Title: Optimal recovery of sparse additive signals
Authors: Natalia A Stepanova - Carleton University (Canada) [presenting]
Cristina Butucea - University Paris-Est Marne (France)
Abstract: The problem of exact and almost full recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model is considered. We assume that $f$ is smooth and has an additive sparse structure determined by the parameter $s$, the number of nonzero univariate signals contributing to $f$. We also assume that the dimension $d$ increases and that the parameter $s$ remains ``small'' relative to $d$. With these assumptions, the recovery problem becomes that of determining which sparse additive components of $f$ are nonzero. The latter may be viewed as the problem of variable selection in high dimensions. We give conditions under which exact and almost full variable selections are possible and, in both regimes, we propose the best possible (in the asymptotically minimax sense) variable selection procedures. The proposed procedures are adaptive in the parameter $s$.