University of Illinois Urbana-Champaign

Simultaneous estimation approaches to large-scale multivariate regression

Wang, Yihe

Content Files
WANG-DISSERTATION-2021.pdf

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

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
Date of Ingest
2021-09-17T04:04:05Z
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
Permalink
http://hdl.handle.net/2142/110785
Copyright and License Information
Copyright 2021 Yihe Wang

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