{ "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 crossroads of statistics and differential geometry, focused on the study of probability distributions from a geometric point of view. One of the tools of information geometry is the Fisher information distance, which allows to compare probability distributions inside a given parametric family. In that sense, information geometry is an alternative approach to optimal transport. \n", "\n", "The Fisher information metric or Fisher-Rao metric - although the latter usually denotes its non parametric counterpart - is a Riemannian metric defined on the space of parameters of a family of distributions using the Fisher information matrix. This metric is invariant under change of parameterization. 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 information geometry of the family of normal distributions is arguably the most well-known. 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 information 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 information 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", "text/plain": [ "
" ] }, "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 information 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", "text/plain": [ "
" ] }, "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 information 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": 9, "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", "text/plain": [ "
" ] }, "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 an application to the study of the leaf inclination angle distribution of plants. The leaf angle distribution among a common plant species can be appropriately represented by a beta distribution ([CPR2018](#References)). The dataset `leaves` ([CPR2018](#References)) contains pairs of beta distribution parameters, each describing the distribution of the inclination angles of leaves inside a given plant species. These species are divided into 5 categories according to inclination angle distribution type: spherical, erectophile, uniform, planophile and plagiophile." ] }, { "cell_type": "code", "execution_count": 11, "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": 12, "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=(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": 13, "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": 14, "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=(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", ".. [CPR2018] F. Chianucci, J. Pisek, K. Raabe et al. A dataset of leaf inclination angles for temperate and boreal broadleaf woody species. Annals of Forest Science Vol. 75, No. 50, 2018. https://doi.org/10.17632/4rmc7r8zvy.2.\n", "\n", ".. [LGRP2020] A. Le Brigant, N. Guigui, S. Rebbah and S. Puechmorel, Classifying histograms of medical data using information geometry of beta distributions. IFAC-PapersOnLine, Vol. 54, No. 9, 514-520, 2021." ] } ], "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 }