Simultaneous estimation approaches to large-scale multivariate regression

Wang, Yihe

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https://hdl.handle.net/2142/110785 Copy

Description

Title

Simultaneous estimation approaches to large-scale multivariate regression

Author(s)

Wang, Yihe

Issue Date

2021-03-30

Director of Research (if dissertation) or Advisor (if thesis)

Zhao, Sihai Dave

Doctoral Committee Chair(s)

Zhao, Sihai Dave

Committee Member(s)

• Liang, Feng
• Eck, Daniel J
• Zhu, Ruoqing

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• multivariate regression
• compound decision
• nonparametric
• empirical Bayes
• Stein's unbiased risk

Abstract

Large-scale multivariate regression has various applications in machine learning fields, especially in image recognition, gene expression prediction and multivariate time series prediction. Numerous approaches have been developed to solve this problem. Some popular statistical methods are group lasso and multivariate ridge regression. Most existing methods either leverage the information of the error covariance matrix or assume specific parameter structures. However, in practice, this information is not available. To resolve these issues, we start with formulating multivariate regression as a compound decision problem. In Chapter 2, we propose an empirical Bayes-based approach where the prior distribution of unknown parameters is estimated nonparametrically from the data. Unlike existing methods, the proposed method does not assume any structure of parameters. In Chapter 3, we propose a method that linearly shrinks each coordinate of ordinary least squares estimator. Both theoretical and numerical results are available. In Chapter 4, some nonlinear shrinkage methods based on soft threshold operator are also proposed. Taking the advantage of large number of related outcomes, the proposed methods outperform popular existing methods.

Graduation Semester

2021-05

Type of Resource

Thesis

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http://hdl.handle.net/2142/110785

Copyright and License Information

Copyright 2021 Yihe Wang

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