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Title:Simultaneous estimation approaches to large-scale multivariate regression
Author(s):Wang, Yihe
Director of Research:Zhao, Sihai Dave
Doctoral Committee Chair(s):Zhao, Sihai Dave
Doctoral Committee Member(s):Liang, Feng; Eck, Daniel J; Zhu, Ruoqing
Department / Program:Statistics
Discipline:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2021-03-30
Type:Thesis
URI:http://hdl.handle.net/2142/110785
Rights Information:Copyright 2021 Yihe Wang
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05


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