e+00, 5.86109459e-01, 3.43524298e-01, 2.01342840e-01],\n",
              "       [1.00000000e+00, 8.02557963e-01, 6.44099283e-01, 5.16927009e-01],\n",
              "       [1.00000000e+00, 8.09657516e-01, 6.55545293e-01, 5.30767174e-01],\n",
              "       [1.00000000e+00, 4.40000000e-01, 1.93600000e-01, 8.51840000e-02],\n",
              "       [1.00000000e+00, 3.00000000e-02, 9.00000000e-04, 2.70000000e-05]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ERVT_tDy6Gzm"
      },
      "source": [
        "### Creating Polynomial features\n",
        "\n",
        "We'll write a function to encapsulate what we learnt about creating the polynomial features."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_H8K2jZv6Gzm"
      },
      "source": [
        "def make_features(train_set, test_set, degrees):\n",
        "    train_dict = {}\n",
        "    test_dict = {}\n",
        "    for d in degrees:\n",
        "        traintestdict={}\n",
        "        train_dict[d] = PolynomialFeatures(d).fit_transform(train_set.reshape(-1,1))\n",
        "        test_dict[d] = PolynomialFeatures(d).fit_transform(test_set.reshape(-1,1))\n",
        "    return train_dict, test_dict"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rU5yQkNE6Gzn"
      },
      "source": [
        "### Doing the fit\n",
        "\n",
        "We first create our features, and some arrays to store the errors."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dU2VoRsZ6Gzn"
      },
      "source": [
        "degrees=range(21)\n",
        "train_dict, test_dict = make_features(xtrain, xtest, degrees)"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cMO6CLLb6Gzn"
      },
      "source": [
        "error_train=np.empty(len(degrees))\n",
        "error_test=np.empty(len(degrees))"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GrbQAwOM6Gzo"
      },
      "source": [
        "What is the fitting process? We first loop over all the **hypothesis set**s that we wish to consider: in our case this is a loop over the complexity parameter $d$, the degree of the polynomials we will try and fit. That is we start with ${\\cal H_0}$, the set of all 0th order polynomials, then do ${\\cal H_1}$, then ${\\cal H_2}$, and so on... We use the notation ${\\cal H}$ to indicate a hypothesis set. Then for each degree $d$, we obtain a best fit model. We then \"test\" this model by predicting on the test chunk, obtaining the test set error for the best-fit polynomial coefficients and for degree $d$. We move on to the next degree $d$ and repeat the process, just like before. We compare all the test set errors, and pick the degree $d_*$ and the model in ${\\cal H_{d_*}}$ which minimizes this test set error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JAwGRtzF6Gzo"
      },
      "source": [
        "#for each degree, we now fit on the training set and predict on the test set\n",
        "#we accumulate the MSE on both sets in error_train and error_test\n",
        "for d in degrees:#for increasing polynomial degrees 0,1,2...\n",
        "    Xtrain = train_dict[d]\n",
        "    Xtest = test_dict[d]\n",
        "    #set up model\n",
        "    est = LinearRegression()\n",
        "    #fit\n",
        "    est.fit(Xtrain, ytrain)\n",
        "    #predict\n",
        "    prediction_on_training = est.predict(Xtrain)\n",
        "    prediction_on_test = est.predict(Xtest)\n",
        "    #calculate mean squared error\n",
        "    error_train[d] = mean_squared_error(ytrain, prediction_on_training)\n",
        "    error_test[d] = mean_squared_error(ytest, prediction_on_test)"
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R8Tlvzxb6Gzp"
      },
      "source": [
        "We can find the best degree thus:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dPpImsvv6Gzp"
      },
      "source": [
        "bestd = np.argmin(error_test)"
      ],
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5UWar0LQ6Gzp",
        "outputId": "de57f8aa-ce92-4971-807e-175fff0316d3"
      },
      "source": [
        "bestd"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 431
        },
        "id": "pA7x_33a6Gzq",
        "outputId": "c23d0a8d-29a9-4f34-addf-70fe7f935bf5"
      },
      "source": [
        "plt.figure(figsize=(12,8))\n",
        "plt.plot(degrees, error_train, marker='o', label='train (in-sample)')\n",
        "plt.plot(degrees, error_test, marker='o', label='test')\n",
        "plt.axvline(bestd, 0,0.5, color='r', label=\"min test error at d=%d\"%bestd, alpha=0.3)\n",
        "plt.ylabel('mean squared error')\n",
        "plt.xlabel('degree')\n",
        "plt.legend(loc='upper left')\n",
        "plt.yscale(\"log\")"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e25VtUlU6Gzq"
      },
      "source": [
        "![m:caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/complexity-error-plot.png?raw=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-4q6tFxE6Gzr"
      },
      "source": [
        "## Validation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JXNJlV_f6Gzs"
      },
      "source": [
        "What we have done in picking a given $d$ as the best hypothesis is that we have used the test set as a training set. \n",
        "If we choose the best $d$ based on minimizing the test set error, we have then \"fit for\" hyperparameter $d$ on the test set. \n",
        "\n",
        "In this case, the test-set error will underestimate the true out of sample error. Furthermore, we have **contaminated the test set** by fitting for $d$ on it; it is no longer a true test set.\n",
        "\n",
        "Thus, we introduce a new **validation set** on which the complexity parameter $d$ is fit, and leave out a test set which we can use to estimate the true out-of-sample performance of our learner. The place of this set in the scheme of things is shown below:\n",
        "\n",
