{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem Sheet 8 - Ridge and Lasso" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last exercise we looked at subset selection techniques for linear regression models.\n", "These methods used standard linear regression on all (or a subset of) possible models incorporating different numbers of predictors.\n", "\n", "In this exercise we consider two common shrinkage techniques for feature selection and model regularization.\n", "These techniques have long been well-established in mathematical optimization, and have received interest for data science due to their ability to shrink the coefficients of a linear model.\n", "This becomes advantageous as it enables one to trade off between variance and bias in our model.\n", "\n", "We start this lab by exploring the methods provided in `scikit-learn`.\n", "In the first two problems, we consider the diabetes data set.\n", "The goal of these problems is to understand the two main functions for shrinkage, i.e., `sklearn.linear_model.Ridge` and `sklearn.linear_model.Lasso`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 8.1 - Ridge regression (aka Tikhonov regularization)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**: Execute the following code cell to import the diabetes data set. The command `print(dia.DESCR)`, displays a description of the data set." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import load_diabetes\n", "import pandas as pd\n", "dia = load_diabetes()\n", "df = pd.DataFrame(dia.data, columns=dia.feature_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**: Split your data randomly into a test and training set.\n", "Use the function\n", "\n", " from sklearn.model_selection import train_test_split\n", " \n", "with `random_state=1`.\n", "\n", "Your test set should contain approx. 30\\% of the data (*Hint*: Use the appropriate optional parameter)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell applies ridge regression for `m` different regularization parameters $\\alpha$.\n", "As you know from the lecture, ridge regression adds a penalty term to the RSS term in standard linear regression, i.e., instead of considering the optimization problem\n", "\n", "$$ \\min_{\\beta \\in \\mathbb{R}^{p+1}} \\|y - X \\beta\\|_2^2 = \\min_{\\beta \\in \\mathbb{R}^{p+1}} \\sum_{i=1}^n \\left( y_i - \\sum_{j=0}^p x_{i,j} \\beta_j \\right)^2 $$\n", "\n", "we solve in **ridge regression** the regularized problem\n", "\n", "$$ \\min_{\\beta \\in \\mathbb{R}^{p+1}} \\|y - X \\beta\\|_2^2 + \\alpha \\| \\beta \\|_2^2 = \\min_{\\beta \\in \\mathbb{R}^{p+1}} \\sum_{i=1}^n \\left( y_i - \\sum_{j=0}^p x_{i,j} \\beta_j \\right)^2 + \\alpha \\sum_{j=1}^p \\beta_j^2$$\n", "\n", "**Task**: The following code fragment performs ridge regression for different values of $\\alpha$ and stores the coefficients in an array called `Coeffs`.\n", "Afterwards, the coefficients are plotted for different regression parameters.\n", "If you named your training and test data `X_train, X_test` and `y_train, y_test`, the following code cell should be executable." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from sklearn.linear_model import Ridge\n", "\n", "# Get dimensions of X_train\n", "n,p = X_train.shape\n", "m = 50\n", "Alpha = np.logspace(-4,4,m)\n", "Coeffs = np.zeros((m,p+1))\n", "\n", "for (i,a) in enumerate(Alpha):\n", " lmr = Ridge(alpha=a)\n", " lmr.fit(X_train, y_train)\n", " Coeffs[i,0] = lmr.intercept_\n", " Coeffs[i,1:] = lmr.coef_\n", " \n", "# Plot the output\n", "import matplotlib.pyplot as plt\n", "plt.semilogx(Alpha, Coeffs[:,:])\n", "plt.xlabel('Alpha')\n", "plt.ylabel('Coefficients');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 8.2 - Lasso regression (aka $\\ell^1$-regularization)\n", "\n", "The **Lasso** is another modification of classical linear regression, and uses the $\\ell^1$ norm in the penalization term instead of the $\\ell^2$ norm in ridge regression. The optimization problem reads\n", "\n", "$$ \\min_{\\beta \\in \\mathbb{R}^{p+1}} \\|y - X \\beta\\|_2^2 + \\alpha \\| \\beta \\|_1 = \\min_{\\beta \\in \\mathbb{R}^{p+1}} \\sum_{i=1}^n \\left( y_i - \\sum_{j=0}^p x_{i,j} \\beta_j \\right)^2 + \\alpha \\sum_{j=1}^p |\\beta_j|$$\n", "\n", "Both the lasso and the ridge regression lead to (strictly) convex optimization problems, that are problems with a unique solution.\n", "This is true even in the case of $p > n$, while classical linear regression does not possess a unique solution.\n", "While the coefficients in ridge regression decrease in absolute value in general as the penalty parameter $\\alpha$ increases, they will never be exactly zero.\n", "In contrast to this, the coefficients in the lasso can become zero, when their influence becomes negligible.\n", "\n", "**Task**: Copy the code used for illustrating the influence of the penalty parameter in ridge regression and modify or expand the code to plot the coefficients obtained by the **Lasso** instead." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem 8.3 Is scaling always important?