{ "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": "2021-02-02T07:03:48.348959Z", "iopub.status.busy": "2021-02-02T07:03:48.348223Z", "iopub.status.idle": "2021-02-02T07:03:52.076618Z", "shell.execute_reply": "2021-02-02T07:03:52.077318Z" } }, "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": "2021-02-02T07:03:52.087034Z", "iopub.status.busy": "2021-02-02T07:03:52.080712Z", "iopub.status.idle": "2021-02-02T07:03:52.095983Z", "shell.execute_reply": "2021-02-02T07:03:52.094965Z" } }, "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": "2021-02-02T07:03:52.104941Z", "iopub.status.busy": "2021-02-02T07:03:52.104152Z", "iopub.status.idle": "2021-02-02T07:03:52.118474Z", "shell.execute_reply": "2021-02-02T07:03:52.117467Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:03:52.279437Z", "iopub.status.busy": "2021-02-02T07:03:52.278508Z", "iopub.status.idle": "2021-02-02T07:03:53.264478Z", "shell.execute_reply": "2021-02-02T07:03:53.263779Z" } }, "outputs": [ { "data": { 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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(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": { "execution": { "iopub.execute_input": "2021-02-02T07:03:53.270024Z", "iopub.status.busy": "2021-02-02T07:03:53.269243Z", "iopub.status.idle": "2021-02-02T07:03:53.278453Z", "shell.execute_reply": "2021-02-02T07:03:53.277798Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "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": "2021-02-02T07:03:53.287371Z", "iopub.status.busy": "2021-02-02T07:03:53.286585Z", "iopub.status.idle": "2021-02-02T07:03:54.234758Z", "shell.execute_reply": "2021-02-02T07:03:54.235395Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:03:54.245233Z", "iopub.status.busy": "2021-02-02T07:03:54.244435Z", "iopub.status.idle": "2021-02-02T07:03:55.325787Z", "shell.execute_reply": "2021-02-02T07:03:55.326873Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:03:55.331790Z", "iopub.status.busy": "2021-02-02T07:03:55.330357Z", "iopub.status.idle": "2021-02-02T07:03:55.351816Z", "shell.execute_reply": "2021-02-02T07:03:55.350723Z" } }, "outputs": [ { "data": { "text/plain": [ "['gau', 'epa', 'uni', 'tri', 'biw', 'triw', 'cos', 'cos2']" ] }, "execution_count": 1, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:03:55.360536Z", "iopub.status.busy": "2021-02-02T07:03:55.354704Z", "iopub.status.idle": "2021-02-02T07:03:58.814008Z", "shell.execute_reply": "2021-02-02T07:03:58.815105Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:03:58.820149Z", "iopub.status.busy": "2021-02-02T07:03:58.818661Z", "iopub.status.idle": "2021-02-02T07:04:01.947451Z", "shell.execute_reply": "2021-02-02T07:04:01.948122Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:04:01.954941Z", "iopub.status.busy": "2021-02-02T07:04:01.954154Z", "iopub.status.idle": "2021-02-02T07:04:01.964396Z", "shell.execute_reply": "2021-02-02T07:04:01.963553Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:04:01.969651Z", "iopub.status.busy": "2021-02-02T07:04:01.968875Z", "iopub.status.idle": "2021-02-02T07:04:01.973643Z", "shell.execute_reply": "2021-02-02T07:04:01.974280Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "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": "2021-02-02T07:04:01.993591Z", "iopub.status.busy": "2021-02-02T07:04:01.992799Z", "iopub.status.idle": "2021-02-02T07:04:02.707102Z", "shell.execute_reply": "2021-02-02T07:04:02.708393Z" } }, "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": { "execution": { "iopub.execute_input": "2021-02-02T07:04:02.715120Z", "iopub.status.busy": "2021-02-02T07:04:02.714336Z", "iopub.status.idle": "2021-02-02T07:04:02.733173Z", "shell.execute_reply": "2021-02-02T07:04:02.733986Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "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": { "execution": { "iopub.execute_input": "2021-02-02T07:04:02.737546Z", "iopub.status.busy": "2021-02-02T07:04:02.736800Z", "iopub.status.idle": "2021-02-02T07:04:02.808003Z", "shell.execute_reply": "2021-02-02T07:04:02.806984Z" } }, "outputs": [ { "data": { "text/plain": [ "1.314324140492138" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kde.entropy" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T07:04:02.814019Z", "iopub.status.busy": "2021-02-02T07:04:02.813263Z", "iopub.status.idle": "2021-02-02T07:04:02.820589Z", "shell.execute_reply": "2021-02-02T07:04:02.821202Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.18085886])" ] }, "execution_count": 1, "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": "2021-02-02T07:04:02.833235Z", "iopub.status.busy": "2021-02-02T07:04:02.832541Z", "iopub.status.idle": "2021-02-02T07:04:07.240481Z", "shell.execute_reply": "2021-02-02T07:04:07.239354Z" } }, "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", "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": "2021-02-02T07:04:07.245062Z", "iopub.status.busy": "2021-02-02T07:04:07.243677Z", "iopub.status.idle": "2021-02-02T07:04:07.881908Z", "shell.execute_reply": "2021-02-02T07:04:07.882963Z" } }, "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 1 }