{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Kernel Density Estimation\n", "\n", "Kernel density estimation is the process of estimating an unknown probability density function using a *kernel function* $K(u)$. While a histogram counts the number of data points in somewhat arbitrary regions, a kernel density estimate is a function defined as the sum of a kernel function on every data point. The kernel function typically exhibits the following properties:\n", "\n", "1. Symmetry such that $K(u) = K(-u)$.\n", "2. Normalization such that $\\int_{-\\infty}^{\\infty} K(u) \\ du = 1$ .\n", "3. Monotonically decreasing such that $K'(u) < 0$ when $u > 0$.\n", "4. Expected value equal to zero such that $\\mathrm{E}[K] = 0$.\n", "\n", "For more information about kernel density estimation, see for instance [Wikipedia - Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation).\n", "\n", "A univariate kernel density estimator is implemented in `sm.nonparametric.KDEUnivariate`.\n", "In this example we will show the following:\n", "\n", "* Basic usage, how to fit the estimator.\n", "* The effect of varying the bandwidth of the kernel using the `bw` argument.\n", "* The various kernel functions available using the `kernel` argument." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:56.066851Z", "iopub.status.busy": "2022-02-08T18:21:56.066400Z", "iopub.status.idle": "2022-02-08T18:21:57.777649Z", "shell.execute_reply": "2022-02-08T18:21:57.778511Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from scipy import stats\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.distributions.mixture_rvs import mixture_rvs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A univariate example" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:57.782487Z", "iopub.status.busy": "2022-02-08T18:21:57.781512Z", "iopub.status.idle": "2022-02-08T18:21:57.786216Z", "shell.execute_reply": "2022-02-08T18:21:57.786873Z" } }, "outputs": [], "source": [ "np.random.seed(12345) # Seed the random number generator for reproducible results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create a bimodal distribution: a mixture of two normal distributions with locations at `-1` and `1`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:57.790033Z", "iopub.status.busy": "2022-02-08T18:21:57.789068Z", "iopub.status.idle": "2022-02-08T18:21:57.794889Z", "shell.execute_reply": "2022-02-08T18:21:57.795544Z" } }, "outputs": [], "source": [ "# Location, scale and weight for the two distributions\n", "dist1_loc, dist1_scale, weight1 = -1, 0.5, 0.25\n", "dist2_loc, dist2_scale, weight2 = 1, 0.5, 0.75\n", "\n", "# Sample from a mixture of distributions\n", "obs_dist = mixture_rvs(\n", " prob=[weight1, weight2],\n", " size=250,\n", " dist=[stats.norm, stats.norm],\n", " kwargs=(\n", " dict(loc=dist1_loc, scale=dist1_scale),\n", " dict(loc=dist2_loc, scale=dist2_scale),\n", " ),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simplest non-parametric technique for density estimation is the histogram." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:57.798626Z", "iopub.status.busy": "2022-02-08T18:21:57.797693Z", "iopub.status.idle": "2022-02-08T18:21:58.071858Z", "shell.execute_reply": "2022-02-08T18:21:58.072543Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "# Scatter plot of data samples and histogram\n", "ax.scatter(\n", " obs_dist,\n", " np.abs(np.random.randn(obs_dist.size)),\n", " zorder=15,\n", " color=\"red\",\n", " marker=\"x\",\n", " alpha=0.5,\n", " label=\"Samples\",\n", ")\n", "lines = ax.hist(obs_dist, bins=20, edgecolor=\"k\", label=\"Histogram\")\n", "\n", "ax.legend(loc=\"best\")\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting with the default arguments" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The histogram above is discontinuous. To compute a continuous probability density function,\n", "we can use kernel density estimation.\n", "\n", "We initialize a univariate kernel density estimator using `KDEUnivariate`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:58.075924Z", "iopub.status.busy": "2022-02-08T18:21:58.074996Z", "iopub.status.idle": "2022-02-08T18:21:58.082102Z", "shell.execute_reply": "2022-02-08T18:21:58.082752Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit() # Estimate the densities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We present a figure of the fit, as well as the true distribution." