Practical1.ipynb

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      "name": "Practical1.ipynb",
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      "name": "python3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "id1w7kwZVF3I"
      },
      "source": [
        "# Practical 1 : Implementation of Linear Regression (Ridge, Lasso)\n",
        "\n",
        "First part:\n",
        "- Implement linear regression model \n",
        "    - using least squares method\n",
        "    - implement directly using the NumPy package\n",
        "\n",
        "Second part:\n",
        "- regularization\n",
        "- polynomial basis expansion\n",
        "- cross validation\n",
        "- scikit-learn: https://scikit-learn.org/\n",
        "\n",
        "You will need to use the following:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CTZv9o5i4gy3"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import _pickle as cp"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b1-ZQWqTVPno"
      },
      "source": [
        "For the purpose of testing, we’ll use the winequality dataset. The dataset is available here:\n",
        "https://archive.ics.uci.edu/ml/datasets/Wine+Quality In order to make it easier to import the dataset, we’ve converted the data to the numpy array format and shuffled it so that you can start the practical directly. The dataset is available on the course website. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TzDL9RQiVaPY"
      },
      "source": [
        "The dataset has two files. We’ll focus on the white wine data, which is the larger dataset. You can load the data from the files as follows:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NYkwbebUVO_i",
        "outputId": "bca1145b-d843-4320-9f59-40255e8a3df2"
      },
      "source": [
        "# load the dataset\n",
        "# X is a matrix such that each row stores a data record \n",
        "# y is a vector of the corresponding labels of the records\n",
        "X, y = cp.load(open('winequality-white.pickle', 'rb'))\n",
        "\n",
        "# check the size of the data\n",
        "print(\"X is a matrix with shape {}, which has {} records and {} attributes.\".format(X.shape, X.shape[0], X.shape[1]))\n",
        "print(\"y is a vector with {} values, which stores the corresponding labels of the data records in X\".format(y.shape[0]))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "X is a matrix with shape (4898, 11), which has 4898 records and 11 attributes.\n",
            "y is a vector with 4898 values, which stores the corresponding labels of the data records in X\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CGuNg0KbWN0z"
      },
      "source": [
        "In order to get consistent results, all students should use the same 80% of the data as training\n",
        "data. We’ll use the remaining as test data. To achieve this split run the following:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6ZqbBa8bWNYg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b4f4af44-bd4f-40ed-99e2-447a473170d4"
      },
      "source": [
        "# The function splits the dataset into the training dataset and the test dataset.\n",
        "# The parameter split_coeff is a percentage value such that\n",
        "# the first split_coeff of the dataset goes to the training dataset, \n",
        "# and the remaining data goes to the test dataset.\n",
        "def split_data(X, y, split_coeff):\n",
        "    N, _ = X.shape # get the number of records (rows)\n",
        "    train_size = int(split_coeff * N) # use the first split_coeff of the data as the training data\n",
        "    X_train = X[:train_size] # the first training_size records\n",
        "    y_train = y[:train_size]\n",
        "    X_test = X[train_size:] # the last test_size records\n",
        "    y_test = y[train_size:]\n",
        "    return X_train, y_train, X_test, y_test\n",
        "\n",
        "X_train, y_train, X_test, y_test = split_data(X, y, 0.8) # use 80% of the data as training data\n",
        "\n",
        "# check the size of the splitted dataset\n",
        "print(\"Shape of X_train:\", X_train.shape)\n",
        "print(\"Shape of y_train:\", y_train.shape)\n",
        "print(\"Shape of X_test:\", X_test.shape)\n",
        "print(\"Shape of y_test:\", y_test.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape of X_train: (3918, 11)\n",
            "Shape of y_train: (3918,)\n",
            "Shape of X_test: (980, 11)\n",
            "Shape of y_test: (980,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RL1N8mKUWYnx"
      },
      "source": [
        "We’ll not touch the test data except for reporting the errors of our learned models"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q2yKNR49Wkn8"
      },
      "source": [
        "## Understanding What We’re Predicting\n",
        "\n",
        "Before we get to training a linear model on the data and using it to make predictions, let’s look\n",
        "at the spread of y values on the training set. The values are integers between 3 and 9 indicating\n",
        "the quality of the wine.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-PMpsZNSWthB"
      },
      "source": [
        "### **Task 1**\n",
        "Make a bar chart showing the distribution of y values appearing in the training data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4L_JDK3dWrsR",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "7d4468bd-c3c7-49f1-ea40-ea38dd0aef97"
      },
      "source": [
        "#@title\n",
        "# Task 1: \n",
        "# the function takes the training dataset as the input, and make the bar chart\n",
        "def plot_bar_chart_score(X_train, y_train):\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    x,counts=np.unique(y_train,return_counts=True)\n",
        "    plt.bar(x,counts)\n",
        "    plt.title('Distribution of scores of wines')\n",
        "    plt.xlabel('Score')\n",
        "    plt.ylabel('Number of wines')\n",
        "    plt.show()\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "plot_bar_chart_score(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GxjlElni2FcH"
      },
      "source": [
        "### **Task 2** \n",
        "Implement the trivial predictor, which uses the average value of y on the training set as the prediction for ever datapoint. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-V3xFYexX1lt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7e33de2e-ca99-4efc-f4b2-a52f0f89960a"
      },
      "source": [
        "#@title\n",
        "# Task 2: implement the simplest predictor\n",
        "# The function computes the average value of y on the training label values\n",
