{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Week 2: Demo Bias Variance Tradeoff\n", "\n", "The demo covers the change in the bias and variance contributions to the MSE when the model complexity increases/decreases throughn either regularization or dimension reduction. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt \n", "\n", "\n", "# Generating noisy samples from a degree 3 polynomial\n", "\n", "xtrain = np.linspace(-1,1,10)\n", "\n", "xtest = np.linspace(-1,1, 50)\n", "\n", "\n", "t = xtrain**3 + xtrain**2 + 2*xtrain + 1\n", "\n", "t_test = xtest**3 + xtest**2 + 2*xtest + 1\n", "\n", "tnoisy = t.reshape(-1,1) + np.random.normal(0,.4,len(xtrain)).reshape(-1,1)\n", "\n", "plt.scatter(xtrain, tnoisy, c='r')\n", "plt.plot(xtest, t_test)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# for 100 XPs, we repeat the following experiment: we generate a \n", "# different set of noisy samples (x_i, t_i) and learn a degree 7 \n", "# polynomial based on a ridge formulation with very mild level of \n", "# regularization\n", "\n", "numXp = 100\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "numfeatures = 7\n", "poly = PolynomialFeatures(numfeatures)\n", "\n", "full_beta = np.zeros((numfeatures+1, numXp))\n", "\n", "\n", "lbda = .0001\n", "\n", "for i in range(numXp):\n", " \n", " # generating points\n", " tnoisy = t+np.random.normal(0,.6,len(xtrain))\n", "\n", " # fitting models\n", " \n", " \n", " Xtilde = poly.fit_transform(xtrain.reshape(-1,1))\n", " \n", " tmp_inv = np.linalg.inv(np.matmul(Xtilde.T, Xtilde) + lbda*np.eye(np.shape(np.matmul(Xtilde.T, Xtilde))[0]) ) \n", " beta = np.matmul(tmp_inv, np.matmul(Xtilde.T, tnoisy))\n", " \n", " full_beta[:,i] = beta\n", "\n", " \n", " \n", "# drawing the plot \n", "\n", "XtildeTest = poly.fit_transform(xtest.reshape(-1,1))\n", "\n", "plt.scatter(xtrain, tnoisy, c='r', label = 'Samples')\n", "\n", "for i in range(numXp):\n", " \n", " plt.plot(xtest, np.matmul(XtildeTest, full_beta[:,i]), c='b', alpha=.05)\n", "\n", "\n", "\n", "plt.plot(xtest, t_test, c='g', label = 'True model')\n", "plt.plot(xtest, np.matmul(XtildeTest, np.mean(full_beta, axis=1)), '--',c = 'r', label = 'Averaged model')\n", "\n", "plt.legend()\n", "\n", "plt.savefig('biasVariance2.png', dpi=300)\n", "\n", "\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# In order to study the result of a reduction in the model complexity, \n", "# we start by increasing the level of regularization, \n", "# setting the lambda to 10. \n", "\n", "numXp = 100\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "numfeatures = 7\n", "poly = PolynomialFeatures(numfeatures)\n", "\n", "full_beta = np.zeros((numfeatures+1, numXp))\n", "\n", "\n", "lbda = 10\n", "\n", "for i in range(numXp):\n", " \n", " # generating points\n", " tnoisy = t+np.random.normal(0,.6,len(xtrain))\n", "\n", " # fitting models\n", " \n", " \n", " Xtilde = poly.fit_transform(xtrain.reshape(-1,1))\n", " \n", " tmp_inv = np.linalg.inv(np.matmul(Xtilde.T, Xtilde) + lbda*np.eye(np.shape(np.matmul(Xtilde.T, Xtilde))[0]) ) \n", " beta = np.matmul(tmp_inv, np.matmul(Xtilde.T, tnoisy))\n", " \n", " full_beta[:,i] = beta\n", "\n", " \n", " \n", "# drawing the plot \n", "\n", "XtildeTest = poly.fit_transform(xtest.reshape(-1,1))\n", "\n", "plt.scatter(xtrain, tnoisy, c='r', label = 'Samples')\n", "\n", "for i in range(numXp):\n", " \n", " plt.plot(xtest, np.matmul(XtildeTest, full_beta[:,i]), c='b', alpha=.05)\n", "\n", "\n", "\n", "plt.plot(xtest, t_test, c='g', label = 'True model')\n", "plt.plot(xtest, np.matmul(XtildeTest, np.mean(full_beta, axis=1)), '--',c = 'r', label = 'Averaged model')\n", "\n", "plt.legend()\n", "\n", "plt.savefig('biasVariance2.png', dpi=300)\n", "\n", "\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Finally, we study the effect on the bias and variance of a reduction in \n", "# the number of features. We repeat the experiments with a simple \n", "# linear model. \n", "\n", "numXp = 100\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "numfeatures = 1\n", "poly = PolynomialFeatures(numfeatures)\n", "\n", "full_beta = np.zeros((numfeatures+1, numXp))\n", "\n", "for i in range(numXp):\n", " \n", " # generating points\n", " tnoisy = t+np.random.normal(0,.6,len(xtrain))\n", "\n", " # fitting models\n", " \n", " \n", " Xtilde = poly.fit_transform(xtrain.reshape(-1,1))\n", " \n", " tmp_inv = np.linalg.inv(np.matmul(Xtilde.T, Xtilde) + lbda*np.eye(np.shape(np.matmul(Xtilde.T, Xtilde))[0]) ) \n", " beta = np.matmul(tmp_inv, np.matmul(Xtilde.T, tnoisy))\n", " \n", " full_beta[:,i] = beta\n", "\n", " \n", " \n", "# drawing the plot \n", "\n", "XtildeTest = poly.fit_transform(xtest.reshape(-1,1))\n", "\n", "plt.scatter(xtrain, tnoisy, c='r', label = 'Samples')\n", "\n", "for i in range(numXp):\n", " \n", " plt.plot(xtest, np.matmul(XtildeTest, full_beta[:,i]), c='b', alpha=.05)\n", "\n", "\n", "plt.plot(xtest, t_test, c='g', label = 'True model')\n", "plt.plot(xtest, np.matmul(XtildeTest, np.mean(full_beta, axis=1)), '--',c = 'r', label = 'Averaged model')\n", "plt.legend()\n", "\n", "plt.savefig('biasVariance4.png', dpi=300)\n", "\n", "\n", "plt.show()\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }