Determinantal Regularization for Ensemble Variable Selection

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Veronika Rockova, Gemma Moran, Edward George ;
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:1105-1113, 2016.

Abstract

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 a “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. By deploying determinantal penalty functions as diversity regularizers, our approach performs regularization over multiple locations of the posterior. The key driver of these determinantal penalties is a kernel function that induces repulsion in the latent model space domain.

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