        "def compute_average(y_train):\n",
        "    # The code below is just for compilation. \n",
        "    # You need to delete it and write your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    return y_train.mean()\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "y_train_avg = compute_average(y_train)\n",
        "print(\"Average of y on the training label values is {}\".format(y_train_avg))\n",
        "\n",
        "# The simplest predictor returns the average value.\n",
        "def simplest_predictor(X_test, y_train_avg):\n",
        "    return y_train_avg\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Average of y on the training label values is 5.878764675855028\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x531Q_SxXV14"
      },
      "source": [
        "### **Task 3**\n",
        "Report the mean squared error, i.e., the average of the squared residuals, using this simplest of predictors on the training and test data. We should hope that our models beat at lease this baseline. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mV8l6Ci9YlgL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4724e97b-1e4d-41c3-e2d1-b56f121ee10d"
      },
      "source": [
        "# We will evaluate our simplest predictor here. \n",
        "# Implement a function that can report the mean squared error \n",
        "# of a predictor on the given test data\n",
        "# Input: test dataset and predictor\n",
        "# Output: mean squared error of the predictor on the given test data\n",
        "def test_data(X_test, y_test, predictor: callable=None):\n",
        "    # Applies the predictor to each row to compute the predicted values\n",
        "    y_predicted = np.apply_along_axis(predictor, 1, X_test)\n",
        "\n",
        "    # TODO: compute the mean squared error of y_predicted\n",
        "    # The code below is just for compilation. \n",
        "    # You need to delete it and write your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    mse = np.square(np.subtract(y_test,y_predicted)).mean()\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "    return mse\n",
        "\n",
        "# use the above function test_data to evaluate the simplest predictor\n",
        "# we use the lambda function here to pass the function simplest_predictor to the evaluator.\n",
        "mse_simplest_predictor_train = test_data(X_train, y_train, lambda x: simplest_predictor(x, y_train_avg))\n",
        "mse_simplest_predictor_test = test_data(X_test, y_test, lambda x: simplest_predictor(x, y_train_avg))\n",
        "\n",
        "# Report the result\n",
        "print('Simplest Predictor')\n",
        "print('--------------------------------------------------------------------------------\\n')\n",
        "print('MSE (Training) = %.4f' % mse_simplest_predictor_train)\n",
        "print('MSE (Testing)  = %.4f' % mse_simplest_predictor_test)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Simplest Predictor\n",
            "--------------------------------------------------------------------------------\n",
            "\n",
            "MSE (Training) = 0.7768\n",
            "MSE (Testing)  = 0.8139\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "geiyM1Nea0az"
      },
      "source": [
        "## Linear Model Using Least Squares\n",
        "\n",
        "Let us first fit a linear regression model and then calculate the training and test error. We’ll\n",
        "actually use the closed form solution of the least squares estimate for the linear model. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cRPPA6HMbNOr"
      },
      "source": [
        "### **Task 4**\n",
        "Is it strictly necessary to standardize the data for the linear model using the least squares method? Why?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9he5QMmfqL3_"
      },
      "source": [
        "No, it is not strictly necessary, but will be useful. First of all, it makes all numerical columns in a same scale to make sure all variables contribute equally. Secondly, Standardization assumes the data follow a Gaussian distribution, and that satisfied the assumption of linear model. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WSEwFGp_bqAI"
      },
      "source": [
        "### **Task 5**\n",
        "Standardize the data, i.e., make the data for every feature have mean 0 and variance 1. \n",
        "\n",
        "We do the standardization using the training data, and we need to remember the means and\n",
        "the standard deviations so that they can be applied to the test data as well. Apply the\n",
        "standardization so that every feature in the training data has mean 0 and variance 1. Apply\n",
        "the same transformation to the test data. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "trjwkcgybhDH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "59f91f41-0d28-4e6c-b697-8749d210eb71"
      },
      "source": [
        "# Input: training data\n",
        "# Output: standardize training data, standard deviations and means\n",
        "def standardize_data(X):\n",
        "    # TODO: compute mean, standard deviations and the standardized data\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    mean=X.mean(axis=0)\n",
        "    std=X.std(axis=0)\n",
        "    X_std = (X-mean)/std\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "    return X_std, mean, std\n",
        "\n",
        "X_train_std, X_train_mean, X_train_std_div = standardize_data(X_train)\n",
        "print(\"X_train_std:\", X_train_std.shape)\n",
        "print(\"Mean:\", X_train_mean)\n",
        "print(\"Standard deviation:\", X_train_std_div)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "X_train_std: (3918, 11)\n",
            "Mean: [6.85427514e+00 2.78390761e-01 3.34892802e-01 6.42623788e+00\n",
            " 4.58213374e-02 3.53263144e+01 1.38513272e+02 9.94040729e-01\n",
            " 3.18647524e+00 4.89055641e-01 1.05115799e+01]\n",
            "Standard deviation: [8.39100902e-01 9.95630176e-02 1.24249975e-01 5.06377532e+00\n",
            " 2.16660282e-02 1.71004677e+01 4.23956179e+01 2.97972269e-03\n",
            " 1.49949475e-01 1.12992053e-01 1.22536544e+00]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RjzbA5JpM759",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d752a94a-d0e0-41f1-bf4f-8436ea76b285"
      },
      "source": [
        "# TODO: Standardize the test data using the mean and standrad deviation you computed for the training data\n",
        "###################################################\n",
        "##### YOUR CODE STARTS HERE #######################\n",
