Disentanglement of Entropy and Coevolution using Spectral Regularization

The rise in the number of protein sequences in the post-genomic era has led to a major breakthrough in fitting generative sequence models for contact prediction, protein design, alignment, and homology search. Despite this success, the interpretability of the modeled pairwise parameters continues to be limited due to the entanglement of coevolution, phylogeny, and entropy. For contact prediction, post-correction methods have been developed to remove the contribution of entropy from the predicted contact maps. However, all remaining applications that rely on the raw parameters, lack a direct method to correct for entropy. In this paper, we investigate the origins of the entropy signal and propose a new spectral regularizer to down weight it during model fitting. We find the added regularizer to GREMLIN, a Markov Random Field or Potts model, allows for the inference of a sparse contact map without loss in precision, meanwhile improving interpretability, and resolving overfitting issues important for sequence evaluation and design.