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:58.085928Z", "iopub.status.busy": "2022-02-08T18:21:58.084959Z", "iopub.status.idle": "2022-02-08T18:21:58.352401Z", "shell.execute_reply": "2022-02-08T18:21:58.353151Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "# Plot the histrogram\n", "ax.hist(\n", " obs_dist,\n", " bins=20,\n", " density=True,\n", " label=\"Histogram from samples\",\n", " zorder=5,\n", " edgecolor=\"k\",\n", " alpha=0.5,\n", ")\n", "\n", "# Plot the KDE as fitted using the default arguments\n", "ax.plot(kde.support, kde.density, lw=3, label=\"KDE from samples\", zorder=10)\n", "\n", "# Plot the true distribution\n", "true_values = (\n", " stats.norm.pdf(loc=dist1_loc, scale=dist1_scale, x=kde.support) * weight1\n", " + stats.norm.pdf(loc=dist2_loc, scale=dist2_scale, x=kde.support) * weight2\n", ")\n", "ax.plot(kde.support, true_values, lw=3, label=\"True distribution\", zorder=15)\n", "\n", "# Plot the samples\n", "ax.scatter(\n", " obs_dist,\n", " np.abs(np.random.randn(obs_dist.size)) / 40,\n", " marker=\"x\",\n", " color=\"red\",\n", " zorder=20,\n", " label=\"Samples\",\n", " alpha=0.5,\n", ")\n", "\n", "ax.legend(loc=\"best\")\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the code above, default arguments were used. We can also vary the bandwidth of the kernel, as we will now see." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying the bandwidth using the `bw` argument" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bandwidth of the kernel can be adjusted using the `bw` argument.\n", "In the following example, a bandwidth of `bw=0.2` seems to fit the data well." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:58.356692Z", "iopub.status.busy": "2022-02-08T18:21:58.355710Z", "iopub.status.idle": "2022-02-08T18:21:58.648639Z", "shell.execute_reply": "2022-02-08T18:21:58.647864Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "# Plot the histrogram\n", "ax.hist(\n", " obs_dist,\n", " bins=25,\n", " label=\"Histogram from samples\",\n", " zorder=5,\n", " edgecolor=\"k\",\n", " density=True,\n", " alpha=0.5,\n", ")\n", "\n", "# Plot the KDE for various bandwidths\n", "for bandwidth in [0.1, 0.2, 0.4]:\n", " kde.fit(bw=bandwidth) # Estimate the densities\n", " ax.plot(\n", " kde.support,\n", " kde.density,\n", " \"--\",\n", " lw=2,\n", " color=\"k\",\n", " zorder=10,\n", " label=\"KDE from samples, bw = {}\".format(round(bandwidth, 2)),\n", " )\n", "\n", "# Plot the true distribution\n", "ax.plot(kde.support, true_values, lw=3, label=\"True distribution\", zorder=15)\n", "\n", "# Plot the samples\n", "ax.scatter(\n", " obs_dist,\n", " np.abs(np.random.randn(obs_dist.size)) / 50,\n", " marker=\"x\",\n", " color=\"red\",\n", " zorder=20,\n", " label=\"Data samples\",\n", " alpha=0.5,\n", ")\n", "\n", "ax.legend(loc=\"best\")\n", "ax.set_xlim([-3, 3])\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparing kernel functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the example above, a Gaussian kernel was used. Several other kernels are also available." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:58.653302Z", "iopub.status.busy": "2022-02-08T18:21:58.652855Z", "iopub.status.idle": "2022-02-08T18:21:58.657734Z", "shell.execute_reply": "2022-02-08T18:21:58.657016Z" } }, "outputs": [ { "data": { "text/plain": [ "['gau', 'epa', 'uni', 'tri', 'biw', 'triw', 'cos', 'cos2', 'tric']" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from statsmodels.nonparametric.kde import kernel_switch\n", "\n", "list(kernel_switch.keys())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The available kernel functions" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:58.663716Z", "iopub.status.busy": "2022-02-08T18:21:58.663256Z", "iopub.status.idle": "2022-02-08T18:21:59.767730Z", "shell.execute_reply": "2022-02-08T18:21:59.768439Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Create a figure\n", "fig = plt.figure(figsize=(12, 5))\n", "\n", "# Enumerate every option for the kernel\n", "for i, (ker_name, ker_class) in enumerate(kernel_switch.items()):\n", "\n", " # Initialize the kernel object\n", " kernel = ker_class()\n", "\n", " # Sample from the domain\n", " domain = kernel.domain or [-3, 3]\n", " x_vals = np.linspace(*domain, num=2 ** 10)\n", " y_vals = kernel(x_vals)\n", "\n", " # Create a subplot, set the title\n", " ax = fig.add_subplot(3, 3, i + 1)\n", " ax.set_title('Kernel function \"{}\"'.format(ker_name))\n", " ax.plot(x_vals, y_vals, lw=3, label=\"{}\".format(ker_name))\n", " ax.scatter([0], [0], marker=\"x\", color=\"red\")\n", " plt.grid(True, zorder=-5)\n", " ax.set_xlim(domain)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The available kernel functions on three data points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now examine how the kernel density estimate will fit to three equally spaced data points." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:21:59.771879Z", "iopub.status.busy": "2022-02-08T18:21:59.770919Z", "iopub.status.idle": "2022-02-08T18:22:00.711719Z", "shell.execute_reply": "2022-02-08T18:22:00.712415Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Create three equidistant points\n", "data = np.linspace(-1, 1, 3)\n", "kde = sm.nonparametric.KDEUnivariate(data)\n", "\n", "# Create a figure\n", "fig = plt.figure(figsize=(12, 5))\n", "\n", "# Enumerate every option for the kernel\n", "for i, kernel in enumerate(kernel_switch.keys()):\n", "\n", " # Create a subplot, set the title\n", " ax = fig.add_subplot(3, 3, i + 1)\n", " ax.set_title('Kernel function \"{}\"'.format(kernel))\n", "\n", " # Fit the model (estimate densities)\n", " kde.fit(kernel=kernel, fft=False, gridsize=2 ** 10)\n", "\n", " # Create the plot\n", " ax.plot(kde.support, kde.density, lw=3, label=\"KDE from samples\", zorder=10)\n", " ax.scatter(data, np.zeros_like(data), marker=\"x\", color=\"red\")\n", " plt.grid(True, zorder=-5)\n", " ax.set_xlim([-3, 3])\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A more difficult case\n", "\n", "The fit is not always perfect. See the example below for a harder case." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:00.715778Z", "iopub.status.busy": "2022-02-08T18:22:00.714848Z", "iopub.status.idle": "2022-02-08T18:22:00.720110Z", "shell.execute_reply": "2022-02-08T18:22:00.720770Z" } }, "outputs": [], "source": [ "obs_dist = mixture_rvs(\n", " [0.25, 0.75],\n", " size=250,\n", " dist=[stats.norm, stats.beta],\n", " kwargs=(dict(loc=-1, scale=0.5), dict(loc=1, scale=1, args=(1, 0.5))),\n", ")" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:00.723887Z", "iopub.status.busy": "2022-02-08T18:22:00.722970Z", "iopub.status.idle": "2022-02-08T18:22:00.729670Z", "shell.execute_reply": "2022-02-08T18:22:00.730321Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:00.733424Z", "iopub.status.busy": "2022-02-08T18:22:00.732499Z", "iopub.status.idle": "2022-02-08T18:22:00.959250Z", "shell.execute_reply": "2022-02-08T18:22:00.959953Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "ax.hist(obs_dist, bins=20, density=True, edgecolor=\"k\", zorder=4, alpha=0.5)\n", "ax.plot(kde.support, kde.density, lw=3, zorder=7)\n", "# Plot the samples\n", "ax.scatter(\n", " obs_dist,\n", " np.abs(np.random.randn(obs_dist.size)) / 50,\n", " marker=\"x\",\n", " color=\"red\",\n", " zorder=20,\n", " label=\"Data samples\",\n", " alpha=0.5,\n", ")\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The KDE is a distribution\n", "\n", "Since the KDE is a distribution, we can access attributes and methods such as:\n", "\n", "- `entropy`\n", "- `evaluate`\n", "- `cdf`\n", "- `icdf`\n", "- `sf`\n", "- `cumhazard`" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:00.963300Z", "iopub.status.busy": "2022-02-08T18:22:00.962365Z", "iopub.status.idle": "2022-02-08T18:22:00.970934Z", "shell.execute_reply": "2022-02-08T18:22:00.971582Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "obs_dist = mixture_rvs(\n", " [0.25, 0.75],\n", " size=1000,\n", " dist=[stats.norm, stats.norm],\n", " kwargs=(dict(loc=-1, scale=0.5), dict(loc=1, scale=0.5)),\n", ")\n", "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit(gridsize=2 ** 10)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:00.974884Z", "iopub.status.busy": "2022-02-08T18:22:00.973866Z", "iopub.status.idle": "2022-02-08T18:22:00.995890Z", "shell.execute_reply": "2022-02-08T18:22:00.996604Z" } }, "outputs": [ { "data": { "text/plain": [ "1.314324140492138" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kde.entropy" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:00.999850Z", "iopub.status.busy": "2022-02-08T18:22:00.998915Z", "iopub.status.idle": "2022-02-08T18:22:01.005179Z", "shell.execute_reply": "2022-02-08T18:22:01.005857Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.18085886])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kde.evaluate(-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cumulative distribution, it's inverse, and the survival function" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:01.009010Z", "iopub.status.busy": "2022-02-08T18:22:01.008083Z", "iopub.status.idle": "2022-02-08T18:22:01.766761Z", "shell.execute_reply": "2022-02-08T18:22:01.767457Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "ax.plot(kde.support, kde.cdf, lw=3, label=\"CDF\")\n", "ax.plot(np.linspace(0, 1, num=kde.icdf.size), kde.icdf, lw=3, label=\"Inverse CDF\")\n", "ax.plot(kde.support, kde.sf, lw=3, label=\"Survival function\")\n", "ax.legend(loc=\"best\")\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Cumulative Hazard Function" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2022-02-08T18:22:01.770758Z", "iopub.status.busy": "2022-02-08T18:22:01.769823Z", "iopub.status.idle": "2022-02-08T18:22:01.935440Z", "shell.execute_reply": "2022-02-08T18:22:01.935843Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "ax.plot(kde.support, kde.cumhazard, lw=3, label=\"Cumulative Hazard Function\")\n", "ax.legend(loc=\"best\")\n", "ax.grid(True, zorder=-5)" ] } ], "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": "3.8.12" } }, "nbformat": 4, "nbformat_minor": 4 }