2005/05/16 by Anatoli Juditsky, Alexander Nazin, Juditsky, Anatoli +6
Computer Science · Engineering · Mathematics · #62G99 #FOS: Mathematics #Face and Expression Recognition #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #math.ST #msc:62G99 #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0505333
29 pages; mai 2005
openalex publication_date 2005/05/16 · arxiv created 2006/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is defined by a stochastic version of the mirror descent algorithm (i.e., of the method which performs gradient descent in the dual space) with an additional averaging. The main result of the paper is an upper bound for the expected accuracy of the proposed estimator. This bound is of the order √((log M)/t) with an explicit and small constant factor, where M is the dimension of the problem and t stands for the sample size. A similar bound is proved for a more general setting that covers, in particular, the regression model with squared loss.