{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Lecture 7: Training III" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "![](https://www.tensorflow.org/images/colab_logo_32px.png)\n", "[Run in colab](https://colab.research.google.com/drive/151rKfOzxrWMK7fiViIGsosquddN07yJg )" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:44.467687Z", "iopub.status.busy": "2024-01-10T00:19:44.467138Z", "iopub.status.idle": "2024-01-10T00:19:44.475581Z", "shell.execute_reply": "2024-01-10T00:19:44.475048Z" }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last executed: 2024-01-10 00:19:44\n" ] } ], "source": [ "import datetime\n", "now = datetime.datetime.now()\n", "print(\"Last executed: \" + now.strftime(\"%Y-%m-%d %H:%M:%S\"))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Polynomial regression" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "So far we have considered only linear regression. Polynomial regression can also be performed with a model that is linear (in the parameters)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:44.516067Z", "iopub.status.busy": "2024-01-10T00:19:44.515424Z", "iopub.status.idle": "2024-01-10T00:19:44.928255Z", "shell.execute_reply": "2024-01-10T00:19:44.927538Z" } }, "outputs": [], "source": [ "# Common imports\n", "import os\n", "import numpy as np\n", "np.random.seed(42) # To make this notebook's output stable across runs\n", "\n", "# To plot pretty figures\n", "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Example data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:44.931698Z", "iopub.status.busy": "2024-01-10T00:19:44.931400Z", "iopub.status.idle": "2024-01-10T00:19:44.935887Z", "shell.execute_reply": "2024-01-10T00:19:44.935221Z" } }, "outputs": [], "source": [ "import numpy.random as rnd\n", "np.random.seed(42)\n", "m = 100\n", "X = 6 * np.random.rand(m, 1) - 3\n", "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:44.938729Z", "iopub.status.busy": "2024-01-10T00:19:44.938267Z", "iopub.status.idle": "2024-01-10T00:19:45.153988Z", "shell.execute_reply": "2024-01-10T00:19:45.153313Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.plot(X, y, \"b.\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.axis([-3, 3, 0, 10]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly a straight line will not fit the data well." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Construct new features\n", "\n", "Can use a linear model by constructing additional features that are powers of existing features:\n", "\n", "$$\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_1^2 + \\theta_3 x_2 + \\theta_4 x_2^2 + \\theta_5 x_1 x_2 + ... $$\n", "\n", "Model remains linear in the parameters $\\theta_j$.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Generate polynomial features" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.157478Z", "iopub.status.busy": "2024-01-10T00:19:45.157015Z", "iopub.status.idle": "2024-01-10T00:19:45.487951Z", "shell.execute_reply": "2024-01-10T00:19:45.487213Z" } }, "outputs": [ { "data": { "text/plain": [ "(array([-0.75275929]), array([-0.75275929, 0.56664654]))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n", "X_poly = poly_features.fit_transform(X)\n", "X[0], X_poly[0]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.491035Z", "iopub.status.busy": "2024-01-10T00:19:45.490576Z", "iopub.status.idle": "2024-01-10T00:19:45.495240Z", "shell.execute_reply": "2024-01-10T00:19:45.494597Z" } }, "outputs": [ { "data": { "text/plain": [ "((100, 1), (100, 2))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.shape, X_poly.shape" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Fit model" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.498108Z", "iopub.status.busy": "2024-01-10T00:19:45.497659Z", "iopub.status.idle": "2024-01-10T00:19:45.555973Z", "shell.execute_reply": "2024-01-10T00:19:45.555227Z" } }, "outputs": [ { "data": { "text/plain": [ "(array([1.78134581]), array([[0.93366893, 0.56456263]]))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "lin_reg = LinearRegression()\n", "lin_reg.fit(X_poly, y)\n", "lin_reg.intercept_, lin_reg.coef_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters are close to the model used to generate the data (2, 1 and 0.5 respectively)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Predictions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.559266Z", "iopub.status.busy": "2024-01-10T00:19:45.558700Z", "iopub.status.idle": "2024-01-10T00:19:45.735843Z", "shell.execute_reply": "2024-01-10T00:19:45.735234Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_new = np.linspace(-3, 3, 100).reshape(100, 1)\n", "X_new_poly = poly_features.transform(X_new)\n", "y_new = lin_reg.predict(X_new_poly)\n", "plt.figure(figsize=(10,5))\n", "plt.plot(X, y, \"b.\")\n", "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.legend(loc=\"upper left\", fontsize=14)\n", "plt.axis([-3, 3, 0, 10]);" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "exercise_pointer" ] }, "source": [ "**Exercises:** *You can now complete Exercise 1 in the exercises associated with this lecture.