Sample dependence in the maximum entropy solution to the generalized moment problem

TL;DR

This paper investigates how the maximum entropy solution to the generalized moment problem depends on empirical samples used to estimate expected values, addressing the stability of the method in practical applications.

Contribution

It provides initial analysis of the sample dependence in maximum entropy solutions for the generalized moment problem, highlighting potential issues in empirical settings.

Findings

Sample dependence affects the maximum entropy solution

Analysis of stability with respect to empirical data

Insights into the robustness of maximum entropy methods

Abstract

The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the variable. In actual practice, such expected values are determined from empirical samples, leaving open the question of the dependence of the solution upon the sample. It is the purpose of this note to take a few steps towards the analysis of such dependence.