{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Demonstration: Linear Regression and Model Validation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import modules" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Common imports\n", "import numpy as np\n", "import os\n", "\n", "# To plot pretty figures\n", "%matplotlib inline\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Let us generate some data from a cubic model with noise\n", "m = 100\n", "minX = -3\n", "maxX = 3\n", "np.random.seed(1)\n", "x = (maxX-minX) * np.random.rand(m, 1) + minX\n", "# up to cubic features, plus random noise\n", "theta_true = np.array([2, 1, 0.5, -0.25])\n", "eps_noise = 1.\n", "y = eps_noise * np.random.randn(m, 1)\n", "for order in range(len(theta_true)):\n", " y += theta_true[order] * x**order" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the data. It is pretty tricky to see the features\n", "fig,ax = plt.subplots(1,1)\n", "\n", "ax.plot(x, y, \"b.\")\n", "ax.set_xlabel(\"$x_1$\")\n", "ax.set_ylabel(\"$y$\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Over- and underfitting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will explore fitting to models that have both too many and too few features." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "order 50: rms theta = 5.7e+12\n", "order 3: rms theta = 1.2e+00\n", "order 1: rms theta = 3.0e-01\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# For these fits we will employ scaling of the data\n", "# We use the built-in StandardScaler to rescale the data to zero mean and unit variance.\n", "# This will make the fit more stable\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.pipeline import Pipeline\n", "\n", "x_new=np.linspace(minX, maxX, 100).reshape(100, 1)\n", "\n", "fig,ax = plt.subplots(1,1,figsize=(8,6))\n", "\n", "for style, degree in ((\"g-\", 50), (\"b--\", 3), (\"r-.\", 1)):\n", " polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n", " std_scaler = StandardScaler()\n", " lin_reg = LinearRegression()\n", " # Here we use a Pipeline that assembles several steps that we\n", " # also could have applied sequentially:\n", " # 1. The design matrix is created with the chosen polynomial features.\n", " # 2. The data is transformed to mean=0 and variance=1 \n", " # (usually makes it numerically more stable)\n", " # 3. Perform the linear regression fit\n", " polynomial_regression = Pipeline([\n", " (\"poly_features\", polybig_features),\n", " (\"std_scaler\", std_scaler),\n", " (\"lin_reg\", lin_reg),\n", " ])\n", " polynomial_regression.fit(x, y)\n", " y_newbig = polynomial_regression.predict(x_new)\n", " ax.plot(x_new, y_newbig, style, label=f'{degree:>3}')\n", " print(f'order {degree:>3}: rms theta = ',\\\n", " f'{np.linalg.norm(lin_reg.coef_,ord=None)/order:3.1e}')\n", "\n", "\n", "ax.plot(x, y, \"b.\")\n", "ax.legend(loc=\"best\")\n", "ax.set_xlabel(\"$x_1$\")\n", "ax.set_ylim([-10,30])\n", "ax.set_ylabel(\"$y$\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Note how the high-degree polynomial produces a very wiggly curve that tries very hard to go through the training data. The model explodes near the edges where there is no more training data. \n", "- The first degree polynomial, on the other hand, fails to pick up some trends in the data that is clearly there. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bias-variance tradeoff" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.model_selection import train_test_split\n", "from sklearn.utils import resample\n", "\n", "np.random.seed(2019)\n", "\n", "n_boostraps = 100\n", "maxdegree = 14\n", "\n", "error = np.zeros(maxdegree)\n", "bias = np.zeros(maxdegree)\n", "variance = np.zeros(maxdegree)\n", "polydegree = range(maxdegree)\n", "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", "\n", "for degree in range(maxdegree):\n", " polybig_features = PolynomialFeatures(degree=degree)\n", " lin_reg = LinearRegression()\n", " polynomial_regression = Pipeline([\n", " (\"poly_features\", polybig_features),\n", " (\"lin_reg\", lin_reg),\n", " ])\n", "\n", " y_pred = np.empty((y_test.shape[0], n_boostraps))\n", " for i in range(n_boostraps):\n", " x_, y_ = resample(x_train, y_train)\n", " # Evaluate the new model on the same test data each time.\n", " y_pred[:, i] = polynomial_regression.fit(x_, y_).predict(x_test).ravel()\n", "\n", " # Note: Expectations and variances taken w.r.t. different training\n", " # data sets, hence the axis=1. Subsequent means are taken across the test data\n", " # set in order to obtain a total value, but before this we have error/bias/variance\n", " # calculated per data point in the test set.\n", " # Note 2: The use of keepdims=True is important in the calculation of bias as this \n", " # maintains the column vector form. Dropping this yields very unexpected results.\n", " error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", " bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", " variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", "\n", "fig,ax = plt.subplots(1,1,figsize=(10,8))\n", "\n", "ax.plot(polydegree, error, label='Error')\n", "ax.plot(polydegree, bias, label='Bias')\n", "ax.plot(polydegree, variance, label='Variance')\n", "ax.legend(loc=\"best\")\n", "ax.set_xlabel(\"degree\")\n", "ax.set_ylabel(\"Bias-Variance\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regularized models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ridge regression" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import Ridge" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def train_ridge_model(x_train, y_train, alpha, x_predict=None, degree=1, **model_kargs):\n", " model = Ridge(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n", " model = Pipeline([\n", " (\"poly_features\", PolynomialFeatures(degree=degree, include_bias=False)),\n", " (\"std_scaler\", StandardScaler()),\n", " (\"regul_reg\", model),\n", " ])\n", " model.fit(x_train, y_train)\n", " if not len(x_predict):\n", " x_predict=x_train\n", " return model.predict(x_predict)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,axs = plt.subplots(1,2,figsize=(8,5))\n", "\n", "lambdas=(0, 1,10, 100)\n", "for i,degree in enumerate((1,6)):\n", " ax = axs[i]\n", " for lam, style in zip(lambdas, (\"b-\", \"k:\", \"g--\", \"r-.