*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Learning curves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How determine whether overfitting or underfitting?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Overfitting with high degree polynomials" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.739185Z", "iopub.status.busy": "2024-01-10T00:19:45.738769Z", "iopub.status.idle": "2024-01-10T00:19:45.934670Z", "shell.execute_reply": "2024-01-10T00:19:45.934005Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.preprocessing import StandardScaler\n", "from sklearn.pipeline import Pipeline\n", "\n", "plt.figure(figsize=(7,3))\n", "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n", " polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n", " std_scaler = StandardScaler()\n", " lin_reg = LinearRegression()\n", " polynomial_regression = Pipeline(\n", " ((\"poly_features\", polybig_features), (\"std_scaler\", std_scaler), (\"lin_reg\", lin_reg)) )\n", " polynomial_regression.fit(X, y)\n", " y_newbig = polynomial_regression.predict(X_new)\n", " plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n", "\n", "plt.plot(X, y, \"b.\", linewidth=3)\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.axis([-3, 3, 0, 10]);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Training data is underfitted for degree 1, fitted well for degree 2, and overfitted for degree 300." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Learning curves provide another way to determine whether model underfitted or overfitted." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider performance on training and validation set *as size of the training set increases*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Plotting learning curves" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.938531Z", "iopub.status.busy": "2024-01-10T00:19:45.937877Z", "iopub.status.idle": "2024-01-10T00:19:45.944402Z", "shell.execute_reply": "2024-01-10T00:19:45.943841Z" } }, "outputs": [], "source": [ "from sklearn.metrics import mean_squared_error\n", "from sklearn.model_selection import train_test_split\n", "\n", "def plot_learning_curves(model, X, y):\n", " X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\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_predict, y_train[:m]))\n", " val_errors.append(mean_squared_error(y_val_predict, y_val))\n", "\n", " plt.figure(figsize=(8,4))\n", " plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"Training set\")\n", " plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n", " plt.legend(loc=\"upper right\", fontsize=14) \n", " plt.xlabel(\"Training set size\", fontsize=14) \n", " plt.ylabel(\"RMSE\", fontsize=14) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Underfitted learning curves" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Learning curve for linear model" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:45.947504Z", "iopub.status.busy": "2024-01-10T00:19:45.946932Z", "iopub.status.idle": "2024-01-10T00:19:46.221925Z", "shell.execute_reply": "2024-01-10T00:19:46.221338Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lin_reg = LinearRegression()\n", "plot_learning_curves(lin_reg, X, y)\n", "plt.axis([0, 80, 0, 3]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- RMSE on training set small for small training set size since model can fit data well for very few data points (perfect for one or two points).\n", "\n", "- RMSE performance on training and validation eventually similar but high since linear model cannot fit the data well (recall data generated by quadratic)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Overfitted learning curves " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Learning curve for poynomial model of degree 10" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:46.225436Z", "iopub.status.busy": "2024-01-10T00:19:46.224761Z", "iopub.status.idle": "2024-01-10T00:19:46.559315Z", "shell.execute_reply": "2024-01-10T00:19:46.558734Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.pipeline import Pipeline\n", "polynomial_regression = Pipeline((\n", " (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n", " (\"lin_reg\", LinearRegression()),\n", " ))\n", "plot_learning_curves(polynomial_regression, X, y)\n", "plt.axis([0, 80, 0, 3]); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- RMSE now much smaller.\n", "- But training and validation set errors remain quite different.\n", "\n", "Model performs much better on training set than validation set, suggesting overfitting." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Well-fitted learning curves " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Learning curve for poynomial model of degree 2" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:46.562771Z", "iopub.status.busy": "2024-01-10T00:19:46.562122Z", "iopub.status.idle": "2024-01-10T00:19:46.882864Z", "shell.execute_reply": "2024-01-10T00:19:46.882258Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.pipeline import Pipeline\n", "polynomial_regression = Pipeline((\n", " (\"poly_features\", PolynomialFeatures(degree=2, include_bias=False)),\n", " (\"lin_reg\", LinearRegression()),\n", " ))\n", "plot_learning_curves(polynomial_regression, X, y)\n", "plt.axis([0, 80, 0, 3]); " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Bias-variance tradeoff" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bias-variance tradeoff refers to the problem of simultaneously reducing the two types of errors that prevents supervised learning algorithms from generalising to other data.