Near-Gaussian entropic functional calculation and density estimation using an asymptotic series

TL;DR

This paper introduces an asymptotic expansion method for calculating entropic functionals of near-Gaussian densities, enabling efficient maximum entropy density estimation from low-order moments with novel insights into non-Gaussian effects.

Contribution

It develops a new asymptotic expansion approach for entropic functionals and simplifies maximum entropy density estimation using algebraic equations.

Findings

Novel asymptotic expansion for entropic functionals

Explicit effects of skewness and higher moments on entropy

Simplified maximum entropy density estimation method

Abstract

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of standard perturbation expansions in quantum field theory. We give novel results on the low-order effects of non-Gaussian even moments and asymmetry (e.g. skewness) on the entropy. The asymptotic expansion is also used to define a best fit maximum entropy density given a set of observed low order moments. The maximum entropy density estimation technique consists simply of the solution of a small set of algebraic equations and is therefore more straightforward numerically than classical maximum-entropy methods which rely on sophisticated convex optimization techniques.