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Activity Number: 466
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #305427
Title: The Sparse-MLE for Variable Screening in Ultra-High-Dimensional Feature Space
Author(s): Chen Xu*+ and Jiahua Chen
Companies: University of British Columbia and SSC
Address: 333-6356 Agricultural Road, Vancouver, BC, V6T 1Z2, Canada
Keywords: Variable screening ; Screening consistency ; Sparse MLE ; High dimensionality ; Penalized likelihood ; Hard thresholding

Variable selection and feature extraction are fundamental for knowledge discovery and statistical modeling with high-dimensionality. For the computational feasibility, reducing the dimension of data is a necessary step before the formal analysis. Fan and Lv (2008) suggested a variable screening strategy based on the marginal correlations between the covariates and the response. In the same spirit, we propose a new screening approach via the sparsity-restricted maximum likelihood estimator (sparse-MLE) to account for more joint effects among the covariates. The new approach efficiently screens out most irrelevant variables from the model while retains those important ones with high probability. The low-dimensional model produced by sparse-MLE then serves as a good starting point for the further selection. We establish the screening consistency of the sparse-MLE and further develop an efficient algorithm for its implementation. The excellent performances of proposed method are supported by extensive numerical studies.

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