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2015 On model selection consistency of regularized M-estimators
Jason D. Lee, Yuekai Sun, Jonathan E. Taylor
Electron. J. Statist. 9(1): 608-642 (2015). DOI: 10.1214/15-EJS1013


Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for estimates of the model parameters to be model selection consistent: the estimates also fall in the model subspace. We develop a general framework for establishing consistency and model selection consistency of regularized M-estimators and show how it applies to some special cases of interest in statistical learning. Our analysis identifies two key properties of regularized M-estimators, referred to as geometric decomposability and irrepresentability, that ensure the estimators are consistent and model selection consistent.


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Jason D. Lee. Yuekai Sun. Jonathan E. Taylor. "On model selection consistency of regularized M-estimators." Electron. J. Statist. 9 (1) 608 - 642, 2015.


Published: 2015
First available in Project Euclid: 2 April 2015

zbMATH: 1309.62044
MathSciNet: MR3331852
Digital Object Identifier: 10.1214/15-EJS1013

Primary: 62F10

Keywords: generalized lasso , geometrically decomposable penalties , group lasso , Lasso , nuclear norm minimization , Regularized M-estimator

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 1 • 2015
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