In this paper, we develop an 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 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. Implementation of the method is illustrated through yeast data to identify significant cell-cycle regulating transcription factors.
The authors would like to thank the associate editor and two reviewers for their constructive comments which led to a significantly improved version of the manuscript. The authors would also like to thank Ms. Sukanya Bhattacharyya for providing additional computational resources without which the extensive numerical studies presented in the paper would not have been possible.
Research reported in this publication was supported by the National Heart, Lung, and Blood Institute of the National Institutes of Health under Award Number R56HL155373. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
"The EAS approach to variable selection for multivariate response data in high-dimensional settings." Electron. J. Statist. 17 (2) 1947 - 1995, 2023. https://doi.org/10.1214/23-EJS2141