On Enumerating Distributions for Associated Vectors in the Entropy Space

TL;DR

This paper introduces a numerical algorithm to find probability distributions for associated entropic vectors close to a target in the entropy space, addressing the challenge of non-entropic vectors under alphabet size constraints.

Contribution

It presents a novel perturbation-based method and an algorithm for approximating distributions for associated vectors in the entropy space, with extensions and applications.

Findings

Algorithm effectively finds distributions near the target vector.

Perturbation approach demonstrates feasibility for non-entropic vectors.

Extensions and comparisons validate the method's utility.

Abstract

This paper focuses on the problem of finding a distribution for an associated entropic vector in the entropy space nearest to a given, possibly non-entropic, target vector for random variables with a constraint on alphabet size. We show the feasibility to find distribution for associated vector via a sequence of perturbations in the probability mass function. Then we present an algorithm for numerically solving the problem together with extensions, applications, and comparison with the known results.