Information Projection and Approximate Inference for Structured Sparse Variables

Approximate inference via information projection has been recently introduced as a general-purpose technique for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient algorithms for approximate inference via information projection that are applicable to any structure on the set of variables that admits enumeration using matroid or knapsack constraints. Further, leveraging recent advances in submodular optimization, we provide an efficient greedy algorithm with strong optimization-theoretic guarantees. The class of probabilistic models that can be expressed in this way is quite broad and, as we show, includes group sparse regression, group sparse principal components analysis and sparse collective matrix factorization, among others. Empirical results on simulated data and high dimensional neuroimaging data highlight the superior performance of the information projection approach as compared to established baselines for a range of probabilistic models.