相关论文: Information geometry and asymptotic geodesics on t…

Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…

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…

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…

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…

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…

This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…

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…

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…

The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define the geometric mean of probability measures…

Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…

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…

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 the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…

We show how the Riemannian distance on $\mathbb{S}^n_{++}$, the cone of $n\times n$ real symmetric or complex Hermitian positive definite matrices, may be used to naturally define a distance between two such matrices of different…

I define a natural measure of the complexity of a parametric distribution relative to a given true distribution called the {\it razor} of a model family. The Minimum Description Length principle (MDL) and Bayesian inference are shown to…

In this paper we consider the space of those probability distributions which maximize the $q$-R\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some…

In problems of parameter estimation from sensor data, the Fisher Information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the…

It is well known that the Fisher information induces a Riemannian geometry on parametric families of probability density functions. Following recent work, we consider the nonparametric generalization of the Fisher geometry. The resulting…

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…

Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…