{ "metadata": { "name": "3a - Linear regression 1D" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Loading data\n", "=====================================================\n", "We load the dataset 'diabetes' using the sklearn load function: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import datasets\n", "# Load the diabetes dataset\n", "diabetes = datasets.load_diabetes()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dataset consists of data and targets. Target tells us what is the desired output for specific example from data: " ] }, { "cell_type": "code", "collapsed": true, "input": [ "X = diabetes.data\n", "y = diabetes.target\n", "print X.shape\n", "print y.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(442, 10)\n", "(442,)\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Splitting the data\n", "==================\n", "We want to split the data into train set and test set. We fit the linear model on the train set, and we show that it performs good on test set. \n", "\n", "Before splitting the data, we shuffle (mix) the examples, because for some datasets the examples are ordered. \n", "\n", "If we wouldn't shuffle, train set and test set could be totally different, thus linear model fitted on train set wouldn't be valid on test set.\n", "Now we shuffle:\n" ] }, { "cell_type": "code", "collapsed": true, "input": [ "from sklearn.utils import shuffle\n", "X, y = shuffle(X, y, random_state=1)\n", "print X.shape\n", "print y.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(442, 10)\n", "(442,)\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each example of data has 10 columns in total.\n", "\n", "We want to work with 1-dim data because it is simple to visualize. Therefore select only one column, e.g column 2 and fit linear model on it:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Use only one column from data\n", "print(X.shape)\n", "X = X[:, 2:3]\n", "print(X.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(442, 10)\n", "(442, 1)\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Split the data into training/testing sets" ] }, { "cell_type": "code", "collapsed": false, "input": [ "train_set_size = 250\n", "X_train = X[:train_set_size] # selects first 250 rows (examples) for train set\n", "X_test = X[train_set_size:] # selects from row 250 until the last one for test set\n", "print(X_train.shape)\n", "print(X_test.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(250, 1)\n", "(192, 1)\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Split the targets into training/testing sets" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_train = y[:train_set_size] # selects first 250 rows (targets) for train set\n", "y_test = y[train_set_size:] # selects from row 250 until the last one for test set\n", "print(y_train.shape)\n", "print(y_test.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(250,)\n", "(192,)\n" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can look at our train data. We can see that the examples have linear relation. \n", "\n", "Therefore, we can use linear model to make good classification of our examples.\n" ] }, { "cell_type": "code", "collapsed": true, "input": [ "plt.scatter(X_train, y_train)\n", "plt.scatter(X_test, y_test)\n", "plt.xlabel('Data')\n", "plt.ylabel('Target');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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MRiNUKtvlUbi6uiIr6yqAuwAcAdxGVlY8nJ2dbSbj3/KOHfsO48ZNw9WrO9GpU2vMm/dG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m/ejEGDBgEABg0ahI0bN972vNjYWDRq1Oi2f6MTvamqq9/R9rWFI/1XFC9T1+PvSPxO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\ngcAhhMEQCAQCgUMIgyEQCAQCh/g/G0IOcEZRbmUAAAAASUVORK5CYII=\n" } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear regression\n", "=================\n", "Create linear regression object, which we use later to apply linear regression on data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import linear_model\n", "regr = linear_model.LinearRegression()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit the model using the training set" ] }, { "cell_type": "code", "collapsed": true, "input": [ "regr.fit(X_train, y_train);" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We found the coefficients and the bias (the intercept)" ] }, { "cell_type": "code", "collapsed": true, "input": [ "print(regr.coef_)\n", "print(regr.intercept_)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 865.04619508]\n", "151.179169728\n" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we calculate the mean square error on the test set" ] }, { "cell_type": "code", "collapsed": true, "input": [ "# The mean square error\n", "print(\"Training error: \", np.mean((regr.predict(X_train) - y_train) ** 2))\n", "print(\"Test error: \", np.mean((regr.predict(X_test) - y_test) ** 2))\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "('Training error: ', 3800.1408249628944)\n", "('Test error: ', 4047.2429967010571)\n" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting data and linear model\n", "==============================\n", "Now we want to plot the train data and teachers (marked as dots). \n", "\n", "With line we represents the data and predictions (linear model that we found):\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Visualises dots, where each dot represent a data exaple and corresponding teacher\n", "plt.scatter(X_train, y_train, color='black')\n", "# Plots the linear model\n", "plt.plot(X_train, regr.predict(X_train), color='blue', linewidth=3);\n", "plt.xlabel('Data')\n", "plt.ylabel('Target')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "output_type": "display_data", "png": 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NmjVL3d6NGzdw5MgRuLq6Ij09Ha+++iqys7MhlUqh1+tx+vTpSo/u6khSU1Px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\nAAAASUVORK5CYII=\n" } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We do similar with test data, and show that linear model is valid for a test set:" ] }, { "cell_type": "code", "collapsed": true, "input": [ "# Visualises dots, where each dot represent a data exaple and corresponding teacher\n", "plt.scatter(X_test, y_test, color='black')\n", "# Plots the linear model\n", "plt.plot(X_test, regr.predict(X_test), color='blue', linewidth=3);\n", "plt.xlabel('Data')\n", "plt.ylabel('Target');" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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+/PhKB8zff/8dW7duhbOzMyZMmGCR7Lu8vDxMmDABJ06cgK+vL77//ns0a9ZM8H4eR6fT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\njBnQarVQKpXQaDRo0KABdu/ebbKUyoIFCySd71OnTi13TI4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} ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 90 } ], "metadata": {} } ] }