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2021 High-dimensional variable selection via low-dimensional adaptive learning
Christian Staerk, Maria Kateri, Ioannis Ntzoufras
Electron. J. Statist. 15(1): 830-879 (2021). DOI: 10.1214/21-EJS1797

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.

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Christian Staerk. Maria Kateri. Ioannis Ntzoufras. "High-dimensional variable selection via low-dimensional adaptive learning." Electron. J. Statist. 15 (1) 830 - 879, 2021. https://doi.org/10.1214/21-EJS1797

Information

Received: 1 October 2019; Published: 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.1214/21-EJS1797

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Vol.15 • No. 1 • 2021
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