Entropic Projections and Dominating Points

TL;DR

This paper explores the mathematical properties of entropic projections and dominating points, providing criteria for their existence and representations through convex duality, with applications across various fields like physics and statistics.

Contribution

It introduces new criteria for the existence of generalized entropic projections and offers their representations via convex conjugate duality and functional analysis.

Findings

Criteria for existence of entropic projections derived

Representations of projections as measure components of entropy minimization

Applicable to diverse fields such as physics, statistics, and inverse problems

Abstract

Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for their existence. Representations of the generalized entropic projections are obtained: they are the ``measure component" of some extended entropy minimization problem.