{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "_bB6LN1u3xOn" }, "source": [ "# Polynomial regression" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T10:46:36.102809Z", "start_time": "2020-07-24T10:46:36.072899Z" }, "id": "ZT-6k9BK3xOp" }, "outputs": [], "source": [ "# Uncomment to upgrade packages\n", "#!pip3 install pandas --upgrade --user --quiet\n", "#!pip3 install numpy --upgrade --user --quiet \n", "#!pip3 install scipy --upgrade --user --quiet\n", "#!pip3 install statsmodels --upgrade --user --quiet \n", "#!pip3 install scikit-learn --upgrade --user --quiet\n", "%load_ext autoreload" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T10:46:37.283749Z", "start_time": "2020-07-24T10:46:36.952293Z" }, "id": "LdkmvYfG3xOx" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\n", "Bad key backend.qt4 in file C:\\Users\\Inanna\\.matplotlib\\matplotlibrc, line 45 ('backend.qt4 : PyQt4')\n", "You probably need to get an updated matplotlibrc file from\n", "https://github.com/matplotlib/matplotlib/blob/v3.4.3/matplotlibrc.template\n", "or from the matplotlib source distribution\n" ] } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from IPython.core.interactiveshell import InteractiveShell\n", "from matplotlib import style\n", "import seaborn as sns\n", "\n", "InteractiveShell.ast_node_interactivity = \"all\"\n", "pd.set_option('precision', 3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:34:35.493395Z", "start_time": "2020-07-24T11:34:35.489710Z" }, "id": "IV-SsOqh3xO6" }, "outputs": [], "source": [ "# extra imports\n", "from numpy.random import uniform, normal\n", "from sklearn.linear_model import Ridge, RidgeCV, LinearRegression, Lasso, LassoCV\n", "from sklearn.metrics import mean_squared_error\n", "from sklearn.metrics import make_scorer" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.rcParams['image.cmap'] = \"bwr\"\n", "plt.rcParams['savefig.bbox'] = \"tight\"\n", "style.use('ggplot') or plt.style.use('ggplot')\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "markdown", "metadata": { "id": "MdTmW7dH3xPB" }, "source": [ "Fix the random number genrator so the experiment is reproducible" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:44:58.773363Z", "start_time": "2020-07-24T11:44:58.767567Z" }, "id": "2Tjyk_E73xPD" }, "outputs": [], "source": [ "np.random.seed(7)" ] }, { "cell_type": "markdown", "metadata": { "id": "h_PphBJc3xPH" }, "source": [ "We will approximate the function $cos(3\\pi x)$ using polynomials" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:44:59.205482Z", "start_time": "2020-07-24T11:44:59.201920Z" }, "id": "zLtGlVBX3xPI" }, "outputs": [], "source": [ "def feval(x):\n", " return np.cos(3*np.pi*x)\n", "\n", "def fgen(N, sigma):\n", " x = np.sort(uniform(a, b, N))\n", " t = feval(x) + normal(loc=0, scale=sigma, size=N) \n", " return x,t" ] }, { "cell_type": "markdown", "metadata": { "id": "6o4ejhyn3xPO" }, "source": [ "## Generate training dataset..\n", "\n", "We start generating a sample of 30 examples generating the data assuming that has gaussian noise $N(0,0.25^2)$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:45:03.038744Z", "start_time": "2020-07-24T11:45:03.034663Z" }, "id": "AKmDgGMA3xPQ" }, "outputs": [], "source": [ "N = 30\n", "a = 0\n", "b = 1\n", "sigma = 0.25" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:45:03.246460Z", "start_time": "2020-07-24T11:45:03.241289Z" }, "id": "U7qv1xcj3xPV" }, "outputs": [], "source": [ "x,t = fgen(N, sigma)\n", "sample = pd.DataFrame({'input':x,'target':t})" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:45:03.662703Z", "start_time": "2020-07-24T11:45:03.564880Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 374 }, "id": "bM4y4JwM3xPZ", "outputId": "63f89b2a-4926-451f-9e62-398e6be96758" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(sample.input, sample.target, 'o')\n", "ax.plot(np.linspace(0, 1,num=30), \n", " feval(np.linspace(0, 1,num=30)));" ] }, { "cell_type": "markdown", "metadata": { "id": "UDfx6rKP3xPe" }, "source": [ "## Generate validation set\n", "\n", "We