The EAS approach to variable selection for multivariate response data in high-dimensional settings

TL;DR

This paper introduces the epsilon admissible subsets (EAS) method for variable selection in high-dimensional multivariate regression, demonstrating its effectiveness and consistency without requiring sparsity assumptions or prior distributions.

Contribution

The paper develops a novel EAS approach for group variable selection that estimates a posterior-like distribution without sparsity assumptions, and proves its strong model selection consistency.

Findings

EAS outperforms existing methods in simulation studies.

EAS achieves strong model selection consistency under certain conditions.

Application to yeast data identifies key transcription factors.

Abstract

In this paper, we develop an {\em epsilon admissible subsets} (EAS) model selection approach for performing group variable selection in the high-dimensional multivariate regression setting. This EAS strategy is designed to estimate a posterior-like, generalized fiducial distribution over a parsimonious class of models in the setting of correlated predictors and/or in the absence of a sparsity assumption. The effectiveness of our approach, to this end, is demonstrated empirically in simulation studies, and is compared to other state-of-the-art model/variable selection procedures. Furthermore, assuming a matrix-Normal linear model we show that the EAS strategy achieves {\em strong model selection consistency} in the high-dimensional setting if there does exist a sparse, true data generating set of predictors. In contrast to Bayesian approaches for model selection, our generalized fiducial approach completely avoids the problem of simultaneously having to specify arbitrary prior distributions for model parameters and penalize model complexity; our approach allows for inference directly on the model complexity. \textcolor{black}{Implementation of the method is illustrated through yeast data to identify significant cell-cycle regulating transcription factors.