Learning of Discrete Graphical Models with Neural Networks

Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint distribution can be solved with near-optimal sample complexity using a convex optimization method known as Generalized Regularized Interaction Screening Estimator (GRISE). But the computational cost of GRISE becomes prohibitive when the energy function of the true graphical model has higher order terms. We introduce NN-GRISE, a neural net based algorithm for graphical model learning, to tackle this limitation of GRISE. We use neural nets as function approximators in an interaction screening objective function. The optimization of this objective then produces a neural-net representation for the conditionals of the graphical model. NN-GRISE algorithm is seen to be a better alternative to GRISE when the energy function of the true model has a high order with a high degree of symmetry. In these cases, NN-GRISE is able to find the correct parsimonious representation for the conditionals without being fed any prior information about the true model. NN-GRISE can also be used to learn the underlying structure of the true model with some simple modifications to its training procedure. In addition, we also show a variant of NN-GRISE that can be used to learn a neural net representation for the full energy function of the true model.