Related papers: Information Geometry on the $\ell^2$-Simplex via t…
The probability simplex is the set of all probability distributions on a finite set and is the most fundamental object in the finite probability theory. In this paper we give a characterization of statistical models on finite sets which are…
The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in…
The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s, one considers an ideal fluid flow as the geodesic motion on…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…
Complex networks are critical in many scientific, technological, and societal contexts due to their ability to represent and analyze intricate systems with interdependent components. Often, after labeling the nodes of a network with a…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
Let $S^*Q$ be the spherization of a closed connected manifold of dimension at least two. Consider a contactomorphism $\varphi$ that can be reached by a contact isotopy that is everywhere positively transverse to the contact structure. In…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
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,…
Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…
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 use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…
Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of 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…
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the…
Information geometry uses the formal tools of differential geometry to describe the space of probability distributions as a Riemannian manifold with an additional dual structure. The formal equivalence of compositional data with discrete…
We present a unified framework for developing and analysing immersed finite element (IFE) spaces for solving typical elliptic interface problems with interface independent meshes. This framework allows us to construct a group of new IFE…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…