        "![m:caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/train-validate-test.png?raw=1)\n",
        "\n",
        "We have split the old training set into a **new smaller training set** and a **validation set**, holding the old test aside for FINAL testing AFTER we have \"fit\" for complexity $d$. Obviously we have decreased the size of the data available for training further, but this is a price we must pay for obtaining a good estimate of the out-of-sample risk $\\cal{E}_{out}$ (also denoted as risk $R_{out}$) through the test risk $\\cal{E}_{test}$ ($R_{test}$).\n",
        "\n",
        "![m:caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/train-validate-test-cont.png?raw=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kBvSHZ5v6Gzs"
      },
      "source": [
        "The validation process is illustrated in these two figures. We first loop over the complexity parameter $d$, the degree of the polynomials we will try and fit. Then for each degree $d$, we obtain a best fit model $g^-_d$ where the \"minus\" superscript indicates that we fit our model on the new training set which is obtained by removing (\"minusing\") a validation chunk (often the same size as the test chunk) from the old training set. We then \"test\" this model on the validation chunk, obtaining the validation error for the best-fit polynomial coefficients and for degree $d$. We move on to the next degree $d$ and repeat the process, just like before. We compare all the validation set errors, just like we did with the test errors earlier, and pick the degree $d_*$ which minimizes this validation set error.\n",
        "\n",
        "![caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/train-validate-test3.png?raw=1)\n",
        "\n",
        "Having picked the hyperparameter $d_*$, we retrain using the hypothesis set $\\cal{H}_{*}$ on the entire old training-set to find the parameters of the polynomial of order $d_*$ and the corresponding best fit hypothesis $g_*$. Note that we left the minus off the $g$ to indicate that it was trained on the entire old traing set. We now compute the test error on the test set as an estimate of the test risk $\\cal{E}_{test}$.\n",
        "\n",
        "Thus the **validation** set if the set on which the hyperparameter is fit. This method of splitting the data $\\cal{D}$ is called the **train-validate-test** split."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YpCSQ8LI6Gzu"
      },
      "source": [
        "### Fit on training and predict on validation\n",
        "\n",
        "\n",
        "We carry out this process for one training/validation split below. Note the smaller size of the new training set. We hold the test set at the same size."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VIjHTL6J6Gzu"
      },
      "source": [
        "#we split the training set down further\n",
        "intrain,invalid = train_test_split(itrain,train_size=36, test_size=12)\n",
        "# why not just use xtrain, xtest here? its the indices we need. How could you use xtrain and xtest?\n",
        "xntrain= sample_df.x[intrain].values\n",
        "fntrain = sample_df.f[intrain].values\n",
        "yntrain = sample_df.y[intrain].values\n",
        "xnvalid= sample_df.x[invalid].values\n",
        "fnvalid = sample_df.f[invalid].values\n",
        "ynvalid = sample_df.y[invalid].values\n",
        "\n",
        "degrees=range(21)\n",
        "train_dict, valid_dict = make_features(xntrain, xnvalid, degrees)"
      ],
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0kBMig5J6Gzv"
      },
      "source": [
        "error_train=np.empty(len(degrees))\n",
        "error_valid=np.empty(len(degrees))\n",
        "#for each degree, we now fit on the smaller training set and predict on the validation set\n",
        "#we accumulate the MSE on both sets in error_train and error_valid\n",
        "#we then find the degree of polynomial that minimizes the MSE on the validation set.\n",
        "for d in degrees:#for increasing polynomial degrees 0,1,2...\n",
        "    #Create polynomials from x\n",
        "    Xntrain = train_dict[d]\n",
        "    Xnvalid = valid_dict[d]\n",
        "    #fit a model linear in polynomial coefficients on the new smaller training set\n",
        "    est = LinearRegression()\n",
        "    est.fit(Xntrain, yntrain)\n",
        "    #predict on new training and validation sets and calculate mean squared error\n",
        "    error_train[d] = mean_squared_error(yntrain, est.predict(Xntrain))\n",
        "    error_valid[d] = mean_squared_error(ynvalid, est.predict(Xnvalid))"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6nLwPvzF6Gzv",
        "outputId": "cba058e1-dae2-4e73-f83d-b09c784999ee"
      },
      "source": [
        "#calculate the degree at which validation error is minimized\n",
        "mindeg = np.argmin(error_valid)\n",
        "mindeg"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XtQqu7P56Gzv",
        "outputId": "8ce5ad87-f529-4305-8694-653dacc8ccfb"
      },
      "source": [
        "#fit on WHOLE training set now. \n",
        "##you will need to remake polynomial features on the whole training set\n",
        "#Put MSE on the test set in variable err.\n",
        "#your code here\n",
        "whole_train_dict, whole_test_dict = make_features(xtrain, xtest, degrees)\n",
        "features_at_mindeg = whole_train_dict[mindeg]\n",
        "features_at_mindeg_test = whole_test_dict[mindeg]\n",
        "whole_est = LinearRegression()\n",
        "whole_est.fit(features_at_mindeg, ytrain)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6Lf7c2LW_quB"
      },
      "source": [
        "err =mean_squared_error(ytest, whole_est.predict (features_at_mindeg_test))"
      ],
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1xtwil636Gzw"
      },
      "source": [
