Related papers: Statistical Bergman geometry
We study bounded domains $\Omega\subset\mathbb{C}^n$ whose Bergman metric is locally symmetric, i.e. its Riemannian curvature tensor is parallel with respect to the Levi-Civita connection. Following the strategy developed in…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…
When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…
Information geometry is an emergent branch of probability theory that consists of assigning a Riemannian differential geometry structure to the space of probability distributions. We present an information geometric investigation of gases…
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $\alpha$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic…
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…
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,…
The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…
Information geometry describes a framework where probability densities can be viewed as differential geometry structures. This approach has shown that the geometry in the space of probability distributions that are parameterized by their…
Domains and more generally complex manifolds whose Bergman metrics have constant holomorphic sectional curvature are characterized. Our approach is to treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the…
We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…
We investigate when the Bergman metric of a bounded domain is, up to a constant factor $\lambda$, induced by the Bergman metric of a finite-dimensional unit ball $\mathbb{B}^N$ via a holomorphic isometric immersion. For a strictly…
The Fefferman--Szeg\H{o} metric \(g_{\operatorname{FS}}^\Omega\) on a \(C^\infty\)-smooth bounded strongly pseudoconvex domain \(\Omega\subset\mathbb C^n\) is an invariant metric defined via the Fefferman surface measure. For this metric,…
In this article, we present recent developments of information geometry, namely, geometry of the Fisher metric, dualistic structures and divergences on the space of probability measures, particularly the theory of geodesics of the Fisher…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
We prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.