Document Type

Article

Date

4-7-2011

Embargo Period

11-17-2011

Disciplines

Mathematics

Description/Abstract

A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function omega with a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and many more. In this paper, we present a general approach for computing the proximity operator of this class of regularizers, under the assumption that the proximity operator of the function \omega is known in advance. Our approach builds on a recent line of research on optimal first order optimization methods and uses fixed point iterations for numerically computing the proximity operator. It is more general than current approaches and, as we show with numerical simulations, computationally more efficient than available first order methods which do not achieve the optimal rate. In particular, our method outperforms state of the art O(1/T) methods for overlapping Group Lasso and matches optimal O(1/T2) methods for the Fused Lasso and tree structured Group Lasso.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1104.1436

Source

Harvested from arXiv.org

Creative Commons License


This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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