Sparse learning : statistical and optimization perspectives
Thesis: S.M., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2018.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2018
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| Online Access: | http://hdl.handle.net/1721.1/119354 |
| _version_ | 1826204913543151616 |
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| author | Dedieu, Antoine |
| author2 | Rahul Mazumder. |
| author_facet | Rahul Mazumder. Dedieu, Antoine |
| author_sort | Dedieu, Antoine |
| collection | MIT |
| description | Thesis: S.M., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2018. |
| first_indexed | 2024-09-23T13:03:21Z |
| format | Thesis |
| id | mit-1721.1/119354 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:03:21Z |
| publishDate | 2018 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1193542019-04-12T23:20:14Z Sparse learning : statistical and optimization perspectives Dedieu, Antoine Rahul Mazumder. Massachusetts Institute of Technology. Operations Research Center. Massachusetts Institute of Technology. Operations Research Center. Operations Research Center. Thesis: S.M., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 101-109). In this thesis, we study the computational and statistical aspects of several sparse models when the number of samples and/or features is large. We propose new statistical estimators and build new computational algorithms - borrowing tools and techniques from areas of convex and discrete optimization. First, we explore an Lq-regularized version of the Best Subset selection procedure which mitigates the poor statistical performance of the best-subsets estimator in the low SNR regimes. The statistical and empirical properties of the estimator are explored, especially when compared to best-subsets selection, Lasso and Ridge. Second, we propose new computational algorithms for a family of penalized linear Support Vector Machine (SVM) problem with a hinge loss function and sparsity-inducing regularizations. Our methods bring together techniques from Column (and Constraint) Generation and modern First Order methods for non-smooth convex optimization. These two components complement each others' strengths, leading to improvements of 2 orders of magnitude when compared to commercial LP solvers. Third, we present a novel framework inspired by Hierarchical Bayesian modeling to predict user session-length on on-line streaming services. The time spent by a user on a platform depends upon user-specific latent variables which are learned via hierarchical shrinkage. Our framework incorporates flexible parametric/nonparametric models on the covariates and outperforms state-of- the-art estimators in terms of efficiency and predictive performance on real world datasets from the internet radio company Pandora Media Inc. by Antoine Dedieu. S.M. 2018-11-28T15:44:33Z 2018-11-28T15:44:33Z 2018 2018 Thesis http://hdl.handle.net/1721.1/119354 1065541961 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 121 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Operations Research Center. Dedieu, Antoine Sparse learning : statistical and optimization perspectives |
| title | Sparse learning : statistical and optimization perspectives |
| title_full | Sparse learning : statistical and optimization perspectives |
| title_fullStr | Sparse learning : statistical and optimization perspectives |
| title_full_unstemmed | Sparse learning : statistical and optimization perspectives |
| title_short | Sparse learning : statistical and optimization perspectives |
| title_sort | sparse learning statistical and optimization perspectives |
| topic | Operations Research Center. |
| url | http://hdl.handle.net/1721.1/119354 |
| work_keys_str_mv | AT dedieuantoine sparselearningstatisticalandoptimizationperspectives |