        "###################################################\n",
        "X_test_std = (X_test-X_train_mean)/X_train_std_div\n",
        "print(X_test_std.shape)\n",
        "###################################################\n",
        "##### YOUR CODE ENDS HERE #########################\n",
        "###################################################"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(980, 11)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vT4_Sl42bxmD"
      },
      "source": [
        "### **Task 6**\n",
        "Implement the linear model predictor, and report the mean squared error using the linear model on the training and test data.\n",
        "\n",
        "We will do this in several steps. We need to implement the function for computing the parameters based on the training dataset. Note we need to add the bias column to the dataset. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A4JtLr6pdJV7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5c876bd5-3d50-4ba7-c81a-ac0e0111fc5d"
      },
      "source": [
        "# the function adds a column of ones to the front of the input matrix\n",
        "def expand_with_ones(X):\n",
        "    # TODO: adds a column of ones to the front of the input matrix\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    X_one = np.ones((np.shape(X)[0], 1))\n",
        "    X_out = np.hstack((X_one,X))\n",
        "    return X_out\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "# The function computes the parameters\n",
        "def least_squares_compute_parameters(X_input, y):\n",
        "    # add the bias column to the dataset\n",
        "    X = expand_with_ones(X_input)\n",
        "\n",
        "    # TODO: compute the parameters based on the expanded X and y\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    X = expand_with_ones(X_input)\n",
        "    T = np.dot(np.dot(np.linalg.inv(np.dot(X.T, X)), X.T), y)\n",
        "    return T\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "# train the linear model parameters\n",
        "w = least_squares_compute_parameters(X_train_std, y_train) \n",
        "print(\"w:\", w.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "w: (12,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lasj_1PpeZib"
      },
      "source": [
        "We then implement the linear model predictor given the dataset and the parameters. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lb-hNagxc3Wj"
      },
      "source": [
        "# Implement the linear model predictor\n",
        "# Input: test data and parameters\n",
        "# Output: predicted values\n",
        "def linear_model_predictor(X, w):\n",
        "    # TODO: compute the predicted values based on the test dataset and the parameters\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    Y_predict = np.dot(X,w)\n",
        "    return Y_predict\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cFOYpwbufz7J"
      },
      "source": [
        "We can now evaluate our linear model predictor on the test dataset. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LuHHmn2RB55j",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5cdcbc9e-68aa-4481-ad73-665e76dd1a44"
      },
      "source": [
        "# use the function test_data to evaluate the linear model predictor\n",
        "mse_linear_model_predictor = test_data(expand_with_ones(X_test_std), y_test, lambda x: linear_model_predictor(x, w))\n",
        "print(\"Mean squared error is {}\".format(mse_linear_model_predictor))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean squared error is 0.5607292042283472\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zqj4HKAihF7Q"
      },
      "source": [
        "## Learning Curves\n",
        "\n",
        "Let us see if the linear model is overfitting or underfitting. Since the dataset is somewhat large and there are only 11 features, our guess should be that it may either be underfitting or be about right."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XDLCsjzWhMCp"
      },
      "source": [
        "Starting with 20 datapoints, we’ll use training datasets of increasing size, in increments of 20 up to about 600 datapoints. For each case train the linear model only using the first n elements of\n",
        "the training data. Calculate the training error (on the data used) and the test error (on the full test set). Plot the training error and test error as a function of the size of the dataset used for\n",
        "training."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MNf11kurCgKF"
      },
      "source": [
        "### **Task 7** \n",
        "Implement a function that evaluates the linear model over the training dataset with the input size.\n",
        "The function takes a dataset and the split coefficient as inputs, and\n",
        "1. splits the data to training and test datasets,\n",
        "2. standardizes the data,\n",
        "3. trains the linear model, and\n",
        "4. reports the mse of the linear model predictor on both training and test datasets. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UcGRQBrEb106",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fde3147f-cc2e-4558-c360-e2f1309df924"
      },
      "source": [
        "# Input: dataset and split coefficient\n",
        "# Output: mse of the linear model predictor on both the training and test datasets\n",
        "def train_and_test(X, y, split_coeff):\n",
        "    # TODO: implement the function \n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    # Hints: use the functions you have implemented\n",
        "    X_train2, y_train2, X_test2, y_test2 = split_data(X, y,split_coeff)\n",
        "    X_train2_std, X_train2_mean, X_train2_std_div=standardize_data(X_train2)\n",
        "    X_test2_std, X_test2_mean, X_test2_std_div=standardize_data(X_test2) \n",
        "    \n",
        "    w = least_squares_compute_parameters(X_train2_std, y_train2) \n",
        "    \n",
        "    mse_train = test_data(expand_with_ones(X_train2_std), y_train2, lambda x: linear_model_predictor(x, w))\n",
        "    mse_test = test_data(expand_with_ones(X_test2_std), y_test2, lambda x: linear_model_predictor(x, w))\n",
        "    return mse_train, mse_test\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "mse_train, mse_test = train_and_test(X, y, 0.8)\n",
        "print('MSE using Linear Models')\n",
        "print('-----------------------\\n')\n",
        "print('MSE (Training) = %.4f' % mse_train)\n",
        "print('MSE (Testing)  = %.4f' % mse_test)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "MSE using Linear Models\n",
            "-----------------------\n",
