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dc.contributor.advisor Dunson, David B en_US
dc.contributor.author Shi, Minghui en_US
dc.date.accessioned 2011-05-20T19:35:38Z
dc.date.available 2011-05-20T19:35:38Z
dc.date.issued 2011 en_US
dc.identifier.uri http://hdl.handle.net/10161/3869
dc.description Dissertation en_US
dc.description.abstract <p>In this thesis, we develop some Bayesian sparse learning methods for high dimensional data analysis. There are two important topics that are related to the idea of sparse learning -- variable selection and factor analysis. We start with Bayesian variable selection problem in regression models. One challenge in Bayesian variable selection is to search the huge model space adequately, while identifying high posterior probability regions. In the past decades, the main focus has been on the use of Markov chain Monte Carlo (MCMC) algorithms for these purposes. In the first part of this thesis, instead of using MCMC, we propose a new computational approach based on sequential Monte Carlo (SMC), which we refer to as particle stochastic search (PSS). We illustrate PSS through applications to linear regression and probit models.</p><p>Besides the Bayesian stochastic search algorithms, there is a rich literature on shrinkage and variable selection methods for high dimensional regression and classification with vector-valued parameters, such as lasso (Tibshirani, 1996) and the relevance vector machine (Tipping, 2001). Comparing with the Bayesian stochastic search algorithms, these methods does not account for model uncertainty but are more computationally efficient. In the second part of this thesis, we generalize this type of ideas to matrix valued parameters and focus on developing efficient variable selection method for multivariate regression. We propose a Bayesian shrinkage model (BSM) and an efficient algorithm for learning the associated parameters .</p><p>In the third part of this thesis, we focus on the topic of factor analysis which has been widely used in unsupervised learnings. One central problem in factor analysis is related to the determination of the number of latent factors. We propose some Bayesian model selection criteria for selecting the number of latent factors based on a graphical factor model. As it is illustrated in Chapter 4, our proposed method achieves good performance in correctly selecting the number of factors in several different settings. As for application, we implement the graphical factor model for several different purposes, such as covariance matrix estimation, latent factor regression and classification.</p> en_US
dc.subject Statistics en_US
dc.subject Factor model en_US
dc.subject High dimensional Data en_US
dc.subject penalized marginal likelihood en_US
dc.subject Variable Selection en_US
dc.title Bayesian Sparse Learning for High Dimensional Data en_US
dc.type Dissertation en_US
dc.department Statistical Science en_US

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