Scalable algorithms for Bayesian variable selection

The innovation of modern technologies drives research and development on high-dimensional data analysis in diverse fields, where variable selection plays a pivotal role to ensure credible model estimation. We focus on scalable algorithms for variable selection that can handle large data sets. Firstly, we propose an EM algorithm that returns the MAP estimate of the set of relevant variables. Due to its particular updating scheme, our algorithm can be implemented efficiently. We also show that the MAP estimate returned by our EM algorithm achieves variable selection consistency. In practice, EM algorithm tends to get stuck at local peaks. So we propose an ensemble version: repeatedly apply the EM algorithm on a subset of Bootstrap sample data and then aggregate the results. Empirical studies demonstrate the superior performance of this Bayesian Bootstrap EM algorithm. Secondly, we propose a hybrid computation framework for Bayesian variable selection. This new algorithm SAB is a combination of the classical EM algorithm and the variational Bayes algorithm. It is very fast in handling high dimensional data with a large number of covariates. To address a critical biological problem, we apply SAB to a state-of-art cancer genomics data set with a goal to understand the complex regulatory relationship between miRNAs and mRNAs in cancer. In the third part, we study the asymptotic behavior of the SAB algorithm in detail and prove that SAB achieves the selection consistency, Bayesian consistency and also an oracle property when the number of covariates grows with the sample size exponentially. Lastly, we extend the hybrid framework of Bayesian variable selection to logistic models, where we adopt the Polya-Gamma specification and show that this specification is equivalent as the local approximation method in the variational Bayes framework.

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

2016

Author dc:creator

• Wang, Jin

Contributors dc:contributor

• Liang, Feng
• Marden, John I.
• Ji, Yuan
• Zhao, Dave
• Park, Trevor

• Variable Selection
• EM
• Ensemble
• Variational Bayes
• Asymptotic Analysis
• Logistic model

Statement dc:rights

• Copyright 2016 Jin Wang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/92827

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F92827