            "\n",
            "MSE (Training) = 0.5640\n",
            "MSE (Testing)  = 0.5621\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NTJw_BrzhRwi"
      },
      "source": [
        "### **Task 8**\n",
        "Report the learning curves plot. Also, explain whether you think the model is underfitting or not and how much data you need before getting the optimal test error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jDsdh4T3hcIU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "59a53389-0edd-4eef-8194-7f46ec3342cb"
      },
      "source": [
        "mse_train_v = []\n",
        "mse_test_v = []\n",
        "\n",
        "TRAINING_SIZE_MAX = 601\n",
        "TRAINING_SIZE_MIN = 20\n",
        "\n",
        "# compute the errors over datasets with different sizes\n",
        "for train_size in range(TRAINING_SIZE_MIN, TRAINING_SIZE_MAX, 20):\n",
        "    # TODO: compute the training error and test error on datasets with size train_size\n",
        "    # and add them to mse_train_v and mse_test_v, respectively\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    w = least_squares_compute_parameters(X_train_std[:train_size], y_train[:train_size]) \n",
        "    mse_train = np.mean(np.square(linear_model_predictor(expand_with_ones(X_train_std)[:train_size], w)-y_train[:train_size]))\n",
        "    mse_test = np.mean(np.square(linear_model_predictor(expand_with_ones(X_test_std), w)-y_test))\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "    mse_train_v.append(mse_train)\n",
        "    mse_test_v.append(mse_test)\n",
        "\n",
        "# The below code outputs the plot of mse from different training sizes\n",
        "plt.figure(2)\n",
        "plt.plot(np.arange(TRAINING_SIZE_MIN, TRAINING_SIZE_MAX, 20), mse_train_v, 'r--', label=\"Training Error\")\n",
        "plt.plot(np.arange(TRAINING_SIZE_MIN, TRAINING_SIZE_MAX, 20), mse_test_v, 'b-', label=\"Test Error\")\n",
        "plt.xlabel('Dataset Size')\n",
        "plt.ylabel('Mean Squared Error')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9A9VqDTzOdfd"
      },
      "source": [
        "The model is right fitting, and the number of data is 220. With data size increases, the MSE is not decreasing. \n",
        "\n",
        "."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "djpsaTu_kK3T"
      },
      "source": [
        "## Polynomial Basis Expansion with Ridge and Lasso\n",
        "\n",
        "For this part use the following from the scikit-learn package. Read the documentation available here: http://scikit-learn.org/stable/modules/classes.html\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pnw2FEvqkdV_"
      },
      "source": [
        "You will need the use the following:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9TM0nkNbkhfM"
      },
      "source": [
        "# You will need the following libs. \n",
        "# Fell free to import other libs. \n",
        "\n",
        "# import the preprocessing libs for standarization and basis expansion\n",
        "from sklearn import preprocessing\n",
        "from sklearn.preprocessing import StandardScaler, PolynomialFeatures \n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn import linear_model\n",
        "# Ridge and Lasso linear model\n",
        "from sklearn.linear_model import Ridge, Lasso "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9fAfOfXCksT9"
      },
      "source": [
        "Try 5 powers of 10 for lambda from 10^-2 to 10^2 and use degree 2 basis expansion. Fit ridge and lasso using degree 2 polynomial expansion with these values of lambda. You should pick the optimal values for lambda using a validation set. Set the last 20% of the training set for the purpose of validation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pCwBPuOXlRF7"
      },
      "source": [
        "### **Task 9**\n",
        "Let's implement the function for expanding the basis of the dataset. \n",
        "\n",
        "Hints: use `PolynomialFeatures`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "50azFolql1qA"
      },
      "source": [
        "def expand_basis(X, degree):\n",
        "    # TODO: expand the basis of X for the degree\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    poly = PolynomialFeatures(degree, include_bias=False)\n",
        "    X = poly.fit_transform(X)\n",
        "    return X\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6jwkPevimQri"
      },
      "source": [
        "### **Task 10**\n",
        "Prepare the training, test and validation data using the expanded dataset. Expand and standardize the the data. \n",
        "\n",
        "Hints: you can use `StandardScaler` and `std_scaler` to standardize the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dQCq4G9YmW7w"
      },
      "source": [
        "# TODO: the training, test and validation data using the expanded dataset.\n",
        "# The code below is just for compilation. \n",
        "# You need to replace it by your own code.\n",
        "def prepare_data(X, y, degree):\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    X = expand_basis(X, degree)\n",
        "    scaler = preprocessing.StandardScaler()\n",
        "    X_scaled = scaler.fit_transform(X)\n",
        "    \n",
        "    N, _ = X_scaled.shape # get the number of records (rows)\n",
        "    train_size = int(0.8 * N) # use the first split_coeff of the data as the training data\n",
        "     # training data\n",
        "    X_train = X_scaled[:train_size] # the first training_size records\n",
        "    y_train = y[:train_size]\n",
        "     # test data\n",
        "    X_test = X_scaled[train_size:] # the last test_size records\n",
        "    y_test = y[train_size:]\n",
        "\n",
        "    # further split the training data to training and validation data\n",
        "    X_train_n, y_train_n, X_train_v, y_train_v = split_data(X_train, y_train, 0.8)\n",
        "\n",
        "    # further split the training data to training and validation data\n",
        "    # training data\n",
        "    N1, _ = X_train.shape # get the number of records (rows)\n",
        "    train_size1 = int(0.8 * N1)\n",
        "    X_train_n = X_train[:train_size1]\n",
        "    y_train_n = y_train[:train_size1]\n",
        "    \n",
        "    # validation data\n",
        "    X_train_v = X_train[train_size1:]\n",
        "    y_train_v = y_train[train_size1:]\n",
        "\n",
        "    return X_train, y_train, X_train_n, y_train_n, X_train_v, y_train_v, X_test, y_test\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "X_train, y_train, X_train_n, y_train_n, X_train_v, y_train_v, X_test, y_test = prepare_data(X, y, 2) # here we expand the dataset with degree 2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i3BxxtM3nghU"
      },
      "source": [
        "### **Task 11**\n",
        "We have prepared the training data and the validation data. We can now choose the hyper parameter lambda for Ridge and Lasso using the validation data. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SvXcAGW1oHq1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        },
        "outputId": "995962e5-26e5-46c7-b5c7-86a1c367723d"
      },
      "source": [
        "# The function takes the training and validation data as inputs, and \n",
        "# returns the lambda value that has the minimal mse\n",
        "# We use is_ridge to indicate the model we consider. \n",
        "# is_ridge = True indicates Ridge while is_ridge = False indicates Lasso\n",
        "def choose_hyper_param(X_train_n, y_train_n, X_train_v, y_train_v, is_ridge: bool):\n",
        "    mse_arr = []\n",
        "    lam_arr = []\n",
        "\n",
        "    # Try lambda values from 10^-2 to 10^2. \n",
        "    # Record the mse and the lambda values in mse_arr and lam_arr\n",
        "    # The code below is just for compilation. \n",
        "    # You need to replace it by your own code.\n",
        "    ###################################################\n",
        "    ##### YOUR CODE STARTS HERE #######################\n",
        "    ###################################################\n",
        "    for pow_lam in range(-2, 2):\n",
        "        lam = 10 ** pow_lam\n",
        "        if is_ridge == True:\n",
        "            model_ridge = Ridge(alpha=lam)\n",
        "            y_ridge_predicted = model_ridge.fit(X_train_n, y_train_n).predict(X_train_n)\n",
        "            w = least_squares_compute_parameters(X_train_n, y_ridge_predicted) \n",
        "        else: \n",
        "            model_lasso = Lasso(alpha=lam)\n",
        "            y_lasso_predicted = model_lasso.fit(X_train_n, y_train_n).predict(X_train_n)\n",
        "            w = least_squares_compute_parameters(X_train_n, y_lasso_predicted) \n",
        "        \n",
        "        mse = test_data(expand_with_ones(X_train_v), y_train_v, lambda x: linear_model_predictor(x, w))\n",
        "        mse_arr.append(mse) # add the mse when using the hyperparameter lam\n",
        "        lam_arr.append(lam)\n",
        "    ###################################################\n",
        "    ##### YOUR CODE ENDS HERE #########################\n",
        "    ###################################################\n",
        "\n",
        "\n",
        "    # get the index of the lambda value that has the minimal use\n",
        "    lambda_idx_min = np.argmin(np.array(mse_arr))\n",
        "    # print(lam_arr[lambda_idx_min])\n",
        "\n",
        "    # plot of the lambda values and their mse\n",
        "    plt.figure()\n",
        "    plt.semilogx(lam_arr, mse_arr)\n",
        "\n",
        "    # return the best lambda value\n",
        "    return lam_arr[lambda_idx_min]\n",
        "\n",
        "# call the function to choose the lambda for Ridge and Lasso\n",
        "lam_ridge = choose_hyper_param(X_train_n, y_train_n, X_train_v, y_train_v, True)\n",
        "lam_lasso = choose_hyper_param(X_train_n, y_train_n, X_train_v, y_train_v, False)\n",
        "\n",
        "print(\"Ridge lambda:\", lam_ridge)\n",
        "print(\"Lasso lambda:\", lam_lasso)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ridge lambda: 0.01\n",
            "Lasso lambda: 0.01\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FAuX0uU5k9qD"
      },
      "source": [
        "### **Task 12**:\n",
        "Once you’ve obtained the optimal values for lambda for Ridge and Lasso, train these models using these hyperparameters on the full training data. Then report\n",
        "the training and test error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VmwHESkg77zK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6e686e3d-7ddb-46ab-b97a-7f492043fe42"
      },
      "source": [
        "# TODO: train the Ridge and Lasso models using their best parameters, and\n",
        "#       report their mse\n",
        "###################################################\n",
        "##### YOUR CODE STARTS HERE #######################\n",
        "###################################################\n",
        "model_ridge = Ridge(alpha=lam_ridge)\n",
        "model_ridge.fit(X_train, y_train)\n",
        "mse_ridge_train = mean_squared_error(y_train, model_ridge.predict(X_train))\n",
        "mse_ridge_test = mean_squared_error(y_test, model_ridge.predict(X_test))\n",
        "\n",
        "model_lasso = Lasso(alpha=lam_lasso)\n",
        "model_lasso.fit(X_train, y_train) \n",
        "mse_lasso_train = mean_squared_error(y_train, model_lasso.predict(X_train))\n",
        "mse_lasso_test = mean_squared_error(y_test, model_lasso.predict(X_test))\n",
        "###################################################\n",
        "##### YOUR CODE ENDS HERE #########################\n",
        "###################################################\n",
        "\n",
        "# Report the result\n",
        "print('For Ridge Regression with using degree %d polynomial expansion and lambda = %.4f' % (2, lam_ridge))\n",
        "print('--------------------------------------------------------------------------------\\n')\n",
        "print('MSE (Training) = %.4f' % mse_ridge_train)\n",
        "print('MSE (Testing)  = %.4f' % mse_ridge_test)\n",
        "\n",
        "print('\\n\\nFor Lasso with using degree %d polynomial expansion and lambda = %.4f' % (2, lam_lasso))\n",
        "print('---------------------------------------------------------------------\\n')\n",
        "print('MSE (Training) = %.4f' % mse_lasso_train)\n",
        "print('MSE (Testing)  = %.4f' % mse_lasso_test)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "For Ridge Regression with using degree 2 polynomial expansion and lambda = 0.0100\n",
            "--------------------------------------------------------------------------------\n",
            "\n",
            "MSE (Training) = 0.5014\n",
            "MSE (Testing)  = 0.5161\n",
            "\n",
            "\n",
            "For Lasso with using degree 2 polynomial expansion and lambda = 0.0100\n",
            "---------------------------------------------------------------------\n",
            "\n",
            "MSE (Training) = 0.5489\n",
            "MSE (Testing)  = 0.5422\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.639680512979794, tolerance: 0.3043413221031145\n",
