Related papers: The Information-Geometric Perspective of Compositi…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…
Motivated by the corrected form of the entropy-area law, and with the help of von Neumann entropy of quantum matter, we construct an emergent spacetime by the virtue of the geometric language of statistical information manifolds. We discuss…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is…
We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…
We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…
In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…
We propose a unified information-geometric framework that formalizes understanding in learning as a trade-off between informativeness and geometric simplicity. An encoder phi is evaluated by U(phi) = I(phi(X); Y) - beta * C(phi), where…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…