Aggregation and Sparsity Via l_1 Penalized Least Squares

摘要

This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via l_1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.