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Title:Bayesian regularization for graphical models and variants: Theory and algorithms
Author(s):Gan, Lingrui
Director of Research:Liang, Feng; Narisetty, Naveen Naidu
Doctoral Committee Chair(s):Liang, Feng; Narisetty, Naveen Naidu
Doctoral Committee Member(s):Qu, Annie; Chen, Xiaohui
Department / Program:Statistics
Discipline:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2019-04-19
Type:Thesis
URI:http://hdl.handle.net/2142/105227
Rights Information:Copyright 2019 Lingrui Gan
Date Available in IDEALS:2019-08-23
Date Deposited:2019-05


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