\n", "\n", "- **Bias**: Expected difference between data and prediction.\n", "\n", "- **Variance**: Expected ability of the model to fluctuate." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "One seeks a model that accurately fits the training data, while also generalising to unseen data.\n", "\n", "Typically impossible to do both simultaneously.\n", "\n", "- On one hand, high-variance models may fit training data well but typically overfit to noise or unrepresentative training data.\n", "\n", "- On the other hand, low-complexity models with a high bias typically underfit training data.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Contributions to the mean square error " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider underlying (true) model:\n", "$ y = f(x) + \\epsilon,$\n", "\n", "where\n", "- $y$ is the target and $x$ features.\n", "- $f$ is the true model, that we will approximate by $h$.\n", "- $\\epsilon$ is the noise, with zero mean and variance $\\sigma^2$.\n", "\n", "\n", "Approximate $f$ by $h$, which is fitted by a learning algorithm and training data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Expected value of the mean square error is given by\n", "\n", "$$\\text{E} \\left[ \\left(y - h(x)\\right)^2 \\right]\n", "= \n", "\\text{Bias}^2\\left[ h(x) \\right]\n", "+\n", "\\text{Var}\\left[ h(x) \\right]\n", "+\n", "\\sigma^2$$\n", "\n", "Three contributions to the error:\n", " \n", "1. Bias: $\\text{Bias}\\left[ h(x) \\right] = \\text{E} \\left[ h(x) - f(x) \\right].$\n", "\n", "2. Variance: $\\text{Var}\\left[ h(x) \\right] = \\text{E} \\left[ h^2(x)\\right] - \\text{E} \\left[ h(x)\\right]^2. $\n", "\n", "3. Irreducible error $\\sigma^2$ due to noise in observations." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Tradeoff \n", "\n", "By choosing a complex model, the bias can be made small but the variance will be large.\n", "\n", "By choosing a simple model, the variance can be made small but the bias will be large.\n", "\n", " \n", "\n", "[Image source](http://francescopochetti.com/bias-v-s-variance-tradeoff/)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Regularization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One approach to mitigate the bias-variance tradeoff is by *regularization*.\n", "\n", "Consider a complex model but place additional constraints to reduce its variance.\n", "\n", "As a consequence the bias is increased but can introduce a regularisation parameter to control the tradeoff." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Add regularization term $R(\\theta)$ to the cost function:\n", "\n", "$$C_\\lambda(\\theta) = C(\\theta) + \\lambda\\ R(\\theta).$$\n", "\n", "The regularization parameter $\\lambda$ controls the amount of regularization." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Regularization should only be added when training. When using fitted model to make predictions, should evaluate cost without regularization term." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Tikhonov regularization \n", "\n", "*Tikhonov* regularization adopts $\\ell_2$ regularising term (also called *Ridge regression*):\n", "\n", "$$ R(\\theta) = \\frac{1}{2} \\sum_{j=1}^n \\theta_j^2 = \\frac{1}{2} \\theta^{\\rm T}\\theta.$$\n", "\n", "\n", "\n", "Acts to keep parameters small.\n", "\n", "Note that the bias term $\\theta_0$ is not regularized (i.e. sum starts from 1 not 0)." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:46.887064Z", "iopub.status.busy": "2024-01-10T00:19:46.886396Z", "iopub.status.idle": "2024-01-10T00:19:46.893828Z", "shell.execute_reply": "2024-01-10T00:19:46.893284Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "from sklearn.linear_model import Ridge\n", "\n", "np.random.seed(42)\n", "m = 20\n", "X = 3 * np.random.rand(m, 1)\n", "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n", "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n", "\n", "def plot_model(model_class, polynomial, alphas, **model_kargs): \n", " # Use alpha for regularization parameter (lambda used already)\n", " for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n", " model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n", " if polynomial:\n", " model = Pipeline((\n", " (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n", " (\"std_scaler\", StandardScaler()),\n", " (\"regul_reg\", model),\n", " ))\n", " model.fit(X, y)\n", " y_new_regul = model.predict(X_new)\n", " lw = 2 if alpha > 0 else 1\n", " plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\lambda = {}$\".format(alpha))\n", " plt.plot(X, y, \"b.