Related papers: Statistical Bergman geometry

Given a planar domain $\Omega$, the Bergman analytic content measures the $L^{2}(\Omega)$-distance between $\bar{z}$ and the Bergman space $A^{2}(\Omega)$. We compute the Bergman analytic content of simply-connected quadrature domains with…

We discover the connection between the Berry curvature and the Riemann curvature tensor in any kinematic space of minimal surfaces anchored on spherical entangling surfaces. This new holographic principle establishes the Riemann geometry in…

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient…

Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…

We extend \emph{Schramm's cofat uniformization theorem} to cofat domains on upper Ahlfors 2-regular metric two-spheres $X$. Specifically, we show that if $\Omega \subset X$ is a cofat domain, then there exists a…

This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates…

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…

We introduce the notion of smooth parametric model of normal positive linear functionals on possibly infinite-dimensional W*-algebras generalizing the notions of parametric models used in classical and quantum information geometry. We then…

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background…

Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…

Invariant geodesic orbit Finsler $(\alpha,\beta)$ metrics $F$ which arise from Riemannian geodesic orbit metrics $\alpha$ on spheres are determined. The relation of Riemannian geodesic graphs with Finslerian geodesic graphs proved in a…

In this paper we consider the semi-continuity of the physical-like measures for diffeomorphisms with dominated splittings. We prove that any weak-* limit of physical-like measures along a sequence of $C^1$ diffeomorphisms $\{f_n\}$ must be…

Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…

The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form…

We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data…

Data sets of multivariate normal distributions abound in many scientific areas like diffusion tensor imaging, structure tensor computer vision, radar signal processing, machine learning, just to name a few. In order to process those normal…

We consider the minimization problem of $\phi$-divergences between a given probability measure $P$ and subsets $\Omega$ of the vector space $\mathcal{M}_\mathcal{F}$ of all signed finite measures which integrate a given class $\mathcal{F}$…