Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization

TL;DR

This paper introduces an algorithm for estimating Dirac mixture densities from finite moments, ensuring moment preservation and uniform coverage of the state space, with entropy regularization enhancing the density estimation process.

Contribution

It presents a novel algorithm that efficiently computes Dirac mixture densities from moments while maintaining coverage and incorporating entropy regularization.

Findings

Effective moment preservation in density estimation

Uniform coverage of the state space achieved

Entropy regularization improves density quality

Abstract

We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous coverage of the state space.