Improved Maximum Entropy Analysis with an Extended Search Space

TL;DR

This paper identifies limitations in the standard Maximum Entropy Method due to SVD-based solution space restrictions and proposes an extended search space approach with an open-source implementation to recover the full solution.

Contribution

It introduces a systematic extension of the search basis in MEM, overcoming SVD limitations and improving solution accuracy with a new C/C++ implementation.

Findings

Standard SVD-based MEM may miss the true solution.

Extending the search basis recovers the full solution space.

Open-source code with high precision arithmetic and LBFGS included.

Abstract

The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.