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A0736
Title: Horseshoe pit: A unified framework for large-scale Bayesian inference Authors:  Francesco Denti - University of California Irvine (United States) [presenting]
Abstract: Variable selection is a central topic in supervised learning models. In a Bayesian linear regression framework, variable selection is performed by adopting a regularizing prior for the regression coefficients to shrink towards zero the irrelevant parameters. There are two main types of priors to accomplish this goal: the spike-and-slab and the continuous scale mixtures of Gaussians. The former is a discrete mixture between two distributions characterized by low and high variance. The latter specifies a hierarchical structure, where a continuous prior is elicited on the scale of a zero-mean Gaussian distribution.In contrast to these existing methods, we propose a discrete mixture of continuous scale mixtures, providing a connection between the two alternatives. We substitute the observation-specific local shrinkage parameters (typical of continuous mixtures) with cluster shrinkage parameters. Our proposal drastically reduces the number of parameters needed in the model and allows sharing statistical strength across coefficients of similar magnitude, improving the shrinkage effect. From a practical perspective, we adopt half-Cauchy priors. This choice leads to a cluster-shrinkage version of the Horseshoe prior, the Horseshoe Pit (HSP). We investigate the performance of the HSP in a multiple testing framework, applying our model to neurological data to detect activated brain regions.