Bayesian models for structured sparse estimation via set cover prior

A number of priors have been recently developed for Bayesian estimation of sparse models. In many applications the variables are simultaneously relevant or irrelevant in groups, and appropriately modeling this correlation is important for improved sample efficiency. Although group sparse priors are also available, most of them are either limited to disjoint groups, or do not infer sparsity at group level, or fail to induce appropriate patterns of support in the posterior. In this paper we tackle this problem by proposing a new framework of prior for overlapped group sparsity. It follows a hierarchical generation from group to variable, allowing group-driven shrinkage and relevance inference. It is also connected with set cover complexity in its maximum a posterior. Analysis on shrinkage profile and conditional dependency unravels favorable statistical behavior compared with existing priors. Experimental results also demonstrate its superior performance in sparse recovery and compressive sensing.