Exact maximum-entropy estimation with Feynman diagrams

TL;DR

This paper introduces a novel method using Feynman diagrams to explicitly compute the maximum-entropy probability measure under given constraints, providing a new analytical approach to a classical problem.

Contribution

The paper presents the first explicit solution for maximum-entropy estimation using perturbative Feynman calculus, expressed as a sum over weighted trees.

Findings

Explicit maximum-entropy measure expressed as a sum over trees

Utilizes Feynman diagram techniques for statistical estimation

Provides a new analytical tool for entropy maximization problems

Abstract

A classical longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.