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Statistical Applications of Linear Programming for Feature Selection via Regularization Methods

Yao, Yonggang

Abstract Details

2008, Doctor of Philosophy, Ohio State University, Statistics.
We consider statistical procedures for feature selection defined by a family of regularizationproblems with convex piecewise linear loss functions and penalties of l1 or l nature. For example, quantile regression and support vector machines with l1 norm penalty fall into the category. Computationally, the regularization problems are linear programming (LP) problems indexed by a single parameter, which are known as “parametric cost LP” or “parametric right-hand-side LP” in the optimization theory. Their solution paths can be generated with certain simplex algorithms. This work exploits the connection between the family of regularization methods and the parametric LP theory and lays out a general simplex algorithm and its variant for generating regularized solution paths for the feature selection problems. The significance of such algorithms is that they allow a complete exploration of the model space along the paths and provide a broad view of persistent features in the data. The implications of the general path-finding algorithms are outlined for various statistical procedures, and they are illustrated with numerical examples.
Yoonkyung Lee (Advisor)
Prem Goel (Committee Member)
Tao Shi (Committee Member)
120 p.

Recommended Citations

Citations

  • Yao, Y. (2008). Statistical Applications of Linear Programming for Feature Selection via Regularization Methods [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1222035715

    APA Style (7th edition)

  • Yao, Yonggang. Statistical Applications of Linear Programming for Feature Selection via Regularization Methods. 2008. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1222035715.

    MLA Style (8th edition)

  • Yao, Yonggang. "Statistical Applications of Linear Programming for Feature Selection via Regularization Methods." Doctoral dissertation, Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1222035715

    Chicago Manual of Style (17th edition)