Variational Pseudolikelihood for Regularized Ising Inference
This work addresses inference challenges in statistical physics and machine learning, offering an incremental improvement for modeling binary data like images.
The paper tackles the problem of inferring Ising model parameters by proposing a variational pseudolikelihood method that is more computationally efficient and better at predicting out-of-sample correlations compared to existing regularized and approximation methods, as demonstrated in a letter recognition task.
I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than $L_2$ regularized maximum pseudolikelihood inference as well as mean field and isolated spin pair approximations with pseudocount regularization. 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.