generate also a vaidation set to evaluate the error with unseen data" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:45:04.703004Z", "start_time": "2020-07-24T11:45:04.697216Z" }, "id": "SpZhQL503xPf" }, "outputs": [], "source": [ "N_valid = 1000\n", "x_valid, t_valid = fgen(N_valid, sigma)\n", "valid_sample = pd.DataFrame({'input':x_valid,'target':t_valid})" ] }, { "cell_type": "markdown", "metadata": { "id": "qi7lFOph3xPj" }, "source": [ "## Fit polynomials for a range of degrees, no regularization" ] }, { "cell_type": "markdown", "metadata": { "id": "D5LXntL73xPp" }, "source": [ "We sample the range (0,1) and plot the predictions" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:48:37.321635Z", "start_time": "2020-07-24T11:48:37.237918Z" }, "id": "8A3KUGAB3xPk" }, "outputs": [], "source": [ "p = 1\n", "q = 26\n", "\n", "coef = []\n", "model = []\n", "norm_mse_train = []\n", "norm_mse_valid = []\n", "\n", "for i in range(p,q):\n", " cmodel = LinearRegression()\n", " cmodel.fit(np.vander(sample.input,i+1, increasing=True), sample.target)\n", " coef.append(cmodel.coef_)\n", " predictions = cmodel.predict(np.vander(sample.input,\n", " i+1, increasing=True)) \n", " \n", " \n", " norm_mse_train.append(mean_squared_error(predictions, sample.target))\n", " \n", " pred_val = cmodel.predict(np.vander(valid_sample.input,\n", " i+1, increasing=True)) \n", " norm_mse_valid.append(mean_squared_error(pred_val, valid_sample.target))\n", " model.append(cmodel)\n", "0;" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:48:53.656588Z", "start_time": "2020-07-24T11:48:53.159071Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 424 }, "id": "0aQzHl-U3xPp", "outputId": "4ffc9fb6-a1a1-4e7b-d90f-e7dde42109ae" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16,7))\n", "\n", "for f, i in enumerate([1,2,3,8,15,25]):\n", " ax = fig.add_subplot(2,3,f+1)\n", " ax.plot(sample.input, sample.target, '+')\n", " ax.plot(np.linspace(0, 1,num=40), \n", " feval(np.linspace(0, 1,num=40)), '.');\n", " ax.plot(np.linspace(0, 1,num=40), \n", " model[i-1].predict(np.vander(np.linspace(0, 1,num=40),\n", " i+1, \n", " increasing=True)));\n", " plt.ylim(-1.2,1.5)\n", " plt.title('Degree %d'%i)\n", "0;" ] }, { "cell_type": "markdown", "metadata": { "id": "yaEp5pK93xPu" }, "source": [ "### Plot training/validation error curves\n", "\n", "This is the difference among the train and validation data" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:49:17.996631Z", "start_time": "2020-07-24T11:49:17.878868Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 374 }, "id": "ODgtfPHm3xPv", "outputId": "1d3b821e-2f71-4c7c-f517-30e84f3f84dc" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pol =15\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "plt.plot(range(1,pol+1), norm_mse_train[0:pol], '-+', label='Error.TR')\n", "plt.plot(range(1,pol+1), norm_mse_valid[0:pol], '-o', label='Error.VA')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "id": "Z6l8N9ZNU2A7" }, "source": [ "### Plot coefficients' average magnitudes as a fn. of degree\n", "\n", "These are the means of the abssolute value of the coefficients fitted for each polynomial in logarithmic scale" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 374 }, "id": "kHy6aS-8U2A8", "outputId": "3139e40d-0a38-4c0c-b681-085e7eaaf0d3" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pol=25\n", "means = []\n", "for m in model:\n", " means.append(np.mean(np.abs(m.coef_)))\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "plt.plot(range(1,pol+1), means[0:pol], '-+', label='Coefficients means')\n", "plt.yscale('log')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:47:23.959998Z", "start_time": "2020-07-24T11:47:23.956044Z" }, "id": "BGEvg1dB3xPy" }, "source": [ "## Fit polynomials, with regularization\n", "\n", "Now we repeat the same but using regularization; we first find the best regularization parameter using cross validation" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:49:31.553253Z", "start_time": "2020-07-24T11:49:31.062672Z" }, "id": "T-UglzLC3xPz" }, "outputs": [], "source": [ "p = 1\n", "q = 26\n", "\n", "coef = []\n", "model = []\n", "norm_mse_train = []\n", "norm_mse_valid = []\n", "\n", "\n", "rlambda = np.linspace(0.001, 0.5, num=50)\n", "for i in range(p,q):\n", " cmodel = RidgeCV(alphas=rlambda, scoring=make_scorer(mean_squared_error, greater_is_better=False))\n", " cmodel.fit(np.vander(sample.input,i+1, increasing=True), sample.target)\n", " coef.append(cmodel.coef_)\n", "\n", " predictions = cmodel.predict(np.vander(sample.input, i+1, increasing=True))\n", " norm_mse_train.append(mean_squared_error(predictions, sample.target))\n", " \n", " pred_val = cmodel.predict(np.vander(valid_sample.input, i+1, increasing=True)) \n", " norm_mse_valid.append(mean_squared_error(pred_val, valid_sample.target))\n", " \n", " model.append(cmodel)\n", "0;" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T12:01:17.212637Z", "start_time": "2020-07-24T12:01:16.714162Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 444 }, "id": "XluJR41_3xP4", "outputId": "f7687abd-dfe4-43f1-be1d-4abc746ee93f" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,7))\n", "\n", "for f, i in enumerate([1,2,3,8,15,25]):\n", " ax = fig.add_subplot(2,3,f+1)\n", " ax.plot(sample.input, sample.target, '+')\n", " ax.plot(np.linspace(0, 1,num=40), \n", " feval(np.linspace(0, 1,num=40)), '.');\n", " ax.plot(np.linspace(0, 1,num=40), \n", " model[i-1].predict(np.vander(np.linspace(0, 1,num=40),\n", " i+1, \n", " increasing=True)));\n", " plt.ylim(-1.2,1.5)\n", " plt.title('Degree %d'%i)\n", "0;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot training/validation error curves, as fn. of degree" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2020-07-24T11:49:56.063337Z", "start_time": "2020-07-24T11:49:55.951720Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 374 }, "id": "7Tb6dhX43xP8", "outputId": "b68b9d5b-ff98-43da-93b9-a70ab1d92699" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "pol =25\n", "plt.plot(range(1,pol+1), norm_mse_train[0:pol], '-+', label='Error.TR')\n", "plt.plot(range(1,pol+1), norm_mse_valid[0:pol], '-o', label='Error.VA')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "id": "gHGHNMUDU2BQ" }, "source": [ "Now the coefficients are smaller due to the regularization, now we do not need logarithmic scale to represent them" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot coefficients' average magnitudes" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 374 }, "id": "s1FHAsYZU2BR", "outputId": "664dce58-5b92-4dd2-a89c-e4fd94379299" }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "means = []\n", "for m in model:\n", " means.append(np.mean(np.abs(m.coef_)))\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "plt.plot(range(1,pol+1), means[0:pol], '-+', label='Coefficients means')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualization of coefficients for regularized ridge and lasso" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization of coefficients of *ridge* linear regression as a function of $\\lambda$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambdas = np.logspace(-10, 3, 200)\n", "coefs = []\n", "\n", "for l in lambdas:\n", " tmp_model = Ridge(alpha=l, fit_intercept=False, normalize=True)\n", " tmp_model.fit(np.vander(sample.input, 10, increasing=True), sample.target)\n", " coefs.append(tmp_model.coef_.flatten())\n", "\n", "fig, ax = plt.subplots(figsize=(7, 3.84))\n", "ax.plot(lambdas, coefs)\n", "ax.set_xscale('log')\n", "ax.set_xlabel('lambda')\n", "ax.set_ylabel('coefficients')\n", "ax.set_title('Coefficients as a function of regularizer');\n", "plt.axis('tight')\n", "0;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization of coefficients of *lasso* linear regression as a function of $\\lambda$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambdas = np.logspace(-10, 3, 200)\n", "coefs = []\n", "\n", "for l in lambdas:\n", " tmp_model = Lasso(alpha=l, fit_intercept=False, normalize=True)\n", " tmp_model.fit(np.vander(sample.input, 10, increasing=True), sample.target)\n", " coefs.append(tmp_model.coef_.flatten())\n", "\n", "fig, ax = plt.subplots(figsize=(7, 3.84))\n", "ax.plot(lambdas, coefs)\n", "ax.set_xscale('log')\n", "ax.set_xlabel('lambda')\n", "ax.set_ylabel('coefficients')\n", "ax.set_title('Coefficients as a function of regularizer');\n", "plt.axis('tight')\n", "0;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison of coefficients for ordinary least squares, ridge and lasso for a fixed degree" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "degrees = 13\n", "\n", "lambdas = np.logspace(-10, 3, 200)\n", "X = np.vander(sample.input, degrees, increasing=True)\n", "names = range(1, degrees+1)\n", "y = sample.target\n", "\n", "# ordinary least squares, ridge and lasso\n", "ols = LinearRegression(fit_intercept=False, normalize=True).fit(X, y)\n", "ridge = RidgeCV(alphas=lambdas, fit_intercept=False, normalize=True).fit(X, y)\n", "lasso = LassoCV(alphas=lambdas, fit_intercept=False, normalize=True).fit(X, y)\n", "\n", "coef = pd.DataFrame({'ols': np.absolute(ols.coef_.flatten()),\n", " 'ridge': np.absolute(ridge.coef_.flatten()),\n", " 'lasso': np.absolute(lasso.coef_.flatten())})\n", "coef.plot.bar(logy=True)\n", "\n", "0;" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
olsridgelasso
05.830e+001.2481.220
13.500e+029.59512.695
28.270e+037.77820.464
39.733e+0459.1954.377
46.622e+052.0123.604
52.843e+0642.7817.409
68.064e+0635.9515.967
71.543e+077.5833.536
81.994e+0717.3911.141
91.709e+0727.3640.000
109.266e+0621.0270.000
112.860e+062.2122.875
123.798e+0523.7604.476
\n", "
" ], "text/plain": [ " ols ridge lasso\n", "0 5.830e+00 1.248 1.220\n", "1 3.500e+02 9.595 12.695\n", "2 8.270e+03 7.778 20.464\n", "3 9.733e+04 59.195 4.377\n", "4 6.622e+05 2.012 3.604\n", "5 2.843e+06 42.781 7.409\n", "6 8.064e+06 35.951 5.967\n", "7 1.543e+07 7.583 3.536\n", "8 1.994e+07 17.391 1.141\n", "9 1.709e+07 27.364 0.000\n", "10 9.266e+06 21.027 0.000\n", "11 2.860e+06 2.212 2.875\n", "12 3.798e+05 23.760 4.476" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coef" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bias/Variance trade-off, with ordinary least squares\n", "\n", "\n", "In this last section, we are going to showcase the effect of bias/variance on the overall MSE error. To this end we are going to generate several datasets with additive independent Gaussian noise, from the same distribution. We are going to:\n", "\n", "1. visualize bias, variance for small and large-degree polynomials\n", "2. compute bias, variance for small and large-degree polynomials\n", "3. compute mse for small and large-degree polynomials, and compare it to the known bound mse = bias^2 + variance + sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualize bias and variance for small degree polynomial" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "def do_visualization_of_degree(degree, x0):\n", " fig = plt.figure(figsize=(14,7))\n", "\n", " repeats = 10\n", " N = 10\n", " sigma = 0.25 # additive noise N(0,sigma^2)\n", "\n", " preds = [None] * repeats # will store predictions for locations in x0 for each sample\n", " \n", " for i in range(repeats):\n", " x, y = fgen(N, sigma) # generate new sample of size N\n", " sample = pd.DataFrame({'input':x, 'target':y})\n", " \n", " # fit model\n", " model = LinearRegression()\n", " model.fit(np.vander(sample.input,degree+1, increasing=True), sample.target)\n", " \n", " # record predictions\n", " preds[i] = model.predict(np.vander(x0, degree+1, increasing=True))\n", " \n", " ax = fig.add_subplot(2, 5, i+1)\n", " ax.plot(sample.input, sample.target, '+')\n", " ax.plot(np.linspace(0, 1,num=40), feval(np.linspace(0, 1,num=40)), '.');\n", " ax.plot(np.linspace(0, 1,num=40), model.predict(np.vander(np.linspace(0, 1,num=40), degree+1, increasing=True)));\n", " plt.ylim(-1.2,1.5)\n", " plt.title(f'Repeat {i+1}') \n", " \n", " return pd.DataFrame(preds, columns=x0)\n", "\n", "def bias_variance(deg, df, x0):\n", " fig, ax = plt.subplots(figsize=(12,4))\n", "\n", " ax.plot(np.linspace(0, 1, num=40), feval(np.linspace(0, 1,num=40)), 'b.');\n", " df2 = df.melt(var_name='x0', value_name='pred')\n", "# ax = sns.violinplot(x=\"groups\", y=\"vals\", data=df2)\n", " ax.plot(x0, df.mean(), 'rx')\n", " ax.plot(df2.x0, df2.pred, 'r.')