        "We plot the training error and validation error against the degree of the polynomial, and show the test set error at the $d$ which minimizes the validation set error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "1GUuvGCO6Gzw",
        "outputId": "cd67f1d0-fb5c-482b-bef1-8fe15c7fba99"
      },
      "source": [
        "plt.figure(figsize=(12,8))\n",
        "plt.plot(degrees, error_train, marker='o', label='train (in-sample)')\n",
        "plt.plot(degrees, error_valid, marker='o', label='validation')\n",
        "plt.plot([mindeg], [err], marker='s', markersize=10, label='test', alpha=0.5, color='r')\n",
        "plt.ylabel('mean squared error')\n",
        "plt.xlabel('degree')\n",
        "plt.legend(loc='upper left')\n",
        "plt.yscale(\"log\")\n",
        "print(mindeg)"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OSk_Nv5h6Gzw"
      },
      "source": [
        "> YOUR TURN HERE: Run the set of cells for the validation process again and again. What do you see? The validation error minimizing polynomial degree might change! What happened?\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7hC_r6im6Gzx"
      },
      "source": [
        "## Cross Validation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZYNtIrng6Gzx"
      },
      "source": [
        "1. You should worry that a given split exposes us to the peculiarity of the data set that got randomly chosen for us. This naturally leads us to want to choose multiple such random splits and somehow average over this process to find the \"best\" validation minimizing polynomial degree or complexity $d$.\n",
        "2. The multiple splits process also allows us to get an estimate of how consistent our prediction error is: in other words, just like in the hair example, it gives us a distribution.\n",
        "3. Furthermore the validation set that we left out has two competing demands on it. The larger the set is, the better is our estimate of the out-of-sample error. So we'd like to hold out as much as possible. But the smaller the validation set is, the more data we have to train our model on. This allows us to have more smaller sets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9vDsypwm6Gzx"
      },
      "source": [
        "The idea is illustrated in the figure below, for a given hypothesis set $\\cal{H}_a$ with complexity parameter $d=a$ (the polynomial degree). We do the train/validate split, not once but multiple times. \n",
        "\n",
        "In the figure below we create 4-folds from the training set part of our data set $\\cal{D}$. By this we mean that we divide our set roughly into 4 equal parts. As illustrated below, this can be done in 4 different ways, or folds. In each fold we train a model on 3 of the parts. The model so trained is denoted as $g^-_{Fi}$, for example $g^-_{F3}$ . The minus sign in the superscript once again indicates that we are training on a reduced set. The $F3$ indicates that this model was trained on the third fold. Note that the model trained on each fold will be different!\n",
        "\n",
        "For each fold, after training the model, we calculate the risk or error on the remaining one validation part. We then add the validation errors together from the different folds, and divide by the number of folds to calculate an average error. Note again that this average error is an average over different models $g^-_{Fi}$. We use this error as the validation error for $d=a$ in the validation process described earlier."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DyUX6eG-6Gzy"
      },
      "source": [
        "![m:caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/train-cv2.png?raw=1)\n",
        "\n",
        "Note that the number of folds is equal to the number of splits in the data. For example, if we have 5 splits, there will be 5 folds. To illustrate cross-validation consider below fits in $\\cal{H}_0$ and $\\cal{H}_1$ (means and straight lines) to a sine curve, with only 3 data points."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qj1osrSx6Gzy"
      },
      "source": [
        "### The entire description of K-fold Cross-validation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ju-ssc6f6Gzy"
      },
      "source": [
        "We put thogether this scheme to calculate the error for a given polynomial degree $d$ with the method we used earlier to choose a model given the validation-set risk as a function of $d$:\n",
        "\n",
        "1. create `n_folds` partitions of the training data. \n",
        "2. We then train on `n_folds -1` of these partitions, and test on the remaining partition. There are `n_folds` such combinations of partitions (or folds), and thus we obtain `n_fold` risks.\n",
        "3. We average the error or risk of all such combinations to obtain, for each value of $d$, $R_{dCV}$.\n",
        "4. We move on to the next value of $d$, and repeat 3\n",
        "5. and then find the optimal value of d that minimizes risk $d=*$.\n",
        "5. We finally use that value to make the final fit in $\\cal{H}_*$ on the entire old training set.\n",
        "\n",
        "![caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/train-cv3.png?raw=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-vMTGQ1k6Gzz"
      },
      "source": [
        "It can also shown that **cross-validation error is an unbiased estimate of the out of sample-error**.\n",
        "\n",
        "Let us now do 4-fold cross-validation on our  data set. We increase the complexity from degree 0 to degree 20. In each case we take the old training set, split in 4 ways into 4 folds, train on 3 folds, and calculate the validation error on the remaining one. We then average the erros over the four folds to get a cross-validation error for that $d$. Then we did what we did before: find the hypothesis space $\\cal{H}_*$ with the lowest cross-validation error, and refit it using the entire training set. We can then use the test set to estimate $E_{out}$.\n",
