Learning Graphical Models for Hypothesis Testing

We propose a novel procedure for learning tractable graphical models from data samples. The traditional approach is to learn models that are generically good approximations of the underlying distributions. In contrast, we are interested in learning models for a specific purpose: binary hypothesis testing. The distributions corresponding to the hypotheses are not available, instead we are given two labelled sets of training samples. Our procedure learns two models, one for each hypothesis, which are then used in a likelihood ratio test for classifying a new unlabelled sample. Each model is learnt from both sets of training samples. Numerical simulations show that our procedure has a lower probability of classification error, as compared to a procedure that learns each model using only its own training set. The gain is more significant when the problem size is larger and the number of training samples available is smaller.