Title: Variable selection in sparse additive models
Authors: Cristina Butucea - University Paris-Est Marne (France) [presenting]
Natalia A Stepanova - Carleton University (Canada)
Abstract: The problem of recovery of an unknown multivariate signal of $d$ variables is considered in a sparse additive model, where a smaller number $s$ of variables are actually used. We assume that the additive components are smooth functions of the significant variables. Attempting to reconstruct most, but not all, non-zero components of $f$, we arrive at the problem of almost full variable selection in high-dimensional regression. For two different choices of a class of smooth functions, we establish conditions under which almost full variable selection is possible,and provide a procedure that achieves this goal. Our procedure is the best possible (in the asymptotically minimax sense) for selecting most non-zero components of $f$. Moreover, it is adaptive in the parameter $s$. In addition to that, we obtain an adaptive exact selector for the class of infinitely-smooth functions. Our theoretical results are illustrated with numerical experiments.