On model selection consistency of regularized M-estimators
Abstract
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 \emph{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.
Cite
@article{arxiv.1305.7477,
title = {On model selection consistency of regularized M-estimators},
author = {Jason D. Lee and Yuekai Sun and Jonathan E. Taylor},
journal= {arXiv preprint arXiv:1305.7477},
year = {2014}
}