\", linewidth=3)\n", " plt.legend(loc=\"upper left\", fontsize=15)\n", " plt.xlabel(\"$x_1$\", fontsize=18)\n", " plt.axis([0, 3, 0, 4])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:46.896773Z", "iopub.status.busy": "2024-01-10T00:19:46.896231Z", "iopub.status.idle": "2024-01-10T00:19:47.338341Z", "shell.execute_reply": "2024-01-10T00:19:47.337595Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.subplot(121)\n", "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.subplot(122)\n", "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "exercise_pointer" ] }, "source": [ "**Exercises:** *You can now complete Exercises 2 and 3 in the exercises associated with this lecture.*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Lasso regularization\n", "\n", "\n", "*Lasso* regularization adopts $\\ell_1$ regularising term:\n", "\n", "$$ R(\\theta) =\\sum_{j=1}^n \\left\\vert \\theta_j \\right\\vert .$$\n", "\n", "Acts to promote sparsity.\n", "\n", "Again, note that the bias term $\\theta_0$ is not regularized (i.e. sum starts from 1 not 0).\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:47.341641Z", "iopub.status.busy": "2024-01-10T00:19:47.341174Z", "iopub.status.idle": "2024-01-10T00:19:47.722342Z", "shell.execute_reply": "2024-01-10T00:19:47.721671Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import Lasso\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.subplot(121)\n", "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.subplot(122)\n", "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Differentiability\n", "\n", "Note that the Lasso penality is non-differentiable at zero.\n", "\n", "Gradient descent can still be used but with gradients replaced by [sub-gradients](https://en.wikipedia.org/wiki/Subderivative) when any $\\theta_j=0$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Elastic Net regularization\n", "\n", "\n", "Provides a mix of Tikhonov and Lasso regularization, controlled by mix ratio $r$:\n", "\n", "$$R(\\theta)\n", "= \n", "r\\sum_{j=1}^n \\left\\vert \\theta_j \\right\\vert\n", "+\n", "\\frac{1-r}{2} \\sum_{j=1}^n \\theta_j^2.$$\n", "\n", "- For $r=0$, corresponds to Tikhonov regularization.\n", "- For $r=1$, corresponds to Lasso regularization." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Stopping early\n", "\n", "Compute RMSE on validation set as train and stop when starts to increase." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:47.725983Z", "iopub.status.busy": "2024-01-10T00:19:47.725495Z", "iopub.status.idle": "2024-01-10T00:19:47.734570Z", "shell.execute_reply": "2024-01-10T00:19:47.733897Z" } }, "outputs": [], "source": [ "from sklearn.linear_model import SGDRegressor\n", "np.random.seed(42)\n", "m = 100\n", "X = 6 * np.random.rand(m, 1) - 3\n", "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n", "\n", "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n", "\n", "poly_scaler = Pipeline((\n", " (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n", " (\"std_scaler\", StandardScaler()),\n", " ))\n", "\n", "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n", "X_val_poly_scaled = poly_scaler.transform(X_val)\n", "\n", "sgd_reg = SGDRegressor(max_iter=1,\n", " penalty=None,\n", " eta0=0.0005,\n", " warm_start=True,\n", " learning_rate=\"constant\",\n", " random_state=42)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:47.737763Z", "iopub.status.busy": "2024-01-10T00:19:47.737190Z", "iopub.status.idle": "2024-01-10T00:19:48.426308Z", "shell.execute_reply": "2024-01-10T00:19:48.425611Z" } }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(action='ignore')\n", "n_epochs = 500\n", "train_errors, val_errors = [], []\n", "for epoch in range(n_epochs):\n", " sgd_reg.fit(X_train_poly_scaled, y_train)\n", " y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n", " y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n", " train_errors.append(mean_squared_error(y_train_predict, y_train))\n", " val_errors.append(mean_squared_error(y_val_predict, y_val))\n", "\n", "best_epoch = np.argmin(val_errors)\n", "best_val_rmse = np.sqrt(val_errors[best_epoch])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:19:48.429987Z", "iopub.status.busy": "2024-01-10T00:19:48.429495Z", "iopub.status.idle": "2024-01-10T00:19:48.654702Z", "shell.execute_reply": "2024-01-10T00:19:48.653840Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.annotate('Best model',\n", " xy=(best_epoch, best_val_rmse),\n", " xytext=(best_epoch, best_val_rmse + 1),\n", " ha=\"center\",\n", " arrowprops=dict(facecolor='black', shrink=0.05),\n", " fontsize=16,\n", " )\n", "\n", "best_val_rmse -= 0.03 # just to make the graph look better\n", "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n", "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n", "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n", "plt.legend(loc=\"upper right\", fontsize=14)\n", "plt.xlabel(\"Epoch\", fontsize=14)\n", "plt.ylabel(\"RMSE\", fontsize=14);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Note that for stochastic or mini-batch gradient descent the RMSE is noisy and may be difficult to know when reach minimum (can employ simple strategies to deal with that)." ] } ], "metadata": { "celltoolbar": "Tags", "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": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 4 }