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Abstract:
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Recent years have seen growing interest in deterministic search approaches to spike-and- slab Bayesian variable selection. Such methods have focused on the goal of finding a global mode to identify the "best model". However, the report of a single model will be a misleading reflection of the model uncertainty inherent in a highly multimodal posterior. Motivated by non-parametric variational Bayes strategies, we move beyond this limitation by proposing an ensemble optimization approach to identify a collection of representative posterior modes. Our approach, called the Particle EM algorithm, performs deterministic posterior exploration using an ensemble of repulsive particles. These particles are geared towards uncharted areas of the posterior, providing a more comprehensive summary of posterior topography than parallel algorithms. An MCMC variant of Particle EM is also presented that explores the posterior by sampling with a set of mutually avoiding particles. Our theoretical insights indicate that the requisite number of particles need not be large in the presence of sparsity.
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