{ "cells": [ { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [], "source": [ "#%matplotlib inline \n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.tri as tri\n", "import scipy.stats as sps\n", "\n", "# Pre-calculate some global data used by functions plot_simplex, plot_dirichlet, and plot_points_in_simplex\n", "_corners = np.array([[0, 0], [1, 0], [0.5, 0.75**0.5]])\n", "_invT = np.linalg.inv(_corners[:2]-_corners[2])\n", "_triangle = tri.Triangulation(_corners[:, 0], _corners[:, 1])\n", "_refiner = tri.UniformTriRefiner(_triangle)\n", "_trimesh = _refiner.refine_triangulation(subdiv=7)\n", "# Now convert _trimesh 2D cartesian coordinates to 3D barycentric coordinates (i.e. 3D point on the 2D simplex)\n", "# as described in https://en.wikipedia.org/wiki/Barycentric_coordinate_system#Edge_approach\n", "# We calculate only the first 2 barycentric coordinates as sps.dirichlet.pdf is happy without the last one (l3 = 1-l1+l2)\n", "_tol=1.e-8\n", "_l1l2 = (np.c_[_trimesh.x, _trimesh.y] -_corners[2]) @ _invT\n", "_l1l2 = np.clip(_l1l2, 2*_tol, 1.0-_tol) - _tol # to make sure that none of the probabilities is exactly zero or one\n", "\n", "def plot_simplex(class_labels=[\"\"]*3): \n", " '''Plot \"axis\" for 2-simplex. It simply plots a triangle into which we will be ploting points\n", " representing Categorical distributions (for 3 categories/topics) or a Dirichlet distribution.\n", " Arguments:\n", " class_labels: list of 3 strings that are used as labels (i.e. category/topic names) for the\n", " simplex (triangle) corners\n", " '''\n", " plt.triplot(_triangle, linewidth=1)\n", " #plt.xlim(0, 1)\n", " #plt.ylim(0, 0.75**0.5)\n", " plt.axis('equal')\n", " plt.axis('off')\n", " plt.text(0, 0, class_labels[0], horizontalalignment='left', verticalalignment='top')\n", " plt.text(1, 0, class_labels[1], horizontalalignment='right', verticalalignment='top')\n", " plt.text(0.5, 0.75**0.5, class_labels[2], horizontalalignment='center', verticalalignment='bottom')\n", "\n", "\n", "def plot_dirichlet(alpha, nlevels=128, **kwargs):\n", " '''Plot Dirichlet pdf in an equilateral triangle (2-simplex).\n", " Arguments:\n", " alpha: Dirichlet distribution parameters.\n", " nlevels (int): Number of contours (shades) to draw.\n", " kwargs: Keyword args passed on to `plt.tricontourf`.\n", " '''\n", " plt.tricontourf(_trimesh, sps.dirichlet.pdf(_l1l2.T, alpha), nlevels, cmap='gray_r', **kwargs)\n", " \n", "def plot_points_in_simplex(X, **kwargs):\n", " '''Plots a set of points in the 2-simplex. Each point can represent\n", " a categorical distribution with 3 categories/topics.\n", " Arguments:\n", " X: A Nx3 array in barycentric coordinates of points to plot.\n", " kwargs: Keyword args passed on to `plt.plot`.\n", " '''\n", " plt.plot(*(X @ _corners).T, **kwargs)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian inference for Categorical distribution\n", "$$\n", "\\DeclareMathOperator{\\Dir}{Dir}\n", "\\DeclareMathOperator{\\aalpha}{\\boldsymbol{\\alpha}}\n", "\\DeclareMathOperator{\\mm}{\\mathbf{m}}\n", "\\DeclareMathOperator{\\Cat}{Cat}\n", "\\DeclareMathOperator{\\ppi}{\\boldsymbol{\\pi}}\n", "$$\n", "\n", "Categorical distribution for categorical variable $x \\in \\{1, 2, \\dots, C\\}$ can be parametrized by vector of probabilities for individual categries $\\ppi = [\\pi_1, \\dots, \\pi_C]$\n", "$$\n", "\\large\n", "p(x \\mid \\ppi) = \\Cat(x \\mid \\ppi) = \\pi_x\n", "$$\n", "\n", "Dirichlet distribution can be used as conjugate prior for parameters $\\ppi$ of Categorical distribution.\n", "\n", "$$\n", "\\large\n", "\\Dir(\\ppi \\mid \\aalpha) = \\frac{\\Gamma\\left (\\sum_{c=1}^C \\alpha_c \\right)}{\\prod_{c=1}^C \\Gamma(\\alpha_c)} \\prod_{c=1}^C \\pi_c^{\\alpha_c - 1}\n", "$$\n", "where $\\aalpha= [\\alpha_1, \\alpha_2, \\dots, \\alpha_C]$ is the vector of prior parameters." ] }, { "cell_type": "code", "execution_count": 438, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot some example NormalGamma distribution\n", "#alpha = [1.0, 1.0, 1.0] # flat prior\n", "#alpha = [0.5, 0.5, 0.5] # Jeffreys prior\n", "alpha = [6.0, 4.0, 3.0]\n", "plot_simplex([1,2,3])\n", "plot_dirichlet(alpha)\n", "\n", "# Obtain few samples from the prior distribution.\n", "pi_sampled = sps.dirichlet.rvs(alpha, 20)\n", "plot_points_in_simplex(pi_sampled, c='b', ls='none', marker='+')\n", "\n", "# Each of these samples represents parameters (probabilities) of a categorical distribution. We will plot them\n", "\n", "plt.figure()\n", "for i, pi in enumerate(pi_sampled):\n", " plt.subplot(5, 4, i+1)\n", " plt.axis([0.9, 3.1, 0, 1])\n", " plt.stem([1,2,3], pi)\n", "plt.subplots_adjust(wspace=0.5, hspace=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given $N$ observations $\\mathbf{x}=[x_1, x_2, \\dots, x_N]$ from categorical distribution $\\Cat(x \\mid \\ppi)$ and given prior $p(\\ppi) = \\Dir(\\ppi \\mid \\aalpha)$ the poterior distribution over parameters $\\ppi$ is:\n", "\n", "$$\n", "\\large\n", "p(\\ppi |\\mathbf{x}) = \\Dir(\\ppi |\\aalpha + \\mm)\n", "$$, \n", "\n", "where\n", "\n", "$\\mm = [m_1, m_2, \\dots, m_C]$ is vector of counts saying how many each category appears in the input observations $\\mathbf{x}$.\n", "\n", "Note that each $\\alpha_c-1$ can be seen as prior count for observing category $c$." ] }, { "cell_type": "code", "execution_count": 468, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Groud truth categorical distribution: [0.5, 0.3, 0.2]\n", "Counts for observations sampled from this distribution: [7 3 0]\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Let's have a Categorical distribution, which we believe to be sampled from the above Dirichlet prior\n", "pi = [0.5, 0.3, 0.2]\n", "\n", "#We could actually sample it from the prior\n", "#pi = sps.dirichlet.rvs(alpha, 1)[0]\n", "print(\"Groud truth categorical distribution:\", pi)\n", "\n", "# Generate observation from a given categorical distribution and obtain the count for each category. \n", "#This corresponds to directly sampling from Multiomial distribution:\n", "\n", "N = 10\n", "m = sps.multinomial.rvs(N, pi)\n", "print(\"Counts for observations sampled from this distribution:\", m)\n", "\n", "# Given Dirichlet prior and the observations (counts), calculate and plot posterior distibution of the parameters of categorical distributions\n", "plot_simplex([1,2,3])\n", "plot_dirichlet(alpha+m)\n", "\n", "# Obtain few samples from the posterior distribution.\n", "pi_sampled = sps.dirichlet.rvs(alpha+m, 100)\n", "plot_points_in_simplex(pi_sampled, c='b', ls='none', marker='+')\n", "plot_points_in_simplex(pi, c='k', ls='none', marker='o', label=\"Ground truth\")\n", "plot_points_in_simplex(m/m.sum(), c='r', ls='none', marker='^', label=\"ML estimate\")\n", "# Maximum of the Dirichlet posterior will be the same as ML estimate for flat prior \\alpha=[1.0 1.0 1.0]\n", "plot_points_in_simplex((alpha+m-1)/(alpha+m-1).sum(), c='m', ls='none', marker='*', label=\"MAP estimate\") \n", "plt.legend()\n", "\n", "# Each of these samples represents parameters (probabilities) of a categorical distribution that could have generated the input observations\n", "plt.figure()\n", "for i, p in enumerate(pi_sampled[:20]):\n", " plt.subplot(5, 4, i+1)\n", " plt.axis([0.9, 3.1, 0, 1])\n", " plt.stem([1,2,3], p)\n", "plt.subplots_adjust(wspace=0.5, hspace=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predictive probability\n", "\n", "For Categorical distribution with Dirichlet prior, the posterior predictive distribution is again Categorical distribution:\n", "\n", "$$\n", "\\large\n", "\\newcommand{\\diff}{\\mathop{}\\!d}\n", "\\begin{align}\n", "p(x' \\mid \\mathbf{x}) \n", "&= \\int p(x'\\mid\\ppi) p(\\ppi \\mid \\mathbf{x}) \\diff\\ppi \\\\\n", "&= \\int \\Cat(x'\\mid\\ppi) \\Dir(\\ppi\\mid \\aalpha+\\mm) \\diff \\ppi \\\\ \n", "&= \\Cat\\left(x'\\middle| \\frac{\\aalpha+\\mm}{\\sum_{c=1}^C \\alpha_c+m_c}\\right) \n", "\\end{align}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 471, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 471, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(-5,5,1000) # x-axis for our plots\n", "# Plot the distribution from which the observations were generated\n", "plt.axis([0.9, 3.1, 0, 1])\n", "plt.stem(np.array([1,2,3]), pi, 'k', markerfmt=\"o\", label=\"Ground true\")\n", "\n", "# Plot the ML estimate of the Categorical distribution\n", "plt.stem(np.array([1,2,3])+0.02, m/m.sum(), 'r', markerfmt=\"^\", label=\"ML\")\n", "\n", "# Plot predictive distribution, which depends on the prior and the observations \n", "# (i.e. depends on the posterior distribution over the parameters \\pi)\n", "plt.stem(np.array([1,2,3])+0.04, (alpha+m)/(alpha+m).sum(), 'g', markerfmt=\"+\", label=\"Posterior predictive\")\n", "\n", "# Take all the sampled Categorical distributions from the previous figure, average them and plot the resulting distribution\n", "# For large number of samples, this should be good approximation to the predictive distribution \n", "#plt.plot(t, pi_sampled.mean(axis=1))\n", "plt.stem(np.array([1,2,3])+0.06, pi_sampled.mean(axis=0), 'b', markerfmt=\"x\", label=\"Empirical predictive\")\n", "plt.legend()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 4 }