        "\n",
        "We will use `KFold` from `scikit-learn`:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dSyvmVZ6AeKz",
        "outputId": "fb6ba4c5-d70e-49c7-aa1a-f3e8ff25ae5c"
      },
      "source": [
        "from sklearn.model_selection import KFold\r\n",
        "n_folds=4\r\n",
        "kfold = KFold(n_folds)\r\n",
        "kfold"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KFold(n_splits=4, random_state=None, shuffle=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WKaMyeEN6Gzz",
        "outputId": "5ff2a8c2-d743-42a9-dc39-b63db0d0e3c4"
      },
      "source": [
        "\n",
        "list(kfold.split(range(48)))"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(array([12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,\n",
              "         29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,\n",
              "         46, 47]), array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])),\n",
              " (array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 24, 25, 26, 27, 28,\n",
              "         29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,\n",
              "         46, 47]), array([12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])),\n",
              " (array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
              "         17, 18, 19, 20, 21, 22, 23, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,\n",
              "         46, 47]), array([24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35])),\n",
              " (array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
              "         17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
              "         34, 35]), array([36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]))]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x4AdnqYw6Gzz"
      },
      "source": [
        "What is wrong with the above? Why must we do the below?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AwNcwmWI6Gzz",
        "outputId": "a6b692c1-d58b-4915-8029-e8d02aefdb08"
      },
      "source": [
        "kfold = KFold(n_folds, shuffle=True)\n",
        "list(kfold.split(range(48)))"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(array([ 2,  3,  4,  5,  9, 10, 11, 14, 16, 17, 18, 19, 20, 22, 24, 25, 26,\n",
              "         27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45,\n",
              "         46, 47]), array([ 0,  1,  6,  7,  8, 12, 13, 15, 21, 23, 38, 44])),\n",
              " (array([ 0,  1,  2,  3,  4,  6,  7,  8, 10, 12, 13, 14, 15, 16, 19, 20, 21,\n",
              "         23, 25, 26, 28, 29, 30, 33, 34, 35, 36, 38, 40, 41, 42, 43, 44, 45,\n",
              "         46, 47]), array([ 5,  9, 11, 17, 18, 22, 24, 27, 31, 32, 37, 39])),\n",
              " (array([ 0,  1,  3,  4,  5,  6,  7,  8,  9, 11, 12, 13, 14, 15, 17, 18, 19,\n",
              "         20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 37, 38, 39, 41, 43,\n",
              "         44, 47]), array([ 2, 10, 16, 30, 33, 34, 35, 36, 40, 42, 45, 46])),\n",
              " (array([ 0,  1,  2,  5,  6,  7,  8,  9, 10, 11, 12, 13, 15, 16, 17, 18, 21,\n",
              "         22, 23, 24, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44,\n",
              "         45, 46]), array([ 3,  4, 14, 19, 20, 25, 26, 28, 29, 41, 43, 47]))]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nGdk2XiQ6Gz0"
      },
      "source": [
        "### 4-fold CV on our data set\n",
        "\n",
        ">YOUR TURN HERE: Carry out 4-Fold validation. For each fold, you will need to first create the polynomial features. for each degree polynomial, fit on the smaller training set and predict on the validation set. Store the MSEs, for each degree and each fold, in `train_errors` and `valid_errors`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MrLJfZ0y6Gz0"
      },
      "source": [
        "n_folds=4\n",
        "degrees=range(21)\n",
        "train_errors = np.zeros((21,4))\n",
        "valid_errors = np.zeros((21,4))"
      ],
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9zXjpn-o6Gz0"
      },
      "source": [
        "# your code here\n",
        "kfold = KFold(n_folds, shuffle=True)\n",
        "kfold_number = 0\n",
        "for train_indices, valid_indices in kfold.split(range(48)):\n",
        "  train_dict, valid_dict = make_features(xtrain[train_indices], xtrain[valid_indices], degrees)\n",
        "\n",
        "  for d in degrees:\n",
        "    est = LinearRegression()\n",
        "    est.fit(train_dict[d], ytrain[train_indices])\n",
        "    pred_train = est.predict(train_dict[d])\n",
        "    pred_valid = est.predict(valid_dict[d])\n",
        "    train_errors[d, kfold_number] = mean_squared_error(ytrain[train_indices], pred_train)\n",
        "    valid_errors[d, kfold_number] = mean_squared_error(ytrain[valid_indices], pred_valid)\n",
        "  \n",
        "  kfold_number +=1"
      ],
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8QY9wuPp6Gz0"
      },
      "source": [
        "We average the MSEs over the folds"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uFBLDY806Gz1"
      },
      "source": [
        "mean_train_errors = train_errors.mean(axis=1)\n",
        "mean_valid_errors = valid_errors.mean(axis=1)\n",
        "std_train_errors = train_errors.std(axis=1)\n",
        "std_valid_errors = valid_errors.std(axis=1)"
      ],
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7nYrhY0BDceF",
        "outputId": "416378fb-3552-41d0-d163-986f64b9aa10"
      },
      "source": [
        "mindeg = np.argmin(mean_valid_errors)\r\n",
        "print(mindeg)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pBEm0ZfV6Gz1"
      },
      "source": [
        "We find the degree that minimizes the `cross-validation` error, and just like before, refit the model on the entire training set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 431
        },
        "id": "8gRqim4Q6Gz1",
        "outputId": "f51340d2-32e6-432a-ee8b-dbf6295f38f9"
      },
      "source": [
        "\n",
        "post_cv_train_dict, test_dict=make_features(xtrain, xtest, degrees)\n",
        "#fit on whole training set now.\n",
        "est = LinearRegression()\n",
        "est.fit(post_cv_train_dict[mindeg], ytrain) # fit\n",
        "pred = est.predict(test_dict[mindeg])\n",
        "err = mean_squared_error(pred, ytest)\n",
        "errtr=mean_squared_error(ytrain, est.predict(post_cv_train_dict[mindeg]))\n",
        "cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
        "c0=cycle[0]\n",
        "c1=cycle[1]\n",
        "#plt.errorbar(degrees, [r[0] for r in results], yerr=[r[3] for r in results], marker='o', label='CV error', alpha=0.5)\n",
        "plt.figure(figsize=(12,8))\n",
        "plt.plot(degrees, mean_train_errors, marker='o', label='CV error', alpha=0.9)\n",
        "plt.plot(degrees, mean_valid_errors, marker='o', label='CV error', alpha=0.9)\n",
        "\n",
        "\n",
        "plt.fill_between(degrees, mean_valid_errors-std_valid_errors, mean_valid_errors+std_valid_errors, color=c1, alpha=0.2)\n",
        "\n",
        "\n",
        "plt.plot([mindeg], [err], 'o',  label='test set error')\n",
        "\n",
        "plt.ylabel('mean squared error')\n",
        "plt.xlabel('degree')\n",
        "plt.legend(loc='upper right')\n",
        "plt.yscale(\"log\")"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f5L_NLIt6Gz2"
      },
      "source": [
        "We see that the cross-validation error minimizes at a low degree, and then increases. Because we have so few data points the spread in fold errors increases as well."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "clguH5Nz6Gz2"
      },
      "source": [
        "## Regularization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KqM74xGh6Gz2"
      },
      "source": [
        "Upto now we have focussed on finding the polynomial with the right degree of complecity $d=*$ given the data that we have.\n",
        "\n",
        "When we **regularize** we smooth or restrict the choices of the kinds of 20th order polynomials that we allow in our fits. \n",
        "\n",
        "That is, if we want to fit with a 20th order polynomial, ok, lets fit with it, but lets reduce the size of, or limit the functions in $\\cal{H}_{20}$ that we allow.\n",
        "\n",
        "\n",
        "We do this by a **soft constraint** by setting:\n",
        "\n",
        "$$\\sum_{i=0}^j a_i^2 < C.$$\n",
        "\n",
        "This setting is called the Ridge.\n",
        "\n",
        "This ensures that the coefficients dont get too high, which makes sure we dont get wildly behaving pilynomials with high coefficients. \n",
        "\n",
        "It turns out that we can do this by adding a term to the risk that we minimize on the training data for $\\cal{H}_j$ (seeing why is beyond the scope here but google on lagrange multipliers and the dual problem):\n",
        "\n",
        "$$\\cal{R}(h_j) =  \\sum_{y_i \\in \\cal{D}} (y_i - h_j(x_i))^2 +\\alpha \\sum_{i=0}^j a_i^2.$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ksufr8IN6Gz2"
      },
      "source": [
        "### Regularization of our model with Cross-Validation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hhk6GgMT6Gz2"
      },
      "source": [
        "def plot_functions(d, est, ax, df, alpha, xtest, Xtest, xtrain, ytrain):\n",
        "    \"\"\"Plot the approximation of ``est`` on axis ``ax``. \"\"\"\n",
        "    ax.plot(df.x, df.f, color='k', label='f')\n",
        "    ax.plot(xtrain, ytrain, 's', label=\"training\", ms=5, alpha=0.3)\n",
        "    ax.plot(xtest, ytest, 's', label=\"testing\", ms=5, alpha=0.3)\n",
        "    transx=np.arange(0,1.1,0.01)\n",
        "    transX = PolynomialFeatures(d).fit_transform(transx.reshape(-1,1))\n",
        "    ax.plot(transx, est.predict(transX),  '.', ms=7, alpha=0.8, label=\"alpha = %s\" % str(alpha))\n",
        "    ax.set_ylim((0, 1))\n",
        "    ax.set_xlim((0, 1))\n",
        "    ax.set_ylabel('y')\n",
        "    ax.set_xlabel('x')\n",
        "    ax.legend(loc='lower right')\n",
        "    \n",
        "def plot_coefficients(est, ax, alpha):\n",
        "    coef = est.coef_.ravel()\n",
        "    ax.semilogy(np.abs(coef), marker='o', label=\"alpha = %s\" % str(alpha))\n",
        "    ax.set_ylim((1e-1, 1e15))\n",
        "    ax.set_ylabel('abs(coefficient)')\n",
        "    ax.set_xlabel('coefficients')\n",
        "    ax.legend(loc='upper left')"
      ],
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9O7xsu_t6Gz3"
      },
      "source": [
        "The addition of a penalty term to the risk or error causes us to choose a smaller subset of the entire set of complex $\\cal{H}_{20}$ polynomials. This is shown in the diagram below where the balance between bias and variance occurs at some subset $S_*$ of the set of 20th order polynomials indexed by $\\alpha_*$ (there is an error on the diagram, the 13 there should actually be a 20).\n",
        "\n",
        "![m:caption](https://github.com/heysatya/ValidationRegularization/blob/main/images/complexity-error-reg.png?raw=1)\n",
        "\n",
        "Lets see what some of the $\\alpha$s do. The diagram below trains on the entire training set, for given values of $\\alpha$, minimizing the penalty-term-added training error.\n",
        "\n",
        "*What is wrong in the code below? It works, but is not quite philosophically right. We are doing it for demonstration purposes*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lagmkIygER4N",
        "outputId": "069e9d0f-4f5c-4043-a57f-33f515ef1356"
      },
      "source": [
        "from sklearn.linear_model import Ridge\r\n",
        "d=20\r\n",
