Related papers: Information Geometry and Classical Cram\'{e}r-Rao …
Using Langer's variation on the Bogomolov-Miyaoka-Yau inequality \cite[Theorem 0.1]{Langer} we provide some Hirzebruch-type inequalities for curve arrangements in the complex projective plane.
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 is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…
There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber J-divergence. Sibson-Burbea-Rao Jensen-Shannon divegernce and Taneja Arithmetic-Geometric…
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We…
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…
We study quasi-Newton methods from the viewpoint of information geometry induced associated with Bregman divergences. Fletcher has studied a variational problem which derives the approximate Hessian update formula of the quasi-Newton…
We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…
There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber J-divergence. Sibson-Burbea-Rao Jensen-Shannon divegernce and Taneja arithemtic-geometric…
We derive some integral inequalities for holomorphic maps between complex manifolds. As applications, some rigidity and degeneracy theorems for holomorphic maps without assuming any pointwise curvature signs for both the domain and target…
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
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…
We study the computation of the $\alpha$-R\'enyi capacity of a classical-quantum (c-q) channel for $\alpha\in(0,1)$. We propose an exponentiated-gradient (mirror descent) iteration that generalizes the Blahut-Arimoto algorithm. Our analysis…
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…
The paper is devoted to an algebraic analogue of a geometric approach to the classical notion of complex dilatation suggested in the paper arXiv:1701.06259 [math.CV] by the author. At the same time it provides an invariant version of this…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…