\n", "\n", " ymin = np.amin([-1.2, df2.pred.min()])\n", " ymax = np.amax([1.5, df2.pred.max()])\n", " \n", " print(f'min:{ymin}, max:{ymax}')\n", " plt.ylim(ymin, ymax)\n", " plt.title(f'Bias/Variance for degree {deg}') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Now print predictions of 10 models trained" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "min:-1.340703157709006, max:1.5\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0 = np.linspace(0,1,5) # locations where to store predictions\n", "\n", "df = do_visualization_of_degree(1, x0)\n", "bias_variance(1, df, x0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Now repeat with higher-degree polynomial" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "min:-11.414321012252381, max:6.213534232616673\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = do_visualization_of_degree(4, x0)\n", "bias_variance(4, df, x0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Finally plot bias^2, variance, mse as a fn. of degree" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [], "source": [ "sigma = 2 # additive noise N(0,sigma^2)\n", "N = 500\n", "x0 = np.linspace(0,1,10) # locations where to store predictions\n", "\n", "def compute_predictions_for_degree(degree, x0, repeats=20):\n", "\n", " preds = [None] * repeats # will store predictions for locations in x0 for each sample\n", " \n", " for i in range(repeats):\n", " x, y = fgen(N, sigma) # generate new sample of size N\n", " sample = pd.DataFrame({'input':x, 'target':y})\n", " \n", " # fit model\n", " model = LinearRegression()\n", " model.fit(np.vander(sample.input,degree+1, increasing=True), sample.target)\n", " \n", " # record predictions\n", " preds[i] = model.predict(np.vander(x0, degree+1, increasing=True))\n", " \n", " return pd.DataFrame(preds, columns=x0)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# for all degrees, compute stats\n", "all_deg = range(1, 15)\n", "data = [None] * len(all_deg)\n", "for i, deg in enumerate(all_deg):\n", " df = compute_predictions_for_degree(deg, x0)\n", "\n", " bias = df.mean(axis=0) - feval(x0) # bias at each location in x0\n", " \n", " bias2 = np.mean(bias**2) # mean squared bias (over points in x0)\n", " var = df.var(axis=0).mean() # mean var (over points in x0)\n", "\n", " res = df.to_numpy() - feval(x0)\n", " res2 = res**2\n", " mse = res2.mean(axis=0).mean() # mean mse (over points in x0)\n", " \n", " data[i] = [deg, bias2, var, sigma**2, mse, bias2+var+sigma**2]\n", "\n", "df = pd.DataFrame(data, columns=['degree', 'bias2', 'var', 'sigma2', 'mse', 'bias2+var+sigma2'])\n", "df.plot(x='degree')" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
degreebias2varsigma2msebias2+var+sigma2
010.5040.09840.5934.602
120.5190.15040.6544.669
230.0990.22540.3014.324
340.1110.21340.3034.324
450.0290.26240.2654.292
560.0710.37640.4094.447
670.0300.45940.4434.489
780.0200.52240.4904.542
890.0310.43740.4254.468
9100.0871.09341.0715.180
10110.6896.93446.92911.623
11120.1021.55541.5025.657
12130.1961.67641.7045.872
13140.56911.410410.83815.979
\n", "
" ], "text/plain": [ " degree bias2 var sigma2 mse bias2+var+sigma2\n", "0 1 0.504 0.098 4 0.593 4.602\n", "1 2 0.519 0.150 4 0.654 4.669\n", "2 3 0.099 0.225 4 0.301 4.324\n", "3 4 0.111 0.213 4 0.303 4.324\n", "4 5 0.029 0.262 4 0.265 4.292\n", "5 6 0.071 0.376 4 0.409 4.447\n", "6 7 0.030 0.459 4 0.443 4.489\n", "7 8 0.020 0.522 4 0.490 4.542\n", "8 9 0.031 0.437 4 0.425 4.468\n", "9 10 0.087 1.093 4 1.071 5.180\n", "10 11 0.689 6.934 4 6.929 11.623\n", "11 12 0.102 1.555 4 1.502 5.657\n", "12 13 0.196 1.676 4 1.704 5.872\n", "13 14 0.569 11.410 4 10.838 15.979" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "APA01-MLIntro.ipynb", "provenance": [], "toc_visible": true }, "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": "3.9.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "165px" }, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }