linear_regression.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/github/tnleang/machineLearning/blob/master/linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
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      "source": [
        "<h2>Assignment 1 - Linear Regression on Boston Housing Data</h2>"
      ]
    },
    {
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      "source": [
        "# The modules we're going to use\n",
        "from __future__ import print_function\n",
        "from sklearn import preprocessing\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn import datasets, linear_model\n",
        "from scipy import linalg\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "# When you execute a code to plot with a simple SHIFT-ENTER, the plot will be shown directly under the code cell\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
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      "source": [
        ""
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      "source": [
        "# Load data from scikit-learn, which returns (data, target)\n",
        "# note: if you call \"boston = load_boston()\", it returns a dictionary-like object\n",
        "data, target = datasets.load_boston(True)\n",
        "\n",
        "# Split the data into two parts: training data and testing data\n",
        "train_data,test_data,train_target,test_target = train_test_split(data,(target[:, np.newaxis]), test_size=0.2, random_state=42)\n",
        "\n",
        "\n",
        "\n",
        "# based function to perform the tasks below\n",
        "# MSE using numpy\n",
        "def mean_square_err(test_target,predict_target):\n",
        "  return np.square(np.subtract(test_target, predict_target)).sum() /(2 * len(test_target))\n",
        "\n",
        "# compute loss\n",
        "def lossFunction(X,y):\n",
        "  return mean_square_err(X,y)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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        "id": "NA3ezrA-bSjt",
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      },
      "source": [
        "<h4>Use scikit-learn library in the following cell</h4>"
      ]
    },
    {
      "cell_type": "code",
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        "outputId": "14fde78d-6ba4-41b4-d064-35967cd2ddda",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        }
      },
      "source": [
        "# Task 1-1: use linear regression in sklearn\n",
        "regr = linear_model.LinearRegression()\n",
        "regr.fit(train_data,train_target)\n",
        "predict_ptarget = regr.predict(test_data)\n",
        "train_predict = regr.predict(train_data)\n",
        "\n",
        "#print(test_target)\n",
        "#print(predict_ptarget)\n",
        "# Task 1-2: show intercept and coefficents\n",
        "print('Intercept: \\n', regr.intercept_ )\n",
        "print('Coefficients: \\n', regr.coef_)\n",
        "\n",
        "# Task 1-3: show errors on training dataset and testing dataset\n",
        "print(\"Mean squared error train data: %.2f\" %  mean_square_err(train_target,train_predict)) \n",
        "print(\"Mean squared error test data: %.2f\" %  mean_square_err(test_target,predict_ptarget)) "
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Intercept: \n",
            " [30.24675099]\n",
            "Coefficients: \n",
            " [[-1.13055924e-01  3.01104641e-02  4.03807204e-02  2.78443820e+00\n",
            "  -1.72026334e+01  4.43883520e+00 -6.29636221e-03 -1.44786537e+00\n",
            "   2.62429736e-01 -1.06467863e-02 -9.15456240e-01  1.23513347e-02\n",
            "  -5.08571424e-01]]\n",
            "Mean squared error train data: 10.82\n",
            "Mean squared error test data: 12.15\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "RpX2tOa5bSjv",
        "colab_type": "text"
      },
      "source": [
        "<h4>Use analytical solution (normal equation) to perform linear regression in the following cell</h4>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": true,
        "editable": true,
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        "colab": {
