{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: Information geometry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Disclaimer: this notebook requires the use of the ```numpy``` backend." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "Information geometry is a branch of mathematics at the crossroad of statistics and differential geometry, focused on the study of probability distributions from a geometric point of view. Although it has been extended to the non parametric case, this framework is foremost concerned with parameteric families of probability distributions. The space of parameters, an open subset of the Euclidean space, is seen as a differential manifold and the Fisher information matrix is used to define a Riemannian metric on it, called the Fisher-Rao metric or Fisher information metric. This metric is invariant under change of parameterization, which makes it a natural choice. Moreover it is the only Riemannian metric compatible with the notion of information contained by the model on the parameter, in the sense that it is the only metric that preserves the geometry of a parametric model after transformation by a sufficient statistic (Cencov's theorem). For an overview, see [[A2016]](#References)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before starting this tutorial, we set the working directory to be the root of the geomstats repository. In order to have the code working on your machine, you need to change this path to the path of your geomstats repository." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Working directory: /Users/alicelebrigant/ownCloud/Python/SpyderProjects/geomstats\n" ] } ], "source": [ "import os\n", "import subprocess\n", "\n", "geomstats_gitroot_path = subprocess.check_output(\n", " ['git', 'rev-parse', '--show-toplevel'], \n", " universal_newlines=True)\n", "\n", "os.chdir(geomstats_gitroot_path[:-1])\n", "\n", "print('Working directory: ', os.getcwd())" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO: Using numpy backend\n" ] } ], "source": [ "import matplotlib\n", "import matplotlib.image as mpimg\n", "import matplotlib.pyplot as plt\n", "from matplotlib.lines import Line2D\n", "\n", "import geomstats.backend as gs\n", "import geomstats.visualization as visualization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normal distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Fisher-Rao geometry of the family of normal distributions is arguably the simplest example of two-dimensional information geometry. The space of parameters is the upper half-plane where the x-coordinate encodes the mean and the y-coordinate the standard deviation. Quite remarkably, the Fisher-Rao metric induces the hyperbolic geometry of the Poincare half plane [[AM1981]](#References). To start, we need an instance of the class ```NormalDistributions``` and its Fisher-Rao metric." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from geomstats.information_geometry.normal import NormalDistributions\n", "\n", "normal = NormalDistributions()\n", "fisher_metric = normal.metric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the ```visualization``` module, we can plot the geodesic between two points, each defining the parameters (mean and standard deviation) for a normal distribution. We recognise the shape of a geodesic of the Poincare half-plane, namely a half-circle orthogonal to the x-axis." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "point_a = gs.array([1., 1.])\n", "point_b = gs.array([3., 1.])\n", "\n", "geodesic_ab_fisher = fisher_metric.geodesic(point_a, point_b)\n", "\n", "n_points = 20\n", "t = gs.linspace(0, 1, n_points)" ] }, { "cell_type": "code", "execution_count": 5, "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=(10, 5))\n", "ax = fig.add_subplot(111)\n", "cc = gs.zeros((n_points, 3))\n", "cc[:, 2] = gs.linspace(0, 1, n_points)\n", "\n", "visualization.plot(\n", " geodesic_ab_fisher(t), ax=ax, space='H2_poincare_half_plane', label='point on geodesic', color=cc)\n", "\n", "ax.set_xlim(0., 4.)\n", "ax.set_ylim(0., 2.)\n", "ax.set_title('Geodesic between two normal distributions for the Fisher-Rao metric')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each point of the geodesic defines a normal distribution, and so we obtain an optimal interpolation between the distributions corresponding to ```point_a``` and ```point_b```, which we can visualize in terms of probability density functions." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pdfs = normal.point_to_pdf(geodesic_ab_fisher(t))\n", "x = gs.linspace(-3., 7., 100)\n", "\n", "fig = plt.figure(figsize=(10, 5))\n", "for i in range(n_points):\n", " plt.plot(x, pdfs(x)[:, i], color=cc[i, :])\n", "plt.title('Corresponding interpolation between pdfs');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another possibility to compare probability distributions is given by the $L^2$-Wasserstein metric, central in optimal transport. In the case of normal distributions, the $L^2$-Wasserstein metric induces the Euclidean geometry on the upper half plane [[BGKL2017]](#References). Therefore, the Wasserstein distance between two normal distributions with different means and same variance (```point_a``` and ```point_b```) will not change when this common variance is increased (```point_c``` and ```point_d```), while the corresponding Fisher-Rao distance will decrease, as can be deduced from the shape of the geodesic. This can be interpreted as a consequence of the increasing overlap of the corresponding probability densities." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from geomstats.geometry.euclidean import Euclidean\n", "\n", "plane = Euclidean(2)\n", "wasserstein_metric = plane.metric\n", "\n", "point_c = gs.array([1., 3.])\n", "point_d = gs.array([3., 3.])\n", "\n", "geodesic_cd_fisher = fisher_metric.geodesic(point_c, point_d)\n", "geodesic_ab_wasserstein = wasserstein_metric.geodesic(point_a, point_b)\n", "geodesic_cd_wasserstein = wasserstein_metric.geodesic(point_c, point_d)\n", "\n", "points = gs.stack((point_a, point_b, point_c, point_d))\n", "pdfs = normal.point_to_pdf(points)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "fig = plt.figure(figsize=(12, 5))\n", "ax1 = fig.add_subplot(121)\n", "\n", "visualization.plot(\n", " gs.vstack((geodesic_ab_fisher(t), geodesic_cd_fisher(t))), \n", " ax=ax1, space='H2_poincare_half_plane', label='Fisher-Rao geodesic',\n", " color='black')\n", "visualization.plot(\n", " gs.vstack((geodesic_ab_wasserstein(t), geodesic_cd_wasserstein(t))),\n", " ax=ax1, space='H2_poincare_half_plane', label='Wasserstein geodesic',\n", " color='black', alpha=0.5)\n", "visualization.plot(\n", " gs.stack((point_a, point_b)), ax=ax1, space='H2_poincare_half_plane', \n", " label='points a and b', s=100)\n", "visualization.plot(\n", " gs.stack((point_c, point_d)), ax=ax1, space='H2_poincare_half_plane', \n", " label='points c and d', s=100)\n", "\n", "ax1.set_xlim(0., 4.)\n", "ax1.set_ylim(0., 4.)\n", "ax1.legend();\n", "\n", "ax2 = fig.add_subplot(122)\n", "x = gs.linspace(-3., 7., 100)\n", "lines = [Line2D([0], [0], color='C0'),\n", " Line2D([0], [0], color='C1')]\n", "ax2.plot(x, pdfs(x)[:, :2], c='C0')\n", "ax2.plot(x, pdfs(x)[:, 2:], c='C1')\n", "ax2.legend(lines, ['pdfs a and b', 'pdfs c and d']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beta distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now consider the example of beta distributions, where the space of parameters is the first quadrant. In this case, the geodesics for the Fisher-Rao metric do not have a closed form, but can be found numerically [[LGRP2020]](#References). Here we plot an example of geodesic ball." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from geomstats.information_geometry.beta import BetaDistributions\n", "\n", "beta = BetaDistributions()" ] }, { "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": [ "n_rays = 50\n", "center = gs.array([2., 2.])\n", "theta = gs.linspace(-gs.pi, gs.pi, n_rays)\n", "directions = gs.transpose(\n", " gs.stack((gs.cos(theta), gs.sin(theta))))\n", "\n", "fig = plt.figure(figsize=(5, 5))\n", "ax = fig.add_subplot(111)\n", "ray_length = 0.25\n", "direction_norms = beta.metric.squared_norm(directions, center)**(1/2)\n", "unit_vectors = directions/gs.expand_dims(direction_norms, 1)\n", "initial_vectors = ray_length * unit_vectors\n", "\n", "n_points = 10\n", "t = gs.linspace(0., 1., n_points)\n", "for j in range(n_rays):\n", " geod = beta.metric.geodesic(\n", " initial_point=center, initial_tangent_vec=initial_vectors[j, :])\n", " ax.plot(*gs.transpose(gs.array([geod(k) for k in t])))\n", "ax.set_xlim(1, 3)\n", "ax.set_ylim(1, 3)\n", "ax.set_title('Geodesic ball of the space of beta distributions');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we consider the dataset ```leaves```, which contains parameters of beta distributions fitted to inclination angles of leaves of different plant species (*A dataset of leaf inclination angles for temperate and boreal broadleaf woody species*, https://doi.org/10.17632/4rmc7r8zvy.2). These species are divided into 5 categories according to inclination angle distribution type: spherical, erectophile, uniform, planophile and plagiophile. For each species, a beta distribution is fitted to the set of inclination angle measurements. Each species can therefore be represented by a point in the manifold of beta distributions." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import geomstats.datasets.utils as data_utils\n", "\n", "beta_param, distrib_type = data_utils.load_leaves()" ] }, { "cell_type": "code", "execution_count": 5, "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=(5, 5))\n", "for distrib in set(distrib_type):\n", " points = beta_param[distrib_type==distrib, :]\n", " plt.plot(points[:, 0], points[:, 1], 'o', label=distrib)\n", "plt.title('Beta parameters of the leaf inclination angle distributions of 172 different species')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the ```FrechetMean``` learning class, we can compute the leaf inclination angle mean distribution among the species of type 'planophile'." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from geomstats.learning.frechet_mean import FrechetMean\n", "\n", "points_plan = beta_param[distrib_type=='planophile', :]\n", "\n", "mean = FrechetMean(metric=beta.metric)\n", "mean.fit(points_plan)\n", "\n", "mean_estimate = mean.estimate_" ] }, { "cell_type": "code", "execution_count": 7, "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=(5, 5))\n", "plt.plot(points_plan[:, 0], points_plan[:, 1], 'o', label='planophile')\n", "plt.plot(*mean_estimate, 'o', markersize=10, label='mean planophile')\n", "plt.title('Beta parameters of the leaf inclination angle mean distribution '\n", " 'of species of planophile type')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", ".. [A2016] S. Amari. Information geometry and its applications. Vol. 194. Springer, 2016.\n", "\n", ".. [AM1981] C. Atkinson and A. FS Mitchell. Rao’s distance measure. Sankhya: The Indian Journal of Statistics. Series A, pp. 345–365, 1981.\n", "\n", ".. [BGKL2017] J. Bigot, R. Gouet, T. Klein and A. López. Geodesic PCA in the Wasserstein space by convex PCA. In Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. Vol. 53. No. 1. Institut Henri Poincaré, 2017.\n", "\n", ".. [LGRP2020] A. Le Brigant, N. Guigui, S. Rebbah and S. Puechmorel, Classifying histograms of medical data using information geometry of beta distributions. arXiv preprint arXiv:2006.04511, 2020." ] } ], "metadata": { "celltoolbar": "Tags", "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 4 }