Sparse learning : statistical and optimization perspectives
Name
1065541961-MIT.pdf
Description
Full printable version
Size
8.56 MB
Format
Adobe PDF
Checksum (MD5)
a982217009710fd2caac1c428100fcb4
Author(s)
Dedieu, Antoine
Advisor(s)
Rahul Mazumder.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Operations Research Center.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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