Two-Step Mixed-Type Multivariate Bayesian Sparse Variable Selection with Shrinkage Priors
arxiv(2022)
摘要
We introduce a Bayesian framework for mixed-type multivariate regression
using continuous shrinkage priors. Our framework enables joint analysis of
mixed continuous and discrete outcomes and facilitates variable selection from
the p covariates. Theoretical studies of Bayesian mixed-type multivariate
response models have not been conducted previously and require more intricate
arguments than the corresponding theory for univariate response models due to
the correlations between the responses. In this paper, we investigate necessary
and sufficient conditions for posterior contraction of our method when p
grows faster than sample size n. The existing literature on Bayesian
high-dimensional asymptotics has focused only on cases where p grows
subexponentially with n. In contrast, we study the asymptotic regime where
p is allowed to grow exponentially terms of n. We develop a novel two-step
approach for variable selection which possesses the sure screening property and
provably achieves posterior contraction even under exponential growth of p.
We demonstrate the utility of our method through simulation studies and
applications to real data, including a cancer genomics dataset where n=174
and p=9183. The R code to implement our method is available at
https://github.com/raybai07/MtMBSP.
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