Generalized maximum entropy estimation

TL;DR

This paper introduces a novel approximation scheme for maximum entropy estimation under moment constraints, leveraging convex duality and smoothing techniques, with applications to chemical master equations and complex decision processes.

Contribution

It presents a new fast gradient-based approximation method with explicit error bounds for maximum entropy problems, extending its application to chemical and decision process modeling.

Findings

Efficient approximation scheme with explicit error bounds.

Application to chemical master equation via zero-information closure.

Use in approximate dynamic programming for complex MDPs.

Abstract

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme using a smoothed fast gradient method that is equipped with explicit bounds on the approximation error. We further demonstrate how the presented scheme can be used for approximating the chemical master equation through the zero-information moment closure method, and for an approximate dynamic programming approach in the context of constrained Markov decision processes with uncountable state and action spaces.