Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior
This work addresses a bottleneck in probabilistic graphical modeling for researchers and practitioners by offering a more robust alternative to L1-based methods, though it is incremental as it builds on prior Bayesian and regularization techniques.
The authors tackled the problem of learning sparse connectivity structures in Markov Random Fields, which existing L1-regularized methods handle poorly due to issues like model uncertainty and hyperparameter sensitivity, by proposing a fully Bayesian approach with a spike and slab prior that improves predictive robustness without separate tuning.
In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and expensive cross-validation to find the optimal regularization parameter. Moreover, the model's predictive performance may degrade dramatically with a suboptimal value of the regularization parameter (which is sometimes desirable to induce sparseness). We propose a fully Bayesian approach based on a "spike and slab" prior (similar to L0 regularization) that does not suffer from these shortcomings. We develop an approximate MCMC method combining Langevin dynamics and reversible jump MCMC to conduct inference in this model. Experiments show that the proposed model learns a good combination of the structure and parameter values without the need for separate hyper-parameter tuning. Moreover, the model's predictive performance is much more robust than L1-based methods with hyper-parameter settings that induce highly sparse model structures.