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Comparison of Regression Methods with Non-Convex Penalties

Pipher, Brandon
http://orcid.org/0000-0002-2553-3212
http://rave.ohiolink.edu/etdc/view?acc_num=kent1573056251025985

Abstract Details

2019, MS, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
We examine a solution to the problem of sparse selection in linear models. The method used is a mixed norm ℓp-ℓq algorithm with a focus on non-convex, q < 1, penalty parameters. Classical regression, Ordinary Least Squares, has low bias but high variance and prediction accuracy can sometimes be improved by increasing bias to decrease variance. By inducing sparsity we can improve model interpretability, especially in the setting of high-dimensional data. These methods of penalized regression also provide solutions when the Ordinary Least Squares solution is ill-posed under a high-dimensional setting, and have a history of producing accurate and parsimonious models. A simulation study is conducted utilizing another method of penalized regression using non-convex penalties, the SparseNet algorithm, which had previously been compared independently against several other proposed sparsity inducing non-convex solutions. We also include a comparison with other more common penalties such as LASSO, Ridge/Tikhonov, and Elastic Net.
Omar De la Cruz Cabrera (Advisor)
Lothar Reichel (Committee Member)
Oana Mocioalca (Committee Member)
27 p.
Applied Mathematics; Mathematics; Statistics
Regression

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Citations

  • Pipher, B. (2019). Comparison of Regression Methods with Non-Convex Penalties [Master's thesis, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1573056251025985

    APA Style (7th edition)

  • Pipher, Brandon. Comparison of Regression Methods with Non-Convex Penalties. 2019. Kent State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1573056251025985.

    MLA Style (8th edition)

  • Pipher, Brandon. "Comparison of Regression Methods with Non-Convex Penalties." Master's thesis, Kent State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1573056251025985

    Chicago Manual of Style (17th edition)

kent1573056251025985
62,121
© 2019, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.