Faculty Advisor or Committee Member

Lifeng Lai, Advisor

Faculty Advisor or Committee Member

Donald Richard Brown III, Committee Member

Faculty Advisor or Committee Member

Weiyu Xu, Committee Member

Identifier

etd-081417-195305

Abstract

"Statistical inference plays an increasingly important role in science, finance and industry. Despite the extensive research and wide application of statistical inference, most of the efforts focus on uniform models. This thesis considers the statistical inference in models with abrupt changes instead. The task is to estimate change-points where the underlying models change. We first study low dimensional linear regression problems for which the underlying model undergoes multiple changes. Our goal is to estimate the number and locations of change-points that segment available data into different regions, and further produce sparse and interpretable models for each region. To address challenges of the existing approaches and to produce interpretable models, we propose a sparse group Lasso (SGL) based approach for linear regression problems with change-points. Then we extend our method to high dimensional nonhomogeneous linear regression models. Under certain assumptions and using a properly chosen regularization parameter, we show several desirable properties of the method. We further extend our studies to generalized linear models (GLM) and prove similar results. In practice, change-points inference usually involves high dimensional data, hence it is prone to tackle for distributed learning with feature partitioning data, which implies each machine in the cluster stores a part of the features. One bottleneck for distributed learning is communication. For this implementation concern, we design communication efficient algorithm for feature partitioning data sets to speed up not only change-points inference but also other classes of machine learning problem including Lasso, support vector machine (SVM) and logistic regression."

Publisher

Worcester Polytechnic Institute

Degree Name

PhD

Department

Electrical & Computer Engineering

Project Type

Dissertation

Date Accepted

2017-08-14

Accessibility

Unrestricted

Subjects

change-points, machine learning, distributed learning

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