Open Access
2010 Sparse regression with exact clustering
Yiyuan She
Electron. J. Statist. 4: 1055-1096 (2010). DOI: 10.1214/10-EJS578


This paper studies a generic sparse regression problem with a customizable sparsity pattern matrix, motivated by, but not limited to, a supervised gene clustering problem in microarray data analysis. The clustered lasso method is proposed with the l1-type penalties imposed on both the coefficients and their pairwise differences. Somewhat surprisingly, it behaves differently than the lasso or the fused lasso – the exact clustering effect expected from the l1 penalization is rarely seen in applications. An asymptotic study is performed to investigate the power and limitations of the l1-penalty in sparse regression. We propose to combine data-augmentation and weights to improve the l1 technique. To address the computational issues in high dimensions, we successfully generalize a popular iterative algorithm both in practice and in theory and propose an ‘annealing’ algorithm applicable to generic sparse regressions (including the fused/clustered lasso). Some effective accelerating techniques are further investigated to boost the convergence. The accelerated annealing (AA) algorithm, involving only matrix multiplications and thresholdings, can handle a large design matrix as well as a large sparsity pattern matrix.


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Yiyuan She. "Sparse regression with exact clustering." Electron. J. Statist. 4 1055 - 1096, 2010.


Published: 2010
First available in Project Euclid: 12 October 2010

zbMATH: 1329.62327
MathSciNet: MR2727453
Digital Object Identifier: 10.1214/10-EJS578

Primary: 62H30 , 62J07

Keywords: clustering , Lasso , Sparsity , thresholding

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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