Variational Pseudolikelihood for Regularized Ising Inference

I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The key to the approach is a variational energy that regularizes the inference problem by shrinking the couplings towards zero, while still allowing some large couplings to explain strong correlations. The utility of the variational pseudolikelihood approach is illustrated by training an Ising model to represent the letters A-J using samples of letters from different computer fonts. Statistical mechanical models constructed from experimental observations provide a valuable tool for studying complex systems. The utility of the statistical mechanics approach to data-driven modeling is especially apparent in biology, providing insights into the behavior of flocking birds [1], the organization of neural networks in the brain [2-4], the structure and evolution of proteins [5-9], and many other topics [10, 11].