2012/09/30 by Sohail Bahmani, Petros T. Boufounos, Bhiksha Raj
Computer Science · Mathematics · #cs.LG #math.OC #msc:62FXX #msc:65KXX #stat.ML
paper · pdf · doi:10.1109/tit.2016.2515078
published as IEEE Transactions on Information Theory 62(4):2092--2099, 2016
arxiv created 2016/01/27 · arxiv updated 2016/03/23
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic exercise. Furthermore, the estimate that these methods produce might not belong to the desired sparsity model, albeit accurately approximating the true parameter. Therefore, greedy-type algorithms could often be more desirable in estimating structured-sparse parameters. So far, these greedy methods have mostly focused on linear statistical models. In this paper we study the projected gradient descent with non-convex structured-sparse parameter model as the constraint set. Should the cost function have a Stable Model-Restricted Hessian the algorithm produces an approximation for the desired minimizer. As an example we elaborate on application of the main results to estimation in Generalized Linear Model.