A Swarm Intelligence Approach To Density Function Reconstruction From Moments Using Entropy Optimization

Document Type

Article

Publication Date

4-14-2026

School

Mathematics and Natural Sciences

Abstract

This paper presents a bioinspired optimization approach to address a class of inverse problems involving entropy optimization (EOP) from knowledge of the moments of a distribution function. In particular, we study the Hausdorff moment problem, where one seeks to reconstruct a (probability) density distribution by inverting a completely monotonic sequence of moments of the distribution in a bounded interval. It is shown that the resulting EOP can be handled very efficiently using the collective intelligence of a swarm (of optimizers), which provides a robust and accurate solution by effectively incorporating information from up to a thousand moments of the density. The efficacy of the approach is demonstrated by reconstructing the invariant density functions for the logistics map, spectral densities of large real-symmetric random matrices, encountered in the study of physics of disordered solids, and financial time series involving daily price fluctuations of a mutual fund. The agreement between true densities and the corresponding maximum-entropy approximants is examined by comparing the Kullback–Leibler divergence and the Fisher information of the densities.

Publication Title

Proceedings of the National Academy of Sciences of the United States of America

Volume

123

Issue

15

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