\n", "In this problem, we consider a new data set.\n", "The data set consists of 1499 samples of a particular red wine from Minho, Portugal, called *Vinho verde*.\n", "The first 11 columns in the csv file contain different measurements, the last column contains an expert rating of the quality.\n", "This set became popular in a kaggle competition, but is also publicly available [here](http://www3.dsi.uminho.pt/pcortez/wine/).\n", "The data set resides also on our [webpage](https://www.tu-chemnitz.de/mathematik/numa/lehre/ds-2018/).\n", "\n", "**Task**: Download the new csv-files from the lecture's webpage.\n", "The following code cell imports the csv-file `wine-train.csv` (adjust the path if necessary).\n", "Have a short look at the data set." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('./datasets/wine-train.csv', sep=\";\")\n", "X = df.loc[:, df.columns != 'quality'].values\n", "y = df['quality'].values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we want to look at the coefficient selection for both the scaled and unscaled case.\n", "In this example, *scaled* means that we shift the mean of the features to *zero* and scale the standard deviation to *one*.\n", "This can be easily done by the `scale`-function from `sklearn.preprocessing`.\n", "\n", "**Task**: Normalize your predictor matrix `X` using the function `scale` and store the scaled matrix as `Xscaled`.\n", "You can check this using the methods `mean(axis=0)` and `std(axis=0)` of a numpy array." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to compare the coefficients obtained for the scaled and unscaled predictors.\n", "\n", "**Task**: When done correctly, you should be able to execute the following code.\n", "It computes the *Lasso* estimates for `m` different values of the regularization parameter $\\alpha$ and stores the coefficients as well as the cross-validation score for each $\\alpha$.\n", "Finally, it plots the coefficients in the upper part of the figure, and the corresponding cv-scores in the lower part." ] }, { "cell_type": "code", "execution_count": 8, "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", "from sklearn.linear_model import Lasso\n", "from sklearn.preprocessing import scale\n", "from sklearn.model_selection import cross_val_score\n", "\n", "# Get dimensions of X\n", "n,p = X.shape\n", "m = 50\n", "Alpha = np.logspace(-4,1,m)\n", "\n", "cscaled = np.zeros((m,p+1))\n", "corig = np.zeros((m,p+1))\n", "cvscaled = np.zeros((m,))\n", "cvorig = np.zeros((m,))\n", "\n", "for (i,a) in enumerate(Alpha):\n", " lm = Lasso(alpha=a,tol=1e-8)\n", " \n", " lm.fit(Xscaled, y)\n", " cscaled[i,0] = lm.intercept_\n", " cscaled[i,1:] = lm.coef_\n", " \n", " cvscaled[i] = cross_val_score(lm, Xscaled, y, cv=10).mean()\n", " \n", " \n", " lm = Lasso(alpha=a,tol=1e-8)\n", " lm.fit(X, y)\n", " corig[i,0] = lm.intercept_\n", " corig[i,1:] = lm.coef_\n", " \n", " cvorig[i] = cross_val_score(lm, X, y, cv=10).mean()\n", " \n", "# Plot the output\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['figure.figsize']=(15,10)\n", "fig, ax = plt.subplots(2,2)\n", "ax[0][0].semilogx(Alpha, cscaled[:,1:])\n", "ax[0][0].set_title('Scaled predictors')\n", "ax[0][0].set_xlabel('Alpha')\n", "ax[0][0].set_ylabel('Coefficients');\n", "\n", "ax[0][1].semilogx(Alpha, corig[:,1:])\n", "ax[0][1].set_title('Unscaled predictors')\n", "ax[0][1].set_xlabel('Alpha')\n", "ax[0][1].set_ylabel('Coefficients');\n", "\n", "ax[1][0].semilogx(Alpha, cvscaled)\n", "ax[1][0].set_xlabel('Alpha')\n", "ax[1][0].set_ylabel('cv-score');\n", "ax[1][1].semilogx(Alpha, cvorig);\n", "ax[1][1].set_xlabel('Alpha')\n", "ax[1][1].set_ylabel('cv-score');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**: What do you observe?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observation**:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**:\n", "Compute the values of $\\alpha$, for which the cv-scores are maximized." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**: Now we want to compare the mean squared errors for both regressions using the value of $\\alpha$ which maximizes the cv-score.\n", "What do you observe?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observation**:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You should observe, that the mean squared errors are very close. Indeed, the MSE for the unscaled problem is even slightly lower than the MSE of the scaled problem.\n", "\n", "**Task**: Import now the csv-file `wine-test.csv` and store the predictors as a numpy array `Xtest` and the target variables as `ytest`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**: Compute the mean squared errors on the test set using the Lasso models from above for the scaled and unscaled version. Don't forget to scale the predictors for your scaled model." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task**: Interpret the results. What could be the reason, why the unscaled model behaves better than the scaled model? Are your predictions good or bad?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }