Related papers: A Generalized Cram\'er-Rao Bound Using Information…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the…

We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…

Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…

Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its…

There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leiber's (1951)relative information and Jeffreys (1946) J-divergence, Information…

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…

Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…

This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…

The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…

Several current ultra-wide band applications, such as millimeter wave radar and communication systems, require high sampling rates and therefore expensive and energy-hungry analogto-digital converters (ADCs). In applications where cost and…

This manuscript introduces the idea of using Distributionally Robust Optimization (DRO) for the Counterfactual Risk Minimization (CRM) problem. Tapping into a rich existing literature, we show that DRO is a principled tool for…

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…

R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…

This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with…

The author studies the Cramer-Rao type bound by a linear programming approach. By this approach, he found a necessary and sufficient condition that the Cramer-Rao type bound is attained by a random measurement. In a spin 1/2 system, this…

This lecture note addresses the common misconception that the Gaussian distribution always yields the largest Cram\'er-Rao Bound (CRB). We show that this property only holds under restrictive conditions: specifically, when the mean and…

Information Bottlenecks (IBs) learn representations that generalize to unseen data by information compression. However, existing IBs are practically unable to guarantee generalization in real-world scenarios due to the vacuous…

This paper aims at providing a fresh look at semiparametric estimation theory and, in particular, at the Semiparametric Cram\'{e}r-Rao Bound (SCRB). Semiparametric models are characterized by a finite-dimensional parameter vector of…

In this paper, a distance between the Gaussian Mixture Models(GMMs) is obtained based on an embedding of the K-component Gaussian Mixture Model into the manifold of the symmetric positive definite matrices. Proof of embedding of K-component…