{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/119354"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/119354","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Sparse learning : statistical and optimization perspectives","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Dedieu, Antoine"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Operations Research Center.","school":null,"contributors":[],"advisors":["Rahul Mazumder."],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-22T22:21:45Z","subjects":["Operations Research Center."],"languages":["eng"],"rights":["MIT theses are protected by copyright. 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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. 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