\")):\n", " y_new_regul = train_ridge_model(x, y, lam, x_predict=x_new, \\\n", " degree=degree, random_state=42)\n", " ax.plot(x_new, y_new_regul, style, label=f'$\\lambda={lam}$')\n", " ax.plot(x, y, \"b.\")\n", " ax.legend(loc=\"upper left\")\n", " ax.set_xlabel(\"$x_1$\")\n", " ax.set_title(f'Ridge regularization; order: {degree}')\n", " #ax.axis([0, 3, 0, 4])\n", "\n", "axs[0].set_ylabel(\"$y$\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## k-fold cross validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Code example to be added later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning curves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to gauge a model's generalization performance (predictive power) it is common to split the data into a *training set* and a *validation set*. We will also see examples of a third set called the *test set*.\n", "\n", "**Learning curves** are plots of the model's performance on both the training and the validation sets, measured by some performance metric such as the mean squared error. This measure is plotted as a function of the size of the training set, or alternatively as a function of the training iterations." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# built-in convenience function for computing the MSE metric\n", "from sklearn.metrics import mean_squared_error\n", "# built-in convenience function for splitting data\n", "from sklearn.model_selection import train_test_split\n", "\n", "def plot_learning_curves(model, x, y, ax=None):\n", " # split the data into training and validation sets\n", " x_train, x_val, y_train, y_val = train_test_split(x, y, train_size=0.7, random_state=42)\n", " train_errors, val_errors = [], []\n", " for m in range(1, len(x_train)):\n", " model.fit(x_train[:m], y_train[:m])\n", " y_train_predict = model.predict(x_train[:m])\n", " y_val_predict = model.predict(x_val)\n", " train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n", " val_errors.append(mean_squared_error(y_val, y_val_predict))\n", "\n", " if not ax:\n", " fig,ax = plt.subplots(1,1)\n", " ax.plot(np.sqrt(train_errors), \"r-+\", label=\"train\")\n", " ax.plot(np.sqrt(val_errors), \"b-\", label=\"validation\")\n", " ax.legend(loc=\"best\")\n", " ax.set_xlabel(\"Training set size\")\n", " ax.set_ylabel(\"MSE\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us use both a first-order and a high-order polynomial to model the training data and plot the learning curve. Recall that a low mean-square error implies that the model predicts the data very well." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.pipeline import Pipeline\n", "\n", "fig,axs = plt.subplots(1,2,figsize=(8,4))\n", "\n", "for i,degree in enumerate((1,15)):\n", " ax = axs[i]\n", " polynomial_regression = Pipeline([\n", " (\"poly_features\", PolynomialFeatures(degree=degree, include_bias=False)),\n", " (\"lin_reg\", LinearRegression()),\n", " ])\n", "\n", " plot_learning_curves(polynomial_regression, x, y, ax=ax)\n", " ax.set_title(f'Learning curve; order: {degree}')\n", " ax.set_ylim([0,4]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Several features in the left-hand panel deserves to be mentioned:\n", "1. The performance on the training set starts at zero when only 1-2 data are in the training set.\n", "1. The error on the training set then increases steadily as more data is added. \n", "1. It finally reaches a plateau.\n", "1. The validation error is initially very high, but reaches a plateau that is very close to the training error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The learning curves in the right hand panel are similar to the underfitting model; but there are some important differences:\n", "1. The training error is much smaller than with the linear model.\n", "1. There is no clear plateau.\n", "1. There is a gap between the curves, which implies that the model performs significantly better on the training data than on the validation set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both these examples that we have just studied demonstrate the so called **bias-variance tradeoff**.\n", "- A high bias model has a relatively large error, most probably due to wrong assumptions about the data features.\n", "- A high variance model is excessively sensitive to small variations in the training data.\n", "- The irreducible error is due to the noisiness of the data itself. It can only be reduced by obtaining better data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We seek a more systematic way of distinguishing between under- and overfitting models, and for quantification of the different kinds of errors. \n", "\n", "We will find that **Bayesian statistics** has the promise to deliver on that ultimate goal." ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.0" }, "nav_menu": {}, "toc": { "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 6, "toc_cell": false, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }