Show simple item record

dc.contributor.advisorPaschalidis, Ioannis Ch.en_US
dc.contributor.authorChen, Ruidien_US
dc.date.accessioned2019-10-08T18:13:09Z
dc.date.available2019-10-08T18:13:09Z
dc.date.issued2019
dc.identifier.urihttps://hdl.handle.net/2144/38236
dc.description.abstractThis dissertation develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. The learning problems that are studied include: (i) Distributionally Robust Linear Regression (DRLR), which estimates a robustified linear regression plane by minimizing the worst-case expected absolute loss over a probabilistic ambiguity set characterized by the Wasserstein metric; (ii) Groupwise Wasserstein Grouped LASSO (GWGL), which aims at inducing sparsity at a group level when there exists a predefined grouping structure for the predictors, through defining a specially structured Wasserstein metric for DRO; (iii) Optimal decision making using DRLR informed K-Nearest Neighbors (K-NN) estimation, which selects among a set of actions the optimal one through predicting the outcome under each action using K-NN with a distance metric weighted by the DRLR solution; and (iv) Distributionally Robust Multivariate Learning, which solves a DRO problem with a multi-dimensional response/label vector, as in Multivariate Linear Regression (MLR) and Multiclass Logistic Regression (MLG), generalizing the univariate response model addressed in DRLR. A tractable DRO relaxation for each problem is being derived, establishing a connection between robustness and regularization, and obtaining upper bounds on the prediction and estimation errors of the solution. The accuracy and robustness of the estimator is verified through a series of synthetic and real data experiments. The experiments with real data are all associated with various health informatics applications, an application area which motivated the work in this dissertation. In addition to estimation (regression and classification), this dissertation also considers outlier detection applications.en_US
dc.language.isoen_US
dc.subjectStatisticsen_US
dc.subjectDistributionally robust optimizationen_US
dc.subjectGrouped variable selectionen_US
dc.subjectHealth informaticsen_US
dc.subjectMultivariate linear regressionen_US
dc.subjectRegressionen_US
dc.subjectClassificationen_US
dc.subjectWasserstein metricen_US
dc.titleDistributionally Robust Learning under the Wasserstein Metricen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2019-09-29T04:01:54Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineSystems Engineeringen_US
etd.degree.grantorBoston Universityen_US
dc.identifier.orcid0000-0002-1508-1742


This item appears in the following Collection(s)

Show simple item record