{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: Non-parametric Density Estimation\n", "## Introduction\n", "In this tutorial we'll show how some of the estimators included in the **UNITE** toolbox can be used to estimate probability density using sample data *aka* non-parametric density estimation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Data\n", "First we'll generate samples of a specific probability distribution for which we want to calculate probability density at specific points $(x)$. In this tutorial we'll be using a mixture of two bivariate Gaussian distributions. Generally, a multivariate Gaussian distribution has the following probability density function (PDF):\n", "\n", "$$\n", " p(X) = \\frac{1}{\\left ( 2\\pi \\right )^{d/2} \\left ( \\det{(\\Sigma)} \\right )^{1/2}} \\exp{\\left ( -\\frac{1}{2}\\left ( x - \\mu \\right )^\\intercal \\Sigma^{-1} \\left ( x - \\mu \\right ) \\right )}\n", "$$\n", "\n", "In this case $X$ would be 2D vector $(x_1, x_2)$. And the distribution would be parameterized by a 2D vector of means $\\mu$ and a $2 \\times 2$ covariance matrix $\\Sigma$.\n", "\n", "For this simple 2D case, the **UNITE** toolbox has auxiliary functions to generate samples through rejection sampling. We only need to define the PDF of the functions we want to sample and the ranges in which to sample.\n", "\n", "Here we'll be a little bit more creative and sample a mixture of 2D Gaussian distributions. Let's do it:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy import stats\n", "\n", "\n", "def pdf_bivariate_gaussian(x, y, params):\n", " z = 0.0\n", " for dist in params:\n", " l, s, w = dist\n", " z += stats.multivariate_normal(mean=l, cov=s).pdf(np.dstack((x, y))) * w\n", " return z\n", "\n", "\n", "# Dist. parameters format: [[mu], [cov], weight]\n", "dist_params = [\n", " [[-2, 0], [[1, -0.5], [-0.5, 1]], 0.5], # 1st component\n", " [[2, 0], [[1, 0.5], [0.5, 1]], 0.5], # 2nd component\n", "]\n", "\n", "dist_lims = [[-25, 25], [-25, 25]] # Lower and upper limits per dimension" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having properly defined our PDF, now we can generate $1\\,000$ samples of this bivariate Gaussian mixture distribution using the **UNITE** toolbox." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from unite_toolbox.utils.sampling import get_samples\n", "\n", "samples = get_samples(\n", " func=pdf_bivariate_gaussian,\n", " limits=dist_lims,\n", " n_samples=1_000,\n", " seed=42,\n", " params=dist_params,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's it! Now we have $1\\,000$ samples to test non-parametric density estimation methods. Before we proceed, let's plot the true distribution and check that the samples were correctly sampled." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "x = np.linspace(-5, 5, 1_000)\n", "y = np.linspace(-5, 5, 1_000)\n", "X, Y = np.meshgrid(x, y)\n", "P = pdf_bivariate_gaussian(X, Y, params=dist_params)\n", "\n", "fig, ax = plt.subplots(figsize=(3, 3))\n", "ax.contourf(X, Y, P, cmap=\"Greys\")\n", "ax.scatter(samples[:, 0], samples[:, 1], c=\"tab:red\", s=0.3)\n", "ax.set_xlabel(\"$x_1$\")\n", "ax.set_xlim([-4.5, 4.5])\n", "ax.set_ylabel(\"$x_2$\")\n", "ax.set_ylim([-2.5, 2.5])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks good! The underlying distribution is colored in black and white and our samples, in red, look clustered around the darker regions which represents higher density. Now we'll test the density estimation methods.\n", "\n", "Before continuing, here we'll define a function to ease plotting later in this Notebook. The cell for this function is collapsed by default but can be expanded for viewing." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import matplotlib.ticker as tkr\n", "\n", "\n", "def plot_density_comparison(X, Y, P, fx):\n", " fig, ax = plt.subplots(figsize=(6, 4))\n", " cs1 = ax.contourf(X, Y, P, cmap=\"Greys\")\n", " cs2 = ax.contourf(X, Y, fx.reshape(X.shape), cmap=\"Reds\", alpha=0.50)\n", " # Details\n", " ax.set_xlabel(\"$x_1$\")\n", " ax.set_xlim([-4.5, 4.5])\n", " ax.set_ylabel(\"$x_2$\")\n", " ax.set_ylim([-2.5, 2.5])\n", " ax.grid(ls=\"--\", alpha=0.50)\n", " # Colorbars\n", " cbar1 = fig.colorbar(cs1)\n", " cbar1.ax.yaxis.set_major_formatter(tkr.FormatStrFormatter(\"%.2f\"))\n", " cbar1.set_label(\"True\", labelpad=-34, y=1.07, rotation=0)\n", " cbar2 = fig.colorbar(cs2)\n", " cbar2.ax.yaxis.set_major_formatter(tkr.FormatStrFormatter(\"%.3f\"))\n", " cbar2.set_label(\"Est.\", labelpad=-32, y=1.07, rotation=0)\n", " return fig, ax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Density Estimation\n", "### Binning\n", "For histogram based density estimation or \"binning\" there are several \"rules-of-thumb\" for selecting an adequate number of bins. The problem is that all of these rules have been developed for one-dimensional data and there are no similar rules for the higher-dimensional cases. As such, binning strategies are highly dependant on a specific user or application.\n", "\n", "As guidance, the **UNITE** toolbox includes a function that estimates the \"ideal\" number of bins across all dimensions of a dataset using some of the well-established rules-of-thumb. The result is given in a dictionary that can be indexed by the name of a specific rule to get a list of the number of bins required per dimension." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rule --> Bins\n", "fd [14, 26]\n", "scott [14, 20]\n", "sturges [12, 12]\n", "doane [13, 13]\n" ] } ], "source": [ "from unite_toolbox.bin_estimators import estimate_ideal_bins\n", "\n", "n_bins = estimate_ideal_bins(samples, counts=True)\n", "print(\"Rule --> Bins\")\n", "for key, val in n_bins.items():\n", " print(f\"{key:<8} {val}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, as the Sturge's rule-of-thumb gives the least amount of bins, we'll choose this one as we'll be using it for plotting later. This might not be optimal in terms of how close the density calculated at each bin is to the \"true\" density but that is not of interest for this example. We just want to see the differences between methods. The selection of a specific binning scheme is highly dependant on a given application. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "n_bins = estimate_ideal_bins(samples, counts=False)[\"sturges\"]\n", "# counts=False to use the binning scheme later as ticks in a plot\n", "# of the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's see how \"binning\" evaluates density! To make this exercise more visual, we'll evaluate a grid of points and plot the estimated densities on top of the true density plot of the bivariate Gaussian distribution. To evaluate density, we just need one function from the **UNITE** toolbox." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from unite_toolbox.bin_estimators import calc_bin_density\n", "\n", "pos = np.column_stack(\n", " (X.flatten(), Y.flatten())\n", ") # stack the X and Y vectors used for plotting\n", "fx2 = calc_bin_density(x=pos, data=samples, edges=n_bins)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we plot using the previously defined function. In addition, we'll use the previously calculated \"sturges\" binning scheme as tick marks in our plot to distinguish between different bins." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot\n", "fig, ax = plot_density_comparison(X, Y, P, fx2) # Previously defined funtion\n", "# Some additional details\n", "ax.set_xticks(n_bins[0])\n", "ax.xaxis.set_tick_params(rotation=60)\n", "ax.set_xlim([-4.5, 4.5])\n", "ax.set_yticks(n_bins[1])\n", "ax.set_ylim([-2.5, 2.5])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nice! Generally, we see the typical grid of a 2D histogram and, based on the estimated densities, we can say that binning using \"sturges\" rule-of-thumb tends to overestimate density." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### KDE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now for KDE the **UNITE** toolbox uses a Gaussian kernel. Therefore, there are not as many options to be tweaked." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "from unite_toolbox.kde_estimators import calc_kde_density\n", "\n", "fx3 = calc_kde_density(x=pos, data=samples)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plot_density_comparison(X, Y, P, fx3) # Previously defined funtion\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "KDE-based estimation is generally very good at matching this case because of the use of a Gaussian kernel. This might not be the case for other types of data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $k$-NN" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we have $k$NN-based estimation which, again, requires very little tweaking. One thing to note though is the number of neighbors $k$ being used for estimation. $k=50$ is much higher than any of the recommended values for estimating information-theoretic quantities where $k$ ranges between $k=1$ and $k=15$. If a lower value of $k$ is used, a lower radius gives less influence to each individual sample and its neighbors." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "from unite_toolbox.knn_estimators import calc_knn_density\n", "\n", "fx4 = calc_knn_density(x=pos, data=samples, k=50)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plot_density_comparison(X, Y, P, fx4) # Previously defined funtion\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another thing to note is the difference in estimated densities for $k$-NN and the true distribution, and the other methods tried previously. The variance of $k$-NN based estimation for density is very high and therefore it's not recommended for density estimation using only one sample. The process does benefit from multiple samples from which the average density can be calculated." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparing Methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's compare the three density estimation methods against the true distribution. As we saw previously, there are significant differences on the magnitude of the densities estimated by each method. Therefore we'll keep the same color scale for the magnitude of the estimated density with the reference being the true distribution. \n", "\n", "Don't worry too much about this code, it's fairly simple but it's only here to generate the last plot and not important to the overall understanding of this tutorial." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot\n", "\n", "fig = plt.figure(figsize=(9, 5))\n", "b = 0.30\n", "h = 0.38\n", "\n", "ax1 = fig.add_axes((0.38, 0.57, b + 0.07, h))\n", "ax2 = fig.add_axes((0.06, 0.09, b, h))\n", "ax3 = fig.add_axes((0.38, 0.09, b, h))\n", "ax4 = fig.add_axes((0.70, 0.09, b, h))\n", "\n", "cbar = ax1.contourf(X, Y, P)\n", "\n", "ax2.contourf(X, Y, fx2.reshape(X.shape), levels=cbar.levels)\n", "ax3.contourf(X, Y, fx3.reshape(X.shape), levels=cbar.levels)\n", "ax4.contourf(X, Y, fx4.reshape(X.shape), levels=cbar.levels)\n", "\n", "for ax in [ax1, ax2, ax3, ax4]:\n", " ax.set_xlim([-4.5, 4.5])\n", " ax.set_ylim([-2.5, 2.5])\n", "\n", "for ax in [ax1, ax2]:\n", " ax.set_ylabel(\"$x_2$\")\n", "\n", "for ax in [ax2, ax3, ax4]:\n", " ax.set_xlabel(\"$x_1$\")\n", "\n", "for ax in [ax3, ax4]:\n", " ax.get_yaxis().set_visible(False)\n", "\n", "ax1.get_xaxis().set_visible(False)\n", "\n", "ax2.set_title(\"Binning\")\n", "ax3.set_title(\"KDE\")\n", "ax4.set_title(\"$k$-NN\")\n", "ax1.set_title(\"True distribution\")\n", "plt.colorbar(cbar)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this plot alone, the differences between methods are very apparent. KDE appears as the most suitable method for density estimation while $k$-NN is not recommended at all. Binning also seems suitable but the choice of an adequate binning scheme remains a challenge that needs to be addressed." ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 2 }