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      },
      "source": [
        "# Task 2-1: Implement a function solving normal equation \n",
        "# Inputs: Training data and  training label\n",
        "# Output: Weights\n",
        "def myNormalEqualFun(X,y):\n",
        "  return (linalg.inv((X.T @ X)) @ X.T) @ y\n",
        "\n",
        "    \n",
        "# Task 2-2: Implement a function performing prediction\n",
        "# Inputs: Testing data and weights\n",
        "# Output: Predictions\n",
        "def myPredictFun(X,w):\n",
        "    return X @ w\n",
        "\n",
        "# Here we insert a column of 1s into training_data and test_data (to be consistent with our lecture slides)\n",
        "train_data_intercept = np.insert(train_data, 0, 1, axis=1)\n",
        "test_data_intercept = np.insert(test_data, 0, 1, axis=1)\n",
        "\n",
        "# Here we call myNormalEqual to train the model and get weights\n",
        "w = myNormalEqualFun(train_data_intercept,train_target)\n",
        "predict_target = myPredictFun(test_data_intercept, w)\n",
        "train_predict = myPredictFun(train_data_intercept, w)\n",
        "\n",
        "\n",
        "# Task 2-3: show intercept and coefficents\n",
        "print('Intercept: \\n', w[0] )\n",
        "print('Coefficents: \\n',w[1:])\n",
        "\n",
        "\n",
        "# Task 2-4: show errors on training dataset and testing dataset\n",
        "print(\"Mean squared error train data: %.2f\" %  mean_square_err(train_target,train_predict)) \n",
        "print(\"Mean squared error test data: %.2f\" %  mean_square_err(test_target,predict_target)) "
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Intercept: \n",
            " [22.79653465]\n",
            "Coefficents: \n",
            " [[-1.00213533]\n",
            " [ 0.69626862]\n",
            " [ 0.27806485]\n",
            " [ 0.7187384 ]\n",
            " [-2.0223194 ]\n",
            " [ 3.14523956]\n",
            " [-0.17604788]\n",
            " [-3.0819076 ]\n",
            " [ 2.25140666]\n",
            " [-1.76701378]\n",
            " [-2.03775151]\n",
            " [ 1.12956831]\n",
            " [-3.61165842]]\n",
            "Mean squared error train data: 10.82\n",
            "Mean squared error test data: 12.15\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "1hhVEfixbSjx",
        "colab_type": "text"
      },
      "source": [
        "<h4>Use numerical solution (basic gradient descent) to perform linear regression in the following cell</h4>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "3H1IxOBubSjy",
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        "outputId": "9be21b97-2144-4254-e8ac-83fb9c9a49bf",
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      "source": [
        "# Feature scaling\n",
        "scaler = preprocessing.StandardScaler().fit(train_data)\n",
        "train_data = scaler.transform(train_data)\n",
        "test_data = scaler.transform(test_data)\n",
        "\n",
        "\n",
        "# Task 3-1: Implement a function performing gradient descent\n",
        "# Inputs: Training data, training label, leaerning rate, number of iterations, Testing data, testing label\n",
        "# Output: the final Weights\n",
        "#         the loss history along iterations\n",
        "def myGradientDescentFun(X,y,learning_rate,numItrs,test_X, test_y):\n",
        "    \n",
        "    n_size = len(y)\n",
        "    w = np.random.rand(np.size(X,1),1)\n",
        "    history = []\n",
        "    history_test = []\n",
        "    \n",
        "    for i in range(numItrs):\n",
        "      # compute gradient and update weights\n",
        "      gradient = -(1 / n_size) * ((X.T @ (y - (X @ w)))) \n",
        "      w = w - learning_rate * gradient \n",
        "      \n",
        "      # compute the loss with train data and test data\n",
        "      y_predict = myPredictFun(X,w)  \n",
        "      y_validate = myPredictFun(test_X,w) \n",
        "      loss = lossFunction(y, y_predict)\n",
        "      loss_validate = lossFunction(test_y, y_validate)\n",
        "      \n",
        "      # store the loss history\n",
        "      history.append(loss)\n",
        "      history_test.append(loss_validate)\n",
        "      \n",
        "    return w,history, history_test\n",
        "\n",
        "# Task 3-2: Implement a function performing prediction\n",
        "# Inputs: Testing data and weights\n",
        "# Output: Predictions\n",
        "def myPredictFun(X,w):\n",
        "    return X @ w\n",
        "\n",
        "# Here we insert a column of 1s into training_data and test_data (to be consistent with our lecture slides)\n",
        "train_data_intercept = np.insert(train_data, 0, 1, axis=1)\n",
        "test_data_intercept = np.insert(test_data, 0, 1, axis=1)\n",
        "\n",
        "# Here we call myGradientDescentFun to train the model and get weights\n",
        "# Note: you need to figure out good learning rate value and the number of iterations\n",
        "w,history, history_test = myGradientDescentFun(train_data_intercept,train_target,0.3,250, test_data_intercept, test_target)\n",
        "\n",
        "predict_target = myPredictFun(test_data_intercept, w)\n",
        "train_predict = myPredictFun(train_data_intercept, w)\n",
        "\n",
        "\n",
        "# Task 3-3: show intercept and coefficents\n",
        "print('Intercept: \\n', w[0] )\n",
        "print('Coefficents: \\n',w[1:])\n",
        "\n",
        "\n",
        "# Task 3-4: show errors on training dataset and testing dataset\n",
        "print(\"Mean squared error train data: %.2f\" %  mean_square_err(train_target,train_predict)) \n",
        "print(\"Mean squared error test data: %.2f\" %  mean_square_err(test_target,predict_target)) \n",
        "\n",
        "\n",
        "# Task 3-5: plot learning curves showing training errors and testing errors along iterations\n",
        "# Get training and test loss histories\n",
        "fig = plt.figure(figsize=[20,10])\n",
        "plt.ylabel('Loss')\n",
        "plt.xlabel('Iteration')\n",
        "plt.plot(history, label='Train_data')\n",
        "plt.plot(history_test, label='Test_data')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Intercept: \n",
            " [22.79653465]\n",
            "Coefficents: \n",
            " [[-1.0009387 ]\n",
            " [ 0.69344751]\n",
            " [ 0.2726685 ]\n",
            " [ 0.71958042]\n",
            " [-2.02172298]\n",
            " [ 3.14654623]\n",
            " [-0.17653382]\n",
            " [-3.08121565]\n",
            " [ 2.23516414]\n",
            " [-1.74888601]\n",
            " [-2.03726629]\n",
            " [ 1.12947043]\n",
            " [-3.61086527]]\n",
            "Mean squared error train data: 10.82\n",
            "Mean squared error test data: 12.15\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AoDdEpQaMhiWLGVqpBAAAAPSGqNSA0aBknEHqZNz1KAAAAADHRVRqwGg4yDiDRFQCAAAA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\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rx1UOqmfcNe0",
        "colab_type": "text"
      },
      "source": [
        "<h4>Use numerical solution (stochastic gradient descent) to perform linear regression in the following cell</h4>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "96_WVyVKcNss",
        "colab_type": "code",
        "outputId": "5917dec0-9308-42b2-a2b2-34e3f50cc5bd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 915
        }
      },
      "source": [
        "# Feature scaling\n",
        "scaler = preprocessing.StandardScaler().fit(train_data)\n",
        "train_data = scaler.transform(train_data)\n",
        "test_data = scaler.transform(test_data)\n",
        "\n",
        "\n",
        "# perform batch\n",
        "# cutting the array of data set into batches\n",
        "def batch_gradient(X,y,batchsize):\n",
        "  for i in range(0,X.shape[0],batchsize):\n",
        "    yield (X[i:i+batchsize], y[i:i+batchsize])\n",
        "\n",
        "\n",
        "# Task 4-1: Implement a function performing gradient descent\n",
        "# Inputs: Training data, training label, learning rate, number of epoches, batch size, Testing data, testing label\n",
        "# Output: the final Weights\n",
        "#         the loss history along batches\n",
        "def myGradientDescentFun(X,y,learning_rate,epoches, batchsize,test_X, test_y):\n",
        "\n",
        "    # initialize\n",
        "    w = np.random.rand(np.size(X,1),1) # weights\n",
        "    history = []   # train loss history\n",
        "    history_test = [] # test loss history\n",
        "    \n",
        "    for i in range(epoches):\n",
        "      for batch in batch_gradient(X,y,batchsize):\n",
        "        # perform LR on each batch\n",
        "        # compute gradient and update weights\n",
        "        gradient = -(1 / len(batch[0]) * ((batch[0].T @ (batch[1] - (batch[0] @ w)))))\n",
        "        w = w - learning_rate * gradient\n",
        "        \n",
        "        # compute the loss with train data and test data\n",
        "        y_predict = myPredictFun(batch[0],w)\n",
        "        y_validate = myPredictFun(test_X,w)\n",
        "        loss = mean_square_err(batch[1], y_predict)\n",
        "        loss_validate = mean_square_err(test_y, y_validate)\n",
        "        \n",
        "        # store the loss history\n",
        "        history.append(loss)\n",
        "        history_test.append(loss_validate)\n",
        "    \n",
        "    return w, history, history_test\n",
        "\n",
        "# Task 4-2: Implement a function performing prediction\n",
        "# Inputs: Testing data and weights\n",
        "# Output: Predictions\n",
        "def myPredictFun(X,w):\n",
        "    return X @ w\n",
        "\n",
        "# Here we insert a column of 1s into training_data and test_data (to be consistent with our lecture slides)\n",
        "train_data_intercept = np.insert(train_data, 0, 1, axis=1)\n",
        "test_data_intercept = np.insert(test_data, 0, 1, axis=1)\n",
        "\n",
        "# Here we call myGradientDescentFun to train the model and get weights\n",
        "# Note: you need to figure out good learning rate value and the number of iterations\n",
        "w,history, history_test = myGradientDescentFun(train_data_intercept,train_target,0.001,100,1, test_data_intercept, test_target)\n",
        "predict_target = myPredictFun(test_data_intercept, w)\n",
        "train_predict = myPredictFun(train_data_intercept, w)\n",
        "\n",
        "\n",
        "# Task 4-3: show intercept and coefficents\n",
        "print('Intercept: \\n', w[0] )\n",
        "print('Coefficents: \\n',w[1:])\n",
        "\n",
        "\n",
        "# Task 4-4: show errors on training dataset and testing dataset\n",
        "print(\"Mean squared error train data: %.2f\" %  mean_square_err(train_target,train_predict)) \n",
        "print(\"Mean squared error test data: %.2f\" %  mean_square_err(test_target,predict_target)) \n",
        "\n",
        "\n",
        "# Task 4-5: plot learning curves showing training errors and testing errors along bath\n",
        "fig = plt.figure(figsize=[20,10])\n",
        "plt.ylabel('Loss')\n",
        "plt.xlabel('Iteration')\n",
        "plt.plot(history, label='Train_data')\n",
        "plt.plot(history_test, label='Test_data')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Intercept: \n",
            " [22.78524252]\n",
            "Coefficents: \n",
            " [[-1.00434044]\n",
            " [ 0.6918346 ]\n",
            " [ 0.26008253]\n",
            " [ 0.76623403]\n",
            " [-2.02058457]\n",
            " [ 3.11490897]\n",
            " [-0.19467501]\n",
            " [-3.10394278]\n",
            " [ 2.16799519]\n",
            " [-1.56669975]\n",
            " [-2.01336812]\n",
            " [ 1.11975627]\n",
            " [-3.62272913]]\n",
            "Mean squared error train data: 10.83\n",
            "Mean squared error test data: 12.10\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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JAAAAgEYJnMaxouh0BQAAAAAjJ3ACAAAAoFECJwAAAAAaJXCCPbjtkRXZsHmo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\n319hePWsTfjgVf6yWbi1j2RtCtAPO75x1zLS8y5+YBU2EPrzZY+uxW3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9AIAf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\nBE4AAAAAzOpPDU+ne/r/A+UAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}