NDLI: Likelihood-based selection and sharp parameter estimation*

Content Provider	PubMed Central
Author	Shen, Xiaotong Pan, Wei Zhu, Yunzhang
Abstract	In high-dimensional data analysis, feature selection becomes one means for dimension reduction, which proceeds with parameter estimation. Concerning accuracy of selection and estimation, we study nonconvex constrained and regularized likelihoods in the presence of nuisance parameters. Theoretically, we show that constrained L 0-likelihood and its computational surrogate are optimal in that they achieve feature selection consistency and sharp parameter estimation, under one necessary condition required for any method to be selection consistent and to achieve sharp parameter estimation. It permits up to exponentially many candidate features. Computationally, we develop difference convex methods to implement the computational surrogate through prime and dual subproblems. These results establish a central role of L 0-constrained and regularized likelihoods in feature selection and parameter estimation involving selection. As applications of the general method and theory, we perform feature selection in linear regression and logistic regression, and estimate a precision matrix in Gaussian graphical models. In these situations, we gain a new theoretical insight and obtain favorable numerical results. Finally, we discuss an application to predict the metastasis status of breast cancer patients with their gene expression profiles.
Related Links	http://dx.doi.org/10.1080/01621459.2011.645783
Ending Page	232
Page Count	10
Starting Page	223
File Format	PDF
ISSN	01621459
e-ISSN	1537274X
Journal	Journal of the American Statistical Association
Issue Number	497
Volume Number	107
Language	English
Publisher Date	2012-03-01
Access Restriction	Open
Subject Keyword	Statistics, Probability and Uncertainty Statistics and Probability Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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