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Activity Number: 509
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #305423
Title: Regularization Parameter Selection in Convex and Non-Convex Penalized Least Squares Estimation
Author(s): Kei Hirose*+ and Shohei Tateishi and Sadanori Konishi
Companies: Osaka University and Toyama Chemical Co., Ltd. and Chuo University
Address: 1-3, Machikaneyama-Cho, Toyonaka,, Osaka 560-8531, , Japan
Keywords: Convex and non-convex penalties ; Degrees of freedom ; Model selection criteria ; Model complexity
Abstract:

Sparse regression modeling via regularization such as the lasso has received much attention as a powerful tool for analyzing high-dimensional data. Crucial issues in the modeling process are the choice of tuning parameters including regularization parameters, which control the model complexity. The appropriate choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. We introduce an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and non-convex penalties. The proposed method can be also applied to the problem of group variable selection such as the group lasso. We use Monte Carlo experiments and real data examples to investigate the properties of our modeling strategy.


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