Reconstruction of pairwise interactions using energy-based models*

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.

Automated summary

Pairwise models like the Ising model or the generalized Potts model have been successfully applied in various fields, while the problem of inverse statistical mechanics aims to infer the parameters of such models from observed data. One open question is how to train these models when data contain higher-order interactions not present in the pairwise model. Proposed a hybrid model approach combining pairwise models and neural networks, showing significant improvements in reconstructing pairwise interactions. Results indicate that hybrids models can retain advantages of both simple interpretable models and complex black-box models.