Bayesian regularization for graphical models and variants: Theory and algorithms

Gan, Lingrui

Permalink

https://hdl.handle.net/2142/105227 Copy

Description

Title

Bayesian regularization for graphical models and variants: Theory and algorithms

Author(s)

Gan, Lingrui

Issue Date

2019-04-19

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

• Liang, Feng
• Narisetty, Naveen Naidu

Doctoral Committee Chair(s)

• Liang, Feng
• Narisetty, Naveen Naidu

Committee Member(s)

• Qu, Annie
• Chen, Xiaohui

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Bayesian Regularization
• Spike and Slab Priors
• Graphical Models
• High Dimensional Estimation
• Scalable Computation

Abstract

The Bayesian framework offers a flexible tool for regularization in the high dimensional setting. In this thesis, I propose a new class of Bayesian regularization methods induced from scale mixtures of Laplace prior distributions and develop novel statistical methods for a variety of statistical models. We provide theoretical guarantees of our methods (both in estimation accuracy and structure recovery) that are stronger than the existing results. The methods and theoretical results developed in the thesis are applicable for many commonly used high dimensional models, with a particular emphasis on graphical models and conditional random fields using the spike and slab Lasso regularization which is a special case of our general Bayesian regularization framework. We propose fast and scalable EM algorithms for computing the maximum a posterior (MAP) estimators and (approximate) posterior probabilities for support recovery. Extensive empirical results on synthetic and real datasets demonstrate that the proposed methods have merits when compared to the alternative methods.

Graduation Semester

2019-05

Type of Resource

text

Permalink

http://hdl.handle.net/2142/105227

Copyright and License Information

Copyright 2019 Lingrui Gan

Owning Collections