High-dimensional variable selection via low-dimensional adaptive learning

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