Sequentially Fitting "Inclusive" Trees for Inference in Noisy-OR Networks

An important class of problems can be cast as inference in noisy-OR Bayesian networks, where the binary state of each variable is a logical OR of noisy versions of the states of the variable's parents. For example, in medical diagnosis, the presence of a symptom can be expressed as a noisy-OR of the diseases that may cause the symptom - on some occasions, a disease may fail to activate the symptom. Inference in richly-connected noisy-OR networks is intractable, but approximate methods (e.g., variational techniques) are showing increasing promise as practical solutions. One problem with most approximations is that they tend to concentrate on a relatively small number of modes in the true posterior, ignoring other plausible configurations of the hidden variables. We introduce a new sequential variational method for bipartite noisy-OR networks, that favors including all modes of the true posterior and models the posterior distribution as a tree. We compare this method with other approximations using an ensemble of networks with network statistics that are comparable to the QMR-DT medical diagnostic network.