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September 2012 Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping
Seyoung Kim, Eric P. Xing
Ann. Appl. Stat. 6(3): 1095-1117 (September 2012). DOI: 10.1214/12-AOAS549

Abstract

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.

Citation

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Seyoung Kim. Eric P. Xing. "Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping." Ann. Appl. Stat. 6 (3) 1095 - 1117, September 2012. https://doi.org/10.1214/12-AOAS549

Information

Published: September 2012
First available in Project Euclid: 31 August 2012

zbMATH: 1254.62112
MathSciNet: MR3012522
Digital Object Identifier: 10.1214/12-AOAS549

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.6 • No. 3 • September 2012
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