            "  positive)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Os9tKKLd8gMU"
      },
      "source": [
        "## Larger Degrees\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sfqRAlv1PBXi"
      },
      "source": [
        "### **Task 13**\n",
        "Try using higher degree basis expansion. You may want to use k-fold cross validation to determine\n",
        "the values of hyperparameters rather than just keeping a validation set. \n",
        "\n",
        "Hints: Use `KFold` to do this automatically. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ra5IFHqouRor",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "fb8858c8-a32e-488a-ec32-f203511b976f"
      },
      "source": [
        "# TODO: Try using higher degree basis expansion. Find the degree that gives the minimal mse. \n",
        "###################################################\n",
        "##### YOUR CODE STARTS HERE #######################\n",
        "###################################################\n",
        "from sklearn.model_selection import KFold\n",
        "X = expand_basis(X, 3)\n",
        "scaler = StandardScaler()\n",
        "X = scaler.fit_transform(X)\n",
        "\n",
        "kf = KFold(n_splits=10)\n",
        "kf.get_n_splits(X)\n",
        "#print(kf)\n",
        "\n",
        "for train_index, test_index in kf.split(X):\n",
        "    #print(\"TRAIN:\", train_index, \"TEST:\", test_index)\n",
        "    X_train, X_test = X[train_index], X[test_index]\n",
        "    y_train, y_test = y[train_index], y[test_index]\n",
        "    \n",
        "    lam_ridge = choose_hyper_param(X_train, y_train, X_test, y_test, True)\n",
        "    lam_lasso = choose_hyper_param(X_train, y_train, X_test, y_test, False)\n",
        "   # print(\"Ridge lambda:\", lam_ridge)\n",
        "    #print(\"Lasso lambda:\", lam_lasso)\n",
        "    \n",
        "ridge = Ridge(alpha=lam_ridge)\n",
        "ridge.fit(X_train, y_train)\n",
        "\n",
        "mse_ridge_train = mean_squared_error(y_train, ridge.predict(X_train))\n",
        "mse_ridge_test = mean_squared_error(y_test, ridge.predict(X_test))\n",
        "\n",
        "lasso = Lasso(alpha=lam_lasso) \n",
        "lasso.fit(X_train,y_train)\n",
        "\n",
        "mse_lasso_train = mean_squared_error(y_train, lasso.predict(X_train))\n",
        "mse_lasso_test = mean_squared_error(y_test, lasso.predict(X_test))\n",
        "\n",
        "# Report the result\n",
        "print('For Ridge Regression with using degree %d polynomial expansion and lambda = %.4f' % (lam_ridge, lam_ridge))\n",
        "print('--------------------------------------------------------------------------------\\n')\n",
        "print('MSE (Training) = %.4f' % mse_ridge_train)\n",
        "print('MSE (Testing)  = %.4f' % mse_ridge_test)\n",
        "\n",
        "print('\\n\\nFor Lasso with using degree %d polynomial expansion and lambda = %.4f' % (lam_lasso, lam_lasso))\n",
        "print('---------------------------------------------------------------------\\n')\n",
        "print('MSE (Training) = %.4f' % mse_lasso_train)\n",
        "print('MSE (Testing)  = %.4f' % mse_lasso_test)\n",
        "###################################################\n",
        "##### YOUR CODE ENDS HERE #########################\n",
        "###################################################"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.47380730263239457, tolerance: 0.3454274954627946\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.45220183082983567, tolerance: 0.3469309437386567\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.3622527015872947, tolerance: 0.35048239564428196\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.4681137292641324, tolerance: 0.34529471415607854\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.40642835885137174, tolerance: 0.34346240925589827\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.4062678758805305, tolerance: 0.34353903379450984\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.4953934708464658, tolerance: 0.3449723746881382\n",
            "  positive)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/linear_model/_coordinate_descent.py:476: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.4953934708464658, tolerance: 0.3449723746881382\n",
            "  positive)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "For Ridge Regression with using degree 10 polynomial expansion and lambda = 10.0000\n",
            "--------------------------------------------------------------------------------\n",
            "\n",
            "MSE (Training) = 0.4751\n",
            "MSE (Testing)  = 0.5075\n",
            "\n",
            "\n",
            "For Lasso with using degree 0 polynomial expansion and lambda = 0.0100\n",
            "---------------------------------------------------------------------\n",
            "\n",
            "MSE (Training) = 0.5363\n",
            "MSE (Testing)  = 0.5405\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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muPuBOh4n0qAaNTIu/FoHLvxaB1Zu3c30N8r486INzFhYxogeWUwelk/fzrpRjSS+SC4BZQObw55vCcaqG2Nmy81slpnl1rB9PPB0tbFfBsfcbWY1vmffzG40sxIzKykvL49guiLR0yM7g7vH9aH4pxdw43mnU/x+OZf8aSFjHlzIyyu3c6QycXpoItVFcgloLDDc3auu608Ezgm/3GNmbYF97n7IzG4Cxrn7hWHbs4DlQCd3Pxw2tgNoCkwFPnD3O443F10Ckljbf6iC50o2M31BGZt3fUbnNqdw3ZA8LivM5VTdqEbi1Mk0gbcC4b/R5wRjR7n7Tnc/FDwtAvpXO8flwF+rfvgHx2z3kEPAo4QuNYnEtVObNWbSkHz++eMLePDKfmS2bMZ/vbSawb9+ld/MeY8duw/GeooiEYvkV5YlQFczyyf0g388cEX4DmaW5e7bg6cjgTXVzjEB+FlNx1joD65HAytPYP4iMZHWyBjRM4sRPbN4e9MnTC8uY+r8DygqLuW7vTsxeVg+Z3fSjWokvtUaAO5eYWZTgLlAGvCIu68yszuAEnefDdxiZiOBCmAXMKnqeDPLI1RBvF7t1E+aWSZgwDLg5pN+NSIx0K/zafS78jQ27zrAows2MHPJJv76zlYGF7TlhvPy+Xo33ahG4pPeCCYSZbs/O8wzwQfQbd99kNMzT+X6oQVc2i+b9Cb6ADppePosIJEGdvhIJf+9YjvTiktZuXUPbU5tylWDunD14C60a6Eb1UjDUQCIxIi782bZLoqKy3j1vQ9pktaIS/pkM3lYPl11oxppAPowOJEYMTMGFbRlUEFbSsv3Mf2NMv7y9hZmlmzm62dmMnloAUPOaKsPoJMGpwpAJAZ27f+cJxdv5LFFG/l4X+hGNZOHFTCydyeaNtYH0El06RKQSBw6VHGEF5dtY3pxGWs/3Ev7ls245tw8rjynM61P0Y1qJDoUACJxzN0pfv9jphWXUvz+xzRvkha6Uc3QfPLbnRrr6UmCUwCIJIi1O/ZSVFzKi8u2cbiykm+e1YEbhhUwIO809QnkhCgARBLMR3sP8vii0I1qPjlwmF45GUweVsDFPTrSWDeqkTpQAIgkqM8+P8Jf3t7CI2+UUfrxfrJbN2fSuXmMG5hLq/QmsZ6eJAAFgEiCq6x0/ue9j5hWXMqbZbto0awx4wbkcu2QPHJO041q5NgUACJJZMWW3RS9Ucrfloc+g3F4j47cMKyAPrmtYzwziUcKAJEktO3Tz3hs4QaeemsTew9WMCDvNK4fWsC3uncgTR9AJwEFgEgS23eogmeXbOaRBWVs+eQzurQ9heuG5HNZYQ6nNNUb/lOdAkAkBVQcqeSV1R8yrbiUdzZ9SkbzJlxxTmcmnZtHh1bpsZ6exIgCQCTFLN0Y+gC6uat2kNbIQjeqGVpA906tYj01aWD6MDiRFNO/Sxv6d2nDpp0HeGRBGc+WbOb5t7cy5Iy2TB5awPndMnWjmhSnCkAkRew+cJinl2xixoIN7NhzkDPat+D6oflc0lc3qkl2ugQkIgB8XvHFjWpWbdtD21ObMnFwF64apBvVJCsFgIh8ibuzuHQXRcWlvPreRzRt3Igx/bK56bzTydMH0CUV9QBE5EvMjMGnt2Xw6W35oOpGNUu38PzbW/nJRWdy7ZB8vZcgyekTpUSE0zNb8KtLelL8bxcwrGsmv/j7Gi5/eBGl5ftiPTWpRwoAETmqfat0pl3dn7vH9Wb9R/sYcW8xRcWlHKlMnEvFEjkFgIh8iZlxSd8c5t16HsO6tuMXf1/DOFUDSUkBICI1ClUDhdw9rjfvqxpISgoAETmmY1UDZR/vj/XUJAoUACJSq6pq4A+X92bdh3sZfs98VQNJQAEgIhExMy7tl8M/bjtf1UCSUACISJ1UrwZG3Duf6W+UUalqIOEoAESkzqqqgXm3nc+Q09vx87+tZtxUVQOJRgEgIiesQ6t0iq4JVQNrd6gaSDQKABE5KceqBjaoGoh7CgARiYqqauD3l4WqgeH3zucRVQNxTQEgIlFjZozpH6oGzj29HXeoGohrCgARiboOrdKZrmog7ikARKReVFUDr9z6RTUwfupiVQNxRAEgIvWqY0aoGvjdZb1Zs2OPqoE4ogAQkXpnZoztn8M8VQNxRQEgIg2mpmrg0QWqBmIlogAws+FmttbM1pvZ7TVsn2Rm5Wa2LHhMDsYvCBtbZmYHzWx0sC3fzN4MzjnTzJpG96WJSDwKrwYGF7Tl/720mvHTFrNxp6qBhlZrAJhZGvAAMALoDkwws+417DrT3fsEjyIAd3+tagy4EDgAvBLsfydwt7ufAXwCXH/yL0dEEkXHjHQemTSAu8b2Ys32PQy/p5gZqgYaVCQVwEBgvbuXuvvnwDPAqBP4t8YCc9z9gJkZoUCYFWx7DBh9AucUkQRmZlxWmMu8W89nUEEb/kvVQIOKJACygc1hz7cEY9WNMbPlZjbLzHJr2D4eeDr4ui3wqbtX1HJOzOxGMysxs5Ly8vIIpisiiUbVQGxEqwn8EpDn7r2AeYR+oz/KzLKAnsDcup7Y3ae6e6G7F2ZmZkZlsiISf8KrgXNUDTSISAJgKxD+G31OMHaUu+9090PB0yKgf7VzXA781d0PB893Aq3NrPGxzikiqaljRjqPThrAb1UN1LtIAmAJ0DX4q52mhC7lzA7fIfgNv8pIYE21c0zgi8s/uLsDrxHqCwBcA7xYt6mLSLIyMy4vzOWVW887Wg1MUDUQdbUGQHCdfgqhyzdrgGfdfZWZ3WFmI4PdbjGzVWb2LnALMKnqeDPLI1RBvF7t1D8FbjOz9YR6AtNP7qWISLLJymh+tBpYvU3VQLRZ6JfxxFBYWOglJSWxnoaIxMD23Z9x+19W8Pq6cs7Jb8NdY3vTue0psZ5WQjCzpe5eWH1c7wQWkYSQldGcGdd+UQ1cdM98Hlu4QdXASVAAiEjCONobuO08Bua34T9nr2LCtMVs2nkg1lNLSAoAEUk4R6uBMUFv4N75/HmRqoG6UgCISEIyMy4fkMvcW89jQF4b/u+Lq7iiSNVAXSgARCShdWr9RTWwaquqgbpQAIhIwguvBgrDqoHNu1QNHI8CQESSRqfWzXns2gHcOaYnq7aG/lJI1cCxKQBEJKmYGeMGdFY1EAEFgIgkpZqqgccXqRoIpwAQkaRVvRr4jxdXcWXRm6oGAgoAEUl6VdXAby7tyYqtu1UNBBQAIpISzIzxA0PVQP8up6kaQAEgIikmu3Vz/nzdwC9XA4s3pmQ1oAAQkZTzlWrghZUpWQ0oAEQkZVVVA79O0WpAASAiKc3MmFCtGrhqempUAwoAERG+XA0s35Ia1YACQEQkkGrVgAJARKSa6tXA8Hvm88TijSTSLXQjoQAQEalBeDXQt/Np/HtQDWz5JHmqAQWAiMhxZLduzuPXD+RXl/Rk2aZPueju+Tz5ZnJUAwoAEZFamBlXnPNFNfB//poc1YACQEQkQjmnnZJU1YACQESkDmqqBiZOfyshqwEFgIjICaiqBn55SQ/e2fRJQlYDCgARkRNkZlx5TpeErQYUACIiJ6l6NTD8nmKeenNT3FcDCgARkSioqgZe/uF59M7N4H//dUXcVwMKABGRKMptcwpPXH9OQlQDCgARkSirqRq4+pG32PrpZ7Ge2pcoAERE6klVNfCL0T14e2PoL4Wefit+qgEFgIhIPTIzrhoUqgZ65WTws+fjpxpQAIiINIDcNqfw5ORQNbA0TqoBBYCISAOpqgbmxkk1oAAQEWlgVb2Bn8e4GlAAiIjEQKNGxsQYVwMKABGRGKqpGnimgaqBiALAzIab2VozW29mt9ewfZKZlZvZsuAxOWxbZzN7xczWmNlqM8sLxmeYWVnYMX2i9aJERBJJeDXQMzuD2xuoGqg1AMwsDXgAGAF0ByaYWfcadp3p7n2CR1HY+J+Bu9z9LGAg8FHYtp+EHbPsxF+GiEjiq/pLoZ+POrtBqoFIKoCBwHp3L3X3z4FngFGRnDwIisbuPg/A3fe5e/x+MIaISIw1amRMHJzH3B+eR4/sVtz+/AqueXQJO3YfjP6/FcE+2cDmsOdbgrHqxpjZcjObZWa5wVg34FMze97M3jGzu4KKosovg2PuNrNmJ/YSRESST26bU3hq8iB+Pups1u7YgxP9KiBaTeCXgDx37wXMAx4LxhsDw4AfAwOAAmBSsO1nwNeC8TbAT2s6sZndaGYlZlZSXl4epemKiMS/qmpg/r9dQFZG8+ifP4J9tgK5Yc9zgrGj3H2nux8KnhYB/YOvtwDLgstHFcALQL/gmO0ecgh4lNClpq9w96nuXujuhZmZmZG+LhGRpNGscVrtO52ASAJgCdDVzPLNrCkwHpgdvoOZZYU9HQmsCTu2tZlV/eS+EFgdfoyZGTAaWHmiL0JEROqucW07uHuFmU0B5gJpwCPuvsrM7gBK3H02cIuZjQQqgF0El3nc/YiZ/Rh4NfhBvxSYFpz6ySAYDFgG3BzdlyYiIsdj8fKxpJEoLCz0kpKSWE9DRCShmNlSdy+sPq53AouIpCgFgIhIilIAiIikKAWAiEiKSqgmsJmVAxurDWcAuyMYawd8XE9Tq01N82mIc0R6TG37HW/7sbZFsi6JviYnep5IjonVmkDs1iXe1ySS/eL1e6WLu3/1jVTuntAPYGqEYyXxNMeGOEekx9S23/G2H2tbJOuS6GtSn+sSqzWJ5brE+5rEcl3qa02S4RLQSxGOxVI05nMi54j0mNr2O972Y22L93WJ1lzqa120Jg17npT8XkmoS0Anw8xKvIa/g5XY0ZrEJ61L/KmvNUmGCiBSU2M9AfkKrUl80rrEn3pZk5SpAERE5MtSqQIQEZEwCgARkRSlABARSVEKAMDMRpvZNDObaWb/K9bzETCzAjObbmazYj2XVGdmp5rZY8H3yJWxno9E7/sj4QPAzB4xs4/MbGW18eFmttbM1pvZ7cc7h7u/4O43ELonwbj6nG8qiNKalLr79fU709RVxzW6FJgVfI+MbPDJpoi6rEm0vj8SPgCAGcDw8IHgxvMPACOA7sAEM+tuZj3N7G/VHu3DDv334Dg5OTOI3ppI/ZhBhGtE6Dawm4PdjjTgHFPNDCJfk6io9Y5g8c7d55tZXrXhgcB6dy8FMLNngFHu/mvgO9XPEdyt7DfAHHd/u35nnPyisSZSv+qyRoTu7Z1D6M59yfBLY1yq45qsjsa/mayLmc0Xv7FA6H/g7OPs/6/AN4GxZqZbU9aPOq2JmbU1s4eAvmb2s/qenADHXqPngTFm9iDx9dERqaDGNYnW90fCVwDR4O73AffFeh7yBXffie4THRfcfT9wbaznIV+I1vdHslYAW4HcsOc5wZjEjtYk/mmN4k+9rkmyBsASoKuZ5ZtZU2A8MDvGc0p1WpP4pzWKP/W6JgkfAGb2NLAIONPMtpjZ9e5eAUwB5gJrgGfdfVUs55lKtCbxT2sUf2KxJvowOBGRFJXwFYCIiJwYBYCISIpSAIiIpCgFgIhIilIAiIikKAWAiEiKUgCIiKQoBYCISIpSAIiIpKj/D9Mkzu5dmS5IAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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har773Cb+bmRfZp87OOg4Iu1KRS8Jz9351soiGpucR7UypSQhFb0kvGcLd/HHjXv512mjGdKnc9BxRNqdil4S2sHjdTyYt4HJWT249cJhQccRCYTm0UtCe+TZjRw4Xs//fPF80lJ1XSPJKaLvfDObbmabzazEzOad4JgbzazYzDaY2W/Ctt9iZu+GPm6JVnCRk/nfd/fx27Xl/MMlwxk/qHvQcUQCc9IrejNLBR4DrgTKgXwzy3P34rBjRgH3Ahe5+wEz6xfa3ht4AMgFHFgbOvdA9L8Ukb+prmvkvmcKyenbha98YlTQcUQCFckV/VSgxN1L3b0OWAzMbHHM7cBj7xe4u+8Nbb8KeMHdq0L7XgCmRye6yIn94I9b2FF1nO/cMImOHbQypSS3SIp+MFAW9rg8tC3caGC0mb1mZm+Y2fRTOBczu8PMCsysoLKyMvL0Iq0oLD/E46+W8pmpQ7hgeJ+g44gELlrvTqUBo4BLgc8APzeznpGe7O6L3D3X3XMzMzOjFEmSUX1jE3OXr6dv1wzmXT026DgiMSGSoq8AssMeZ4W2hSsH8ty93t23AVtoLv5IzhWJmsdf3UbxrsMsmDmRHp20MqUIRFb0+cAoM8sxs3RgDpDX4piVNF/NY2Z9ab6VUwqsAaaZWS8z6wVMC20Tibpt+47xwz9uYfqEAUyfOCDoOCIx46Szbty9wczuprmgU4En3H2DmS0ACtw9j78VejHQCHzd3fcDmNnDNP+wAFjg7lVt8YVIcmtemXI96WkpPDRzQtBxRGKKuXvQGT4gNzfXCwoKgo4hcWbxmzuYt6KQhTdMYs7UIUHHEWl3ZrbW3XNb26dfFZS4t/dwDY+s3sgFw3tz05Tsk58gkmRU9BL3HsjbQG1DE9+5YbJWphRphYpe4trzRbt5rmg3/3LFKHL6dgk6jkhMUtFL3DpUXc/9vyti/MDu3H7x8KDjiMQsrV4pcWvhc5vYd7SWX9wyhQ5amVLkhPTqkLj0Rul+nn5zB7ddPJxJWT2CjiMS01T0Endq6hu5d0UhQ3p35qtXjA46jkjM060biTv/9eK7bNt3jF9/6Xw6pWtlSpGT0RW9xJXinYf52SulfOq8LP5uVN+g44jEBRW9xI2GxibmrVhPz84dmH/tuKDjiMQN3bqRuPHk69tZX36IH998Dj07pwcdRyRu6Ipe4sKO/cf5/h82c8W4flw7aWDQcUTiiopeYp67882VhaSlpPDwrIla5kDkFKnoJeateKuCV9/dx9zpYxjYo1PQcUTijopeYtq+o7U8/GwxuUN78dnzhwYdRyQuqeglpj20qpjjtY0snD2JlBTdshE5HSp6iVl/2riHVe/s5O7LRzKyX7eg44jELRW9xKSjtQ3MX1nE6P5dufPjI4KOIxLXVPQSk/7t+U3sPlzDwtmTSU/Tt6nImdArSGLO2veq+J833uPWC4dx7pBeQccRiXsqeokptQ2NzF1eyKAenbhn2pig44gkBC2BIDHlJy9tpWTvUX75hSl0ydC3p0g06IpeYsaWPUf4ycslzDp7EJeN6Rd0HJGEoaKXmNDY5Mxdvp6uGWl865Pjg44jklBU9BITfvWX7by94yD3XzeePl0zgo4jklBU9BK4ioPVfG/NZj4+OpNZZw8OOo5IwlHRS6DcnfnPFALwyPVamVKkLajoJVB57+zkpc2V3DNtDFm9OgcdRyQhRVT0ZjbdzDabWYmZzWtl/61mVmlm60Ift4XtawzbnhfN8BLfqo7V8dCqYs7K7sktFw4LOo5IwjrpRGUzSwUeA64EyoF8M8tz9+IWhy5x97tbeYpqdz/7zKNKovn2s8Ucrq7nu7MnkaqVKUXaTCRX9FOBEncvdfc6YDEws21jSaJ7ZUslK96q4MuXjmDsgO5BxxFJaJEU/WCgLOxxeWhbS7PNbL2ZLTOz7LDtHc2swMzeMLNZrf0HZnZH6JiCysrKyNNLXDpW28B9KwoZkdmFuy4fGXQckYQXrTdjVwHD3H0y8ALwVNi+oe6eC9wM/NDMPrTmrLsvcvdcd8/NzMyMUiSJVf/xwhYqDlazcPZkMtJSg44jkvAiKfoKIPwKPSu07f+4+353rw09fBw4L2xfRejfUuBl4JwzyCtxbl3ZQX752jY+d8EQpgzrHXQckaQQSdHnA6PMLMfM0oE5wAdmz5jZwLCHM4CNoe29zCwj9Hlf4CKg5Zu4kiTqG5uYt3w9/bp1ZO70sUHHEUkaJ5114+4NZnY3sAZIBZ5w9w1mtgAocPc84CtmNgNoAKqAW0OnjwN+ZmZNNP9QWdjKbB1JEj97ZSubdh/h53+fS7eOHYKOI5I0zN2DzvABubm5XlBQEHQMibKSvUe55kevcuWE/jx287lBxxFJOGa2NvR+6IfoN2OlzTU1OfetKKRTeioPXjch6DgiSUdFL23u6fwdvLm9im9eO47MblqZUqS9qeilTe0+VMPC1Zu4aGQfPn1eVtBxRJKS/labtImSvUdYkl/GircqqG9q4tHrJ2llSpGAqOglao7XNfD79btYml9GwXsHSEsxrhjXn9svyWFony5BxxNJWip6OSPuzjvlh1iSv4NV7+ziaG0DwzO7cN81Y7n+nCzdkxeJASp6OS0HjtXxzNsVLC0oY9PuI3TqkMq1kwcyZ0o25w3tpds0IjFERS8Ra2pyXt+6nyUFZawp2k1dYxNnZfXg0esncd1ZA/VLUCIxSkUvJ7XrUDXLCspZUlBG+YFqenTqwM3nD+GmKdmMG6glhkVinYpeWlXf2MSfNu5hSX4Zr2yppMnhopF9+Mb0sUwb35+OHbTqpEi8UNHLB2ytPMrS/DKWv1XOvqN1DOjekbsuG8mnz8tmSB/9TVeReKSiF47XNbC6cDdL8neQv715WuQnxvVjzpQhXDI6U3/mTyTOqeiTlLtTWHGIxfll5K3b2Twtsm8X7r16LDecq2mRIolERZ9kDh6vY+XbFSzOb54W2bFDCtdOGsRNU7KZMkzTIkUSkYo+CTQ1OW+U7mdxfhnPb9hNXUMTk7N68O1ZE5lx9iC6a1qkSEJT0Sew3YdqWLa2jCUFZZRVVdO9Yxo3Tx3CjbnZjB+kaZEiyUJFn2DqG5t4cdNeluSX8fLmvTQ5XDiiD/dMG8NVEwZoWqRIElLRJ4jSyqMsKShj+doK9h2tpX/3DL586Ug+nZulBcVEkpyKPo5V1zWyunAXS/LLeHN7FakpxuVj+zFnSjYfH51JWqr+3ICIqOjjjrtTVHGYxfk7yFu3kyO1DeT07cLc6WOZfd5g+nXrGHREEYkxKvo4ceh4PSvXVbAkv4ziXYfp2CGFayYO5KYp2UzN6a1pkSJyQir6GNbU5LyxbT9L88tYXdQ8LXLi4O48PGsiM84aRI9OmhYpIienoo9Bew7XsGxtOUsLynhv/3G6dUxjzpRsbszNZuLgHkHHE5E4o6KPEfWNTby0aS9LC8p4cVPztMgLhvfmq1eMZvpETYsUkdOnog/Ytn3HWFpQxrK15VQeqaVftwzu/PgIbszNZlhfTYsUkTOnog9AdV0jzxU1T4v867bmaZGXjWmeFnnpGE2LFJHoUtG3o6KKQyzJL2PlugqO1DQwtE9nvjF9DJ86N4t+3TUtUkTaRkRFb2bTgR8BqcDj7r6wxf5bgX8DKkKbfuzuj4f23QLMD23/trs/FYXcceNQdT1565pXi9yw8zAZaSlcM2kgN+Zmc8FwTYsUkbZ30qI3s1TgMeBKoBzIN7M8dy9ucegSd7+7xbm9gQeAXMCBtaFzD0QlfYxyd/66rYol+WWsLtxFbUMTEwZ15+GZE5hx9mBNixSRdhXJFf1UoMTdSwHMbDEwE2hZ9K25CnjB3atC574ATAeePr24sW3v4RqWvVXO0vwytoemRd6Ym81NUzQtUkSCE0nRDwbKwh6XA+e3ctxsM7sE2AJ81d3LTnDu4JYnmtkdwB0AQ4YMiSx5jGhobOLlzZUszi/jpc17aWxyzs/pzVc+MYqrJw6kU7qmRYpIsKL1Zuwq4Gl3rzWzfwCeAi6P9GR3XwQsAsjNzfUoZWpT28OmRe49UktmtwzuuGQ4N+Zmk6NpkSISQyIp+gogO+xxFn970xUAd98f9vBx4Hth517a4tyXTzVkrKipb+T5ot0szt/BG6VVpBhcPrYfN+Zmc9nYfnTQtEgRiUGRFH0+MMrMcmgu7jnAzeEHmNlAd98VejgD2Bj6fA3wqJn1Cj2eBtx7xqnb2YadoWmRb1dwuKaBIb078/WrxjD73CwG9NC0SBGJbSctendvMLO7aS7tVOAJd99gZguAAnfPA75iZjOABqAKuDV0bpWZPUzzDwuABe+/MRvrDlXXk/fOTpbk76Co4jDpaSlcPXEAN03J5oKcPqSkaFqkiMQHc4+tW+K5ubleUFAQyP/t7rz5/rTIol3U1DcxbmB35kzJZtbZg+nRWdMiRSQ2mdlad89tbZ9+MxbYe6SG5Wsr+G1BGaX7jtEtI43Z52YxZ8oQJg7url9qEpG4lrRF39DYxCtbKlmSX8afNjVPi5w6rDd3XTaSayZpWqSIJI6kK/od+4+ztKCM364tY8/hWvp2Tee2i3O4MTebEZldg44nIhJ1SVH0NfWNrNmwmyX5Zby+dT8pBpeO6ceCmdlcrmmRIpLgErroi3ceZmlBGc+8XcGh6nqye3finmmj+dR52ZoWKSJJI+GK/nBNPave2cmS/DLWlx8iPTWF6RMHMGdKNhcM17RIEUk+CVP0ew/X8N3nN/Ns4U5q6psYO6AbD143nlnnDKZn5/Sg44mIBCZhir5LRhqvlezjhnOzuCk3m8lZPTQtUkSERCv6eZeTqlszIiIfkFDTTVTyIiIfllBFLyIiH6aiFxFJcCp6EZEEp6IXEUlwKnoRkQSnohcRSXAqehGRBBdzf2HKzCqB91rZ1QM4FMG2vsC+Noh2Mq1laa/nifSckx13ov2nsj2WxgSCG5e2HpOP2hfr4xLrr5UzOSbIMRnq7pmt7nH3uPgAFkW4rSBW8rXX80R6zsmOO9H+U9keS2MS5Li09ZjE87jE+mvlTI6J1TGJp1s3qyLcFpRoZTmd54n0nJMdd6L9p7I9lsYEghuXth6Tj9oX6+MS66+VMzkmJsck5m7dnCkzK/AT/IFcCYbGJDZpXGJPW41JPF3RR2pR0AHkQzQmsUnjEnvaZEwS7opeREQ+KBGv6EVEJIyKXkQkwanoRUQSXNIUvZnNMrOfm9kSM5sWdB5pZmbDzewXZrYs6CzJzMy6mNlTodfIZ4POI82i9fqIi6I3syfMbK+ZFbXYPt3MNptZiZnN+6jncPeV7n47cCdwU1vmTRZRGpdSd/9S2yZNTqc4PjcAy0KvkRntHjaJnMq4ROv1ERdFDzwJTA/fYGapwGPA1cB44DNmNt7MJpnZ71t89As7dX7oPDlzTxK9cZHoe5IIxwfIAspChzW2Y8Zk9CSRj0tUxMUfB3f3P5vZsBabpwIl7l4KYGaLgZnu/h3gky2fw8wMWAg85+5vtW3i5BCNcZG2cyrjA5TTXPbriJ8LwLh0iuNSHI3/M54HdDB/uwKB5m/UwR9x/D8BVwCfMrM72zJYkjulcTGzPmb2U+AcM7u3rcPJCcdnBTDbzP6b2FouIVm0Oi7Ren3ExRV9NLj7fwL/GXQO+SB330/z+yYSIHc/Bnwh6BzyQdF6fcTzFX0FkB32OCu0TYKlcYltGp/Y1KbjEs9Fnw+MMrMcM0sH5gB5AWcSjUus0/jEpjYdl7goejN7GvgLMMbMys3sS+7eANwNrAE2AkvdfUOQOZONxiW2aXxiUxDjokXNREQSXFxc0YuIyOlT0YuIJDgVvYhIglPRi4gkOBW9iEiCU9GLiCQ4Fb2ISIJT0YuIJDgVvYhIgvv/DMlWdhvdlQYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DB6VQ1ltuRor"
      },
      "source": [
        "## Short Report"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tUhRjaVQuRor"
      },
      "source": [
        "In this practical, we have implemented a linear regression model on the Wine dataset. By the method of Mean Square Least, the best parameter \"w\" has been calculated. The MSE of training data is 0.5640, and the MSE of testing data is 0.5621. However, by ploting the learning curve, we have found it is right fitting, and the optimal number of data size is 220. Later on, we implemented polynomial basis expansion and regularization. The optimal value of hyperparameter lambda was tuned as 0.01. By Ridge regularization, the MSE of training data is 0.5014 and the MSE of testing data is 0.5161. By Lasso regularization, the MSE od training data is 0.5489 and the MSE of tseting data is 0.5422.\n",
        " \n",
        "Implemening different degrees of polinomial expansion(from degree 1 to degree 5). For ridge regression, the MSE of both training and test data decreased from degree 1 to degree3; starting from degree 4, MSE of test data increased while MSE of training data decreased. For Lasso, both MSE of training and test data decreased from degree 1 to degree3, also both increased from degree 4. Therefore, the degree 3 that gives minimal MSE. (Records listed below)\n",
        "\n",
        "It was difficult for us to run in higher degrees, thus we cannot know what will show in higher degress. \n",
        "\n",
        "For this practical, each of us has done all tasks on our own, compared and chose the best result we all agreed on. \n",
        "__________\n",
        "\n",
        "For Ridge Regression with using degree 1 polynomial expansion and lambda = 0.0100\n",
        "MSE (Training) = 0.5639 MSE (Testing) = 0.5611\n",
        "For Lasso with using degree 1 polynomial expansion and lambda = 0.0100\n",
        "MSE (Training) = 0.5679 MSE (Testing) = 0.5669\n",
        "\n",
        "__________\n",
        "For Ridge Regression with using degree 2 polynomial expansion and lambda = 0.0100\n",
        "MSE (Training) = 0.5015 MSE (Testing) = 0.5143\n",
        "\n",
        "For Lasso with using degree 2 polynomial expansion and lambda = 0.0100\n",
        "MSE (Training) = 0.5459 MSE (Testing) = 0.5530\n",
        "\n",
        "___________\n",
        "For Ridge Regression with using degree 3 polynomial expansion and lambda = 10.0000\n",
        "MSE (Training) = 0.4751 MSE (Testing) = 0.5075\n",
        "\n",
        "For Lasso with using degree 3 polynomial expansion and lambda = 0.0100\n",
        "MSE (Training) = 0.5363 MSE (Testing) = 0.5405\n",
        "\n",
        "__________\n",
        "For Ridge Regression with using degree 4 polynomial expansion and lambda = 10.0000\n",
        "MSE (Training) = 0.4523 MSE (Testing) = 0.5404\n",
        "\n",
        "For Lasso with using degree 4 polynomial expansion and lambda = 1.0000\n",
        "MSE (Training) = 0.7824 MSE (Testing) = 0.8002\n",
        "\n",
        "__________\n",
        "For Ridge Regression with using degree 5 polynomial expansion and lambda = 0.1000\n",
        "MSE (Training) = 0.3515 MSE (Testing) = 0.7858\n",
        "\n",
        "For Lasso with using degree 5 polynomial expansion and lambda = 1.0000\n",
        "MSE (Training) = 0.7824 MSE (Testing) = 0.8002\n"
      ]
    }
  ]
}