Title: Bayesian Inference of Sparse Networks (BISN)
Abstract:
Structure learning of graphical models typically involves careful tuning of penalty parameters, which balance the tradeoff between data fidelity and graph sparsity. Unfortunately, this tuning is often a ``black art'' requiring expert experience or brute-force search. It is therefore tempting to develop tuning-free algorithms that can determine the sparsity of the graph adaptively from the observed data in an automatic fashion. In this talk, we propose a novel approach, named BISN (Bayesian inference of Sparse Networks), for automatic Gaussian graphical model selection. Specifically, we regard the off-diagonal entries in the precision matrix as random variables and impose sparse-promoting priors on them, resulting in automatic sparsity determination. With the help of stochastic gradients, an efficient variational Bayes algorithm is derived to learn the model. Note that the theoretical runtime guarantee of the state-of-the-art methods for automatic graphical model selection is typically a third-order function of the dimension. By contrast, our theoretical analysis shows that the runtime guarantee of BISN scales only quadratically with the dimension. Furthermore, numerical results show that the proposed approach can estimate both the structure and non-zero entries of the precision matrix more accurately, while the computational time is reduced several orders of magnitude compared to the state-of-the-art methods.