        "alphas = [0.0, 1e-6, 1e-5, 1e-3, 0.01, 1]\r\n",
        "train_dict, test_dict = make_features(xtrain, xtest, degrees)\r\n",
        "Xtrain = train_dict[d]\r\n",
        "Xtest = test_dict[d]\r\n",
        "Xtest"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.00000000e+00, 6.37120888e-01, 4.05923025e-01, 2.58622038e-01,\n",
              "        1.64773502e-01, 1.04980640e-01, 6.68853586e-02, 4.26140590e-02,\n",
              "        2.71503071e-02, 1.72980278e-02, 1.10209348e-02, 7.02166776e-03,\n",
              "        4.47365120e-03, 2.85025662e-03, 1.81595803e-03, 1.15698479e-03,\n",
              "        7.37139177e-04, 4.69646767e-04, 2.99221765e-04, 1.90640436e-04,\n",
              "        1.21461004e-04],\n",
              "       [1.00000000e+00, 7.05206764e-01, 4.97316580e-01, 3.50711016e-01,\n",
              "        2.47323781e-01, 1.74414403e-01, 1.22998217e-01, 8.67391747e-02,\n",
              "        6.11690527e-02, 4.31368297e-02, 3.04203841e-02, 2.14526607e-02,\n",
              "        1.51285614e-02, 1.06687638e-02, 7.52368442e-03, 5.30575315e-03,\n",
              "        3.74165301e-03, 2.63863901e-03, 1.86078608e-03, 1.31223893e-03,\n",
              "        9.25399770e-04],\n",
              "       [1.00000000e+00, 5.95162068e-01, 3.54217887e-01, 2.10817050e-01,\n",
              "        1.25470312e-01, 7.46751702e-02, 4.44438288e-02, 2.64512810e-02,\n",
              "        1.57427991e-02, 9.36951689e-03, 5.57638105e-03, 3.31885048e-03,\n",
              "        1.97525391e-03, 1.17559620e-03, 6.99670269e-04, 4.16417204e-04,\n",
              "        2.47835724e-04, 1.47502422e-04, 8.77878467e-05, 5.22479964e-05,\n",
              "        3.10960256e-05],\n",
              "       [1.00000000e+00, 9.15465747e-01, 8.38077534e-01, 7.67231276e-01,\n",
              "        7.02373953e-01, 6.42999296e-01, 5.88643831e-01, 5.38883264e-01,\n",
              "        4.93329170e-01, 4.51625957e-01, 4.13448095e-01, 3.78497569e-01,\n",
              "        3.46501560e-01, 3.17210309e-01, 2.90395173e-01, 2.65846834e-01,\n",
              "        2.43373670e-01, 2.22800259e-01, 2.03966005e-01, 1.86723892e-01,\n",
              "        1.70939327e-01],\n",
              "       [1.00000000e+00, 9.70000000e-01, 9.40900000e-01, 9.12673000e-01,\n",
              "        8.85292810e-01, 8.58734026e-01, 8.32972005e-01, 8.07982845e-01,\n",
              "        7.83743359e-01, 7.60231059e-01, 7.37424127e-01, 7.15301403e-01,\n",
              "        6.93842361e-01, 6.73027090e-01, 6.52836277e-01, 6.33251189e-01,\n",
              "        6.14253653e-01, 5.95826044e-01, 5.77951263e-01, 5.60612725e-01,\n",
              "        5.43794343e-01],\n",
              "       [1.00000000e+00, 3.40000000e-01, 1.15600000e-01, 3.93040000e-02,\n",
              "        1.33633600e-02, 4.54354240e-03, 1.54480442e-03, 5.25233501e-04,\n",
              "        1.78579390e-04, 6.07169928e-05, 2.06437775e-05, 7.01888436e-06,\n",
              "        2.38642068e-06, 8.11383032e-07, 2.75870231e-07, 9.37958786e-08,\n",
              "        3.18905987e-08, 1.08428036e-08, 3.68655321e-09, 1.25342809e-09,\n",
              "        4.26165551e-10],\n",
              "       [1.00000000e+00, 1.30000000e-01, 1.69000000e-02, 2.19700000e-03,\n",
              "        2.85610000e-04, 3.71293000e-05, 4.82680900e-06, 6.27485170e-07,\n",
              "        8.15730721e-08, 1.06044994e-08, 1.37858492e-09, 1.79216039e-10,\n",
              "        2.32980851e-11, 3.02875107e-12, 3.93737639e-13, 5.11858930e-14,\n",
              "        6.65416609e-15, 8.65041592e-16, 1.12455407e-16, 1.46192029e-17,\n",
              "        1.90049638e-18],\n",
              "       [1.00000000e+00, 5.86109459e-01, 3.43524298e-01, 2.01342840e-01,\n",
              "        1.18008943e-01, 6.91661577e-02, 4.05389393e-02, 2.37602557e-02,\n",
              "        1.39261106e-02, 8.16222516e-03, 4.78395737e-03, 2.80392267e-03,\n",
              "        1.64340560e-03, 9.63215564e-04, 5.64549753e-04, 3.30887950e-04,\n",
              "        1.93936557e-04, 1.13668051e-04, 6.66219196e-05, 3.90477372e-05,\n",
              "        2.28862481e-05],\n",
              "       [1.00000000e+00, 8.02557963e-01, 6.44099283e-01, 5.16927009e-01,\n",
              "        4.14863887e-01, 3.32952316e-01, 2.67213532e-01, 2.14454348e-01,\n",
              "        1.72112045e-01, 1.38129892e-01, 1.10857245e-01, 8.89693644e-02,\n",
              "        7.14030718e-02, 5.73051038e-02, 4.59906674e-02, 3.69101763e-02,\n",
              "        2.96225559e-02, 2.37738181e-02, 1.90798670e-02, 1.53126992e-02,\n",
              "        1.22893287e-02],\n",
              "       [1.00000000e+00, 8.09657516e-01, 6.55545293e-01, 5.30767174e-01,\n",
              "        4.29739632e-01, 3.47941923e-01, 2.81713793e-01, 2.28091690e-01,\n",
              "        1.84676151e-01, 1.49524434e-01, 1.21063582e-01, 9.80200387e-02,\n",
              "        7.93626611e-02, 6.42565750e-02, 5.20258189e-02, 4.21230953e-02,\n",
              "        3.41052807e-02, 2.76135969e-02, 2.23575563e-02, 1.81019635e-02,\n",
              "        1.46563908e-02],\n",
              "       [1.00000000e+00, 4.40000000e-01, 1.93600000e-01, 8.51840000e-02,\n",
              "        3.74809600e-02, 1.64916224e-02, 7.25631386e-03, 3.19277810e-03,\n",
              "        1.40482236e-03, 6.18121840e-04, 2.71973609e-04, 1.19668388e-04,\n",
              "        5.26540908e-05, 2.31677999e-05, 1.01938320e-05, 4.48528607e-06,\n",
              "        1.97352587e-06, 8.68351383e-07, 3.82074608e-07, 1.68112828e-07,\n",
              "        7.39696442e-08],\n",
              "       [1.00000000e+00, 3.00000000e-02, 9.00000000e-04, 2.70000000e-05,\n",
              "        8.10000000e-07, 2.43000000e-08, 7.29000000e-10, 2.18700000e-11,\n",
              "        6.56100000e-13, 1.96830000e-14, 5.90490000e-16, 1.77147000e-17,\n",
              "        5.31441000e-19, 1.59432300e-20, 4.78296900e-22, 1.43489070e-23,\n",
              "        4.30467210e-25, 1.29140163e-26, 3.87420489e-28, 1.16226147e-29,\n",
              "        3.48678440e-31]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4tnT3-YBEsc5",
        "outputId": "a71b1e02-d8e9-447d-962c-afb87337c2c1"
      },
      "source": [
        "alphas"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0, 1e-06, 1e-05, 0.001, 0.01, 1]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ltSoREZ6FgQr"
      },
      "source": [
        "alphas = [0.0, 1e-6, 0.01, 0.1, 1, 10]"
      ],
      "execution_count": 104,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "NbOZR_pa6Gz3",
        "outputId": "6a81970f-c442-4fec-dc8c-b56a81ab2be1"
      },
      "source": [
        "fig, rows = plt.subplots(6, 2, figsize=(12, 24))\n",
        "for i, alpha in enumerate(alphas):\n",
        "    l,r=rows[i]\n",
        "    est = Ridge(alpha=alpha)\n",
        "    est.fit(Xtrain, ytrain)\n",
        "    plot_functions(d, est, l, df, alpha, xtest, Xtest, xtrain, ytrain )\n",
        "    plot_coefficients(est, r, alpha)"
      ],
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x1728 with 12 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xIJjuYNU6Gz3"
      },
      "source": [
        "As you can see, as we increase $\\alpha$ from 0 to 1, we start out overfitting, then doing well, and then, our fits, develop a mind of their own irrespective of data, as the penalty term dominates the risk."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZKjsbWU36Gz3"
      },
      "source": [
        "### `GridSearchCV` meta-estimator\n",
        "\n",
        "Lets use cross-validation to figure what this critical $\\alpha_*$ is. To do this we use the concept of a *meta-estimator* from scikit-learn. As the API paper puts it:\n",
        "\n",
        ">In scikit-learn, model selection is supported in two distinct meta-estimators, GridSearchCV and RandomizedSearchCV. They take as input an estimator (basic or composite), whose hyper-parameters must be optimized, and a set of hyperparameter settings to search through.\n",
        "\n",
        "The concept of a meta-estimator allows us to wrap, for example, cross-validation, or methods that build and combine simpler models or schemes. For example:\n",
        "\n",
        "    est = Ridge()\n",
        "    parameters = {\"alpha\": [1e-8, 1e-6, 1e-5, 5e-5, 1e-4, 5e-4, 1e-3, 1e-2, 1e-1, 1.0]}\n",
        "    gridclassifier=GridSearchCV(est, param_grid=parameters, cv=4, scoring=\"mean_squared_error\")\n",
        "    \n",
        "The `GridSearchCV` replaces the manual iteration over thefolds using `KFolds` and the averaging we did previously, doing it all for us. It takes a parameter grid in the shape of a dictionary as input, and sets $\\alpha$ to the appropriate parameter values one by one. It then trains the model, cross-validation fashion, and gets the error. Finally it compares the errors for the different $\\alpha$'s, and picks the best choice model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vgnKP45-6Gz4"
      },
      "source": [
        "from sklearn.model_selection import GridSearchCV\n",
        "def cv_optimize_ridge(X, y, n_folds=4):\n",
        "    est = Ridge()\n",
        "    parameters = {\"alpha\": [1e-8, 1e-6, 1e-5, 5e-5, 1e-4, 5e-4, 1e-3, 1e-2, 1e-1, 1.0, 10.0]}\n",
        "    #the scoring parameter below is the default one in ridge, but you can use a different one\n",
        "    #in the cross-validation phase if you want.\n",
        "    gs = GridSearchCV(est, param_grid=parameters, cv=n_folds, scoring=\"neg_mean_squared_error\")\n",
        "    gs.fit(X, y)\n",
        "    return gs"
      ],
      "execution_count": 106,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RT4KlaCpGk4T"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EAHVaXDY6Gz4"
      },
      "source": [
        "fitmodel = cv_optimize_ridge(Xtrain, ytrain, n_folds=4)"
      ],
      "execution_count": 107,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kjrLNuLe6Gz4",
        "outputId": "c6a29c3d-3794-4ede-eea5-187efceb793d"
      },
      "source": [
        "fitmodel.best_estimator_, fitmodel.best_params_, fitmodel.best_score_"
      ],
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(Ridge(alpha=1e-06, copy_X=True, fit_intercept=True, max_iter=None,\n",
              "       normalize=False, random_state=None, solver='auto', tol=0.001),\n",
              " {'alpha': 1e-06},\n",
              " -0.005167130851878926)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 108
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n7oIEia96Gz4",
        "outputId": "1a3f07af-93f9-484d-8453-42d5f4f7d2f2"
      },
      "source": [
        "fitmodel.cv_results_"
      ],
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'mean_fit_time': array([0.00116986, 0.00084883, 0.00072438, 0.00055641, 0.00052404,\n",
              "        0.00051916, 0.00052428, 0.00050962, 0.00051433, 0.00050074,\n",
              "        0.00051141]),\n",
              " 'mean_score_time': array([0.00055099, 0.00047505, 0.00037098, 0.00030041, 0.00027865,\n",
              "        0.00030577, 0.00027859, 0.00030434, 0.00029874, 0.00030708,\n",
              "        0.00031751]),\n",
              " 'mean_test_score': array([-0.00564457, -0.00516713, -0.00576583, -0.00619065, -0.00632777,\n",
              "        -0.00645081, -0.00644289, -0.00643675, -0.00713646, -0.01281833,\n",
              "        -0.03389567]),\n",
              " 'param_alpha': masked_array(data=[1e-08, 1e-06, 1e-05, 5e-05, 0.0001, 0.0005, 0.001,\n",
              "                    0.01, 0.1, 1.0, 10.0],\n",
              "              mask=[False, False, False, False, False, False, False, False,\n",
