High-dimensional variable selection via low-dimensional adaptive learning

Electronic Journal of Statistics, vol. 15

Abstract

A stochastic search method, the so-called Adaptive Subspace (AdaSub) method, is proposed for variable selection in high-dimensional linear regression models. The method aims at finding the best model with respect to a certain model selection criterion and is based on the idea of adaptively solving low-dimensional sub-problems in order to provide a solution to the original high-dimensional problem. Any of the usual $\ell _{0}$-type model selection criteria can be used, such as Akaike’s Information Criterion (AIC), the Bayesian Information Criterion (BIC) or the Extended BIC (EBIC), with the last being particularly suitable for high-dimensional cases. The limiting properties of the new algorithm are analysed and it is shown that, under certain conditions, AdaSub converges to the best model according to the considered criterion. In a simulation study, the performance of AdaSub is investigated in comparison to alternative methods. The effectiveness of the proposed method is illustrated via various simulated datasets and a high-dimensional real data example.

Authors 3

1. Christian Staerk

   University Hospital Bonn

   Affiliation as printed

   Department of Medical Biometry , Informatics and Epidemiology University Hospital Bonn , Germany

   Department of Medical Biometry, Informatics and Epidemiology, University Hospital Bonn, Germany

2. Maria Kateri Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics RWTH Aachen University , Germany

   Institute of Statistics, RWTH Aachen University, Germany

3. Ioannis Ntzoufras

   Athens University of Economics and Business

   Affiliation as printed

   Department of Statistics Athens University of Economics and Business , Greece

   Department of Statistics, Athens University of Economics and Business, Greece