SE PhD Final Defense of Ruidi Chen

TITLE: DISTRIBUTIONALLY ROBUST LEARNING UNDER THE WASSERSTEIN METRIC

ABSTRACT: We develop 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 in this dissertation 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 (KNN) estimation, which selects among a set of actions the optimal one through predicting the outcome under each action using KNN 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), which generalize the univariate response model addressed in DRLR. We derive a tractable DRO relaxation for each problem, establishing a connection between robustness and regularization, obtain upper bounds on the prediction and estimation errors of the solution, and verify the accuracy and robustness of the estimator 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 thesis. In addition to estimation (regression and classification) we also consider outlier detection applications.

COMMITTEE: ADVISOR Yannis Paschalidis, SE/ECE; David Castanon, SE/ECE; Dimitris Bertsimas, ORC, MIT; Venkatesh Saligrama, SE/ECE; CHAIR, Alexander Olshevsky, SE/ECE