              "                    False, False, False],\n",
              "        fill_value='?',\n",
              "             dtype=object),\n",
              " 'params': [{'alpha': 1e-08},\n",
              "  {'alpha': 1e-06},\n",
              "  {'alpha': 1e-05},\n",
              "  {'alpha': 5e-05},\n",
              "  {'alpha': 0.0001},\n",
              "  {'alpha': 0.0005},\n",
              "  {'alpha': 0.001},\n",
              "  {'alpha': 0.01},\n",
              "  {'alpha': 0.1},\n",
              "  {'alpha': 1.0},\n",
              "  {'alpha': 10.0}],\n",
              " 'rank_test_score': array([ 2,  1,  3,  4,  5,  8,  7,  6,  9, 10, 11], dtype=int32),\n",
              " 'split0_test_score': array([-0.0073668 , -0.00740629, -0.00757472, -0.00757267, -0.00757493,\n",
              "        -0.00769369, -0.0077937 , -0.00827317, -0.00887108, -0.00766674,\n",
              "        -0.00989717]),\n",
              " 'split1_test_score': array([-0.00454992, -0.00283749, -0.00325672, -0.00355455, -0.00366636,\n",
              "        -0.00357288, -0.00343316, -0.00366619, -0.0063878 , -0.02205442,\n",
              "        -0.06090408]),\n",
              " 'split2_test_score': array([-0.00884719, -0.00879596, -0.00883929, -0.00904247, -0.00917101,\n",
              "        -0.00944998, -0.00956212, -0.0099155 , -0.00999444, -0.01121716,\n",
              "        -0.01857176]),\n",
              " 'split3_test_score': array([-0.00181437, -0.00162878, -0.0033926 , -0.00459292, -0.0048988 ,\n",
              "        -0.00508668, -0.00498258, -0.00389215, -0.00329251, -0.01033499,\n",
              "        -0.04620969]),\n",
              " 'std_fit_time': array([2.58103192e-04, 2.32286115e-05, 1.23663120e-04, 3.24920768e-05,\n",
              "        9.18762630e-06, 2.39527626e-05, 2.72611603e-05, 1.33997817e-05,\n",
              "        1.30602196e-05, 7.51562338e-06, 6.94080669e-06]),\n",
              " 'std_score_time': array([5.18339757e-05, 9.15120576e-06, 5.97577513e-05, 1.33758985e-05,\n",
              "        7.88653019e-06, 2.07742496e-05, 4.38489298e-06, 3.58812041e-05,\n",
              "        2.17150773e-05, 2.10700522e-05, 7.61405653e-05]),\n",
              " 'std_test_score': array([0.00269683, 0.00300538, 0.00248224, 0.00221046, 0.0021659 ,\n",
              "        0.00227394, 0.0023846 , 0.00272145, 0.00257456, 0.00549033,\n",
              "        0.02056599])}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 109
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Aq9KPtQr6Gz5"
      },
      "source": [
        "Our best model occurs for $\\alpha=0.01$. We also output the mean cross-validation error at different $\\alpha$ (with a negative sign, as scikit-learn likes to maximize negative error which is equivalent to minimizing error).\n",
        "\n",
        "### Refitting on entire training set\n",
        "\n",
        "We refit the estimator on old training set, and calculate and plot the test set error and the polynomial coefficients. Notice how many of these coefficients have been pushed to lower values or 0.\n",
        "\n",
        "\n",
        ">YOUR TURN NOW: assign to variable est the classifier obtained by fitting the entire training set using the best $\\alpha$ found above."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vdYXfoZH6Gz5",
        "outputId": "4a35aacb-8bca-48ca-9a76-95f0835ce7e4"
      },
      "source": [
        "#Store in est a new classifier fit on the entire training set with the best alpha\n",
        "#your code here\n",
        "#est = fitmodel.best_estimator_\n",
        "alphawechoose=fitmodel.best_params_['alpha']\n",
        "est = Ridge(alpha=alphawechoose)\n",
        "est.fit(Xtrain, ytrain)\n"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ridge(alpha=1e-06, copy_X=True, fit_intercept=True, max_iter=None,\n",
              "      normalize=False, random_state=None, solver='auto', tol=0.001)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PjpzAUjT6Gz5"
      },
      "source": [
        "def plot_functions_onall(est, ax, df, alpha, xtrain, ytrain, Xtrain, xtest, ytest):\n",
        "    \"\"\"Plot the approximation of ``est`` on axis ``ax``. \"\"\"\n",
        "    ax.plot(df.x, df.f, color='k', label='f')\n",
        "    ax.plot(xtrain, ytrain, 's', alpha=0.4, label=\"train\")\n",
        "    ax.plot(xtest, ytest, 's', alpha=0.6, label=\"test\")\n",
        "    transx=np.arange(0,1.1,0.01)\n",
        "    transX = PolynomialFeatures(20).fit_transform(transx.reshape(-1,1))\n",
        "    ax.plot(transx, est.predict(transX), '.', alpha=0.6, label=\"alpha = %s\" % str(alpha))\n",
        "    #print est.predict(transX)\n",
        "    ax.set_ylim((0, 1))\n",
        "    ax.set_xlim((0, 1))\n",
        "    ax.set_ylabel('y')\n",
        "    ax.set_xlabel('x')\n",
        "    ax.legend(loc='lower right')"
      ],
      "execution_count": 98,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "JMrmYLb16Gz5",
        "outputId": "fbf3a5f9-397f-4bf4-e9fe-86734457286f"
      },
      "source": [
        "fig, rows = plt.subplots(1, 2, figsize=(12, 5))\n",
        "l,r=rows\n",
        "plot_functions_onall(est, l, df, alphawechoose, xtrain, ytrain, Xtrain, xtest, ytest)\n",
        "plot_coefficients(est, r, alphawechoose)"
      ],
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ua3QgRLI6Gz6"
      },
      "source": [
        "As we can see, the best fit model is now chosen from the entire set of 20th order polynomials, and a non-zero hyperparameter $\\alpha$ that we fit for ensures that only smooth models amonst these polynomials are chosen, by setting most of the polynomial coefficients to something close to 0 (Lasson sets them exactly to 0).\n",
        "\n",
        "Why do we seem to need a larger alpha than before?"
      ]
    }
  ]
}