  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.
