Simultaneous estimation approaches to large-scale multivariate regression

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Wang, Yihe

Contributors dc:contributor

• Zhao, Sihai Dave
• Liang, Feng
• Eck, Daniel J
• Zhu, Ruoqing

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

Statement dc:rights

• Copyright 2021 Yihe Wang

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/110785