{ "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": {}, "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": {}, "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": {}, "outputs": [], "source": [ "# Location, scale and weight for the two distributions\n", "dist1_loc, dist1_scale, weight1 = -1 , .5, .25\n", "dist2_loc, dist2_scale, weight2 = 1 , .5, .75\n", "\n", "# Sample from a mixture of distributions\n", "obs_dist = mixture_rvs(prob=[weight1, weight2], size=250,\n", " dist=[stats.norm, stats.norm],\n", " kwargs = (dict(loc=dist1_loc, scale=dist1_scale),\n", " dict(loc=dist2_loc, scale=dist2_scale)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simplest non-parametric technique for density estimation is the histogram." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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(obs_dist, np.abs(np.random.randn(obs_dist.size)),\n", " zorder=15, color='red', marker='x', alpha=0.5, label='Samples')\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": {}, "outputs": [], "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": {}, "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(obs_dist, bins=20, density=True, label='Histogram from samples',\n", " zorder=5, edgecolor='k', alpha=0.5)\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 = (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", "ax.plot(kde.support, true_values, lw=3, label='True distribution', zorder=15)\n", "\n", "# Plot the samples\n", "ax.scatter(obs_dist, np.abs(np.random.randn(obs_dist.size))/40,\n", " marker='x', color='red', zorder=20, label='Samples', alpha=0.5)\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": {}, "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(obs_dist, bins=25, label='Histogram from samples',\n", " zorder=5, edgecolor='k', density=True, alpha=0.5)\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(kde.support, kde.density, '--', lw=2, color='k', zorder=10,\n", " label='KDE from samples, bw = {}'.format(round(bandwidth, 2)))\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(obs_dist, np.abs(np.random.randn(obs_dist.size))/50,\n", " marker='x', color='red', zorder=20, label='Data samples', alpha=0.5)\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": {}, "outputs": [ { "data": { "text/plain": [ "['gau', 'epa', 'uni', 'tri', 'biw', 'triw', 'cos', 'cos2']" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from statsmodels.nonparametric.kde import kernel_switch\n", "list(kernel_switch.keys())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The available kernel functions" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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(2, 4, 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": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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(2, 4, 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": {}, "outputs": [], "source": [ "obs_dist = mixture_rvs([.25, .75], size=250, dist=[stats.norm, stats.beta],\n", " kwargs = (dict(loc=-1, scale=.5), dict(loc=1, scale=1, args=(1, .5))))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "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(obs_dist, np.abs(np.random.randn(obs_dist.size))/50,\n", " marker='x', color='red', zorder=20, label='Data samples', alpha=0.5)\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": {}, "outputs": [], "source": [ "obs_dist = mixture_rvs([.25, .75], size=1000, dist=[stats.norm, stats.norm],\n", " kwargs = (dict(loc=-1, scale=.5), dict(loc=1, scale=.5)))\n", "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit(gridsize=2**10)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.314324140492138" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kde.entropy" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "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": {}, "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": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }