Related papers: Information Geometry and Statistical Manifold
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,…
Asymmetric information distances are used to define asymmetric norms and quasimetrics on the statistical manifold and its dual space of random variables. Quasimetric topology, generated by the Kullback-Leibler (KL) divergence, is considered…
Informationally complete measurements form the foundation of universal quantum state reconstruction, while quantum parameter estimation is based on the local structure of the manifold of quantum states. Here we establish a general link…
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…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
Contrast functions play a fundamental role in information geometry, providing a means for generating the geometric structures of a statistical manifold: a pseudo-Riemannian metric and a pair of torsion-free conjugate affine connections.…
Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an…
We incorporate into the empirical measure the auxiliary information given by a finite collection of expectation in an optimal information geometry way. This allows to unify several methods exploiting a side information and to uniquely…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
We discuss the recently proposed description of Kuramoto model in terms of hyperbolic space and relate it to the information geometry. In particular the dynamical equation in Kuramoto all-to-all model is identified with the gradient flow of…
Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework…
Supervised dimensionality reduction maps labeled data into a low-dimensional feature space while preserving class discriminability. A common approach is to maximize a statistical measure of dissimilarity between classes in the feature…
Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled…
The non-parametric version of Amari's dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical…
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…
We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…
In this paper, we use tools of information geometry to compare, average and classify histograms. Beta distributions are fitted to the histograms and the corresponding Fisher information geometry is used for comparison. We show that this…
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…