Reconstruction of Pairwise Interactions using Energy-Based Models

TL;DR

This paper introduces a hybrid approach combining pairwise energy-based models with neural networks to improve the inference of pairwise interactions from data containing higher-order interactions.

Contribution

It proposes a novel method using energy-based models and pseudolikelihood maximization to enhance the reconstruction of pairwise interactions in complex data.

Findings

Hybrid models outperform standard pairwise models in reconstruction accuracy.

Combining interpretable models with neural networks retains advantages of both.

Consistent improvements observed across various datasets.

Abstract

Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is to infer the parameters of such models given observed data. An open problem in this field is the question of how to train these models in the case where the data contain additional higher-order interactions that are not present in the pairwise model. In this work, we propose an approach based on Energy-Based Models and pseudolikelihood maximization to address these complications: we show that hybrid models, which combine a pairwise model and a neural network, can lead to significant improvements in the reconstruction of pairwise interactions. We show these improvements to hold consistently when compared to a standard approach using only the pairwise model and to an approach using only a neural network. This is in line with the general idea that simple interpretable models and complex black-box models are not necessarily a dichotomy: interpolating these two classes of models can allow to keep some advantages of both.