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In recent years a number of methods have been developed for automaticallylearning the (sparse) connectivity structure of Markov Random Fields. Thesemethods are mostly based on L1-regularized optimization which has a number ofdisadvantages such as the inability to assess model uncertainty and expensivecross-validation to find the optimal regularization parameter. Moreover, themodel's predictive performance may degrade dramatically with a suboptimal valueof the regularization parameter (which is sometimes desirable to inducesparseness). We propose a fully Bayesian approach based on a "spike and slab"prior (similar to L0 regularization) that does not suffer from theseshortcomings. We develop an approximate MCMC method combining Langevin dynamicsand reversible jump MCMC to conduct inference in this model. Experiments showthat the proposed model learns a good combination of the structure andparameter values without the need for separate hyper-parameter tuning.Moreover, the model's predictive performance is much more robust than L1-basedmethods with hyper-parameter settings that induce highly sparse modelstructures.

Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior