Lab Papers (GRASP)

Document Type

Journal Article

Date of this Version

1-14-2009

Comments

Postprint version. Published in:

Joint covariate selection and joint subspace selection for multiple classification problems, G. Obozinski, B.Taskar, M.I. Jordan, Statistics and Computing, Jan. 2009.

The original publication is available at www.springerlink.com.
Publisher URL: http://dx.doi.org/10.1007/s11222-008-9111-x

Abstract

We address the problem of recovering a common set of covariates that are relevant simultaneously to several classification problems. By penalizing the sum of ℓ2-norms of the blocks of coefficients associated with each covariate across different classification problems, similar sparsity patterns in all models are encouraged. To take computational advantage of the sparsity of solutions at high regularization levels, we propose a blockwise path-following scheme that approximately traces the regularization path. As the regularization coefficient decreases, the algorithm maintains and updates concurrently a growing set of covariates that are simultaneously active for all problems. We also show how to use random projections to extend this approach to the problem of joint subspace selection, where multiple predictors are found in a common low-dimensional subspace. We present theoretical results showing that this random projection approach converges to the solution yielded by trace-norm regularization. Finally, we present a variety of experimental results exploring joint covariate selection and joint subspace selection, comparing the path-following approach to competing algorithms in terms of prediction accuracy and running time.

Keywords

Variable selection, Subspace selection, Lasso, Group Lasso, Regularization path, Supervised dimensionality reduction, Multitask learning, Block norm, Trace norm, Random projections

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Date Posted: 13 October 2009

This document has been peer reviewed.