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Bayesian Methods for High-dimensiona...
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Zhang, Yan.
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Bayesian Methods for High-dimensional Data.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Bayesian Methods for High-dimensional Data./
作者:
Zhang, Yan.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:
123 p.
附註:
Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:
Dissertation Abstracts International78-08B(E).
標題:
Statistics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583617
ISBN:
9781369622966
Bayesian Methods for High-dimensional Data.
Zhang, Yan.
Bayesian Methods for High-dimensional Data.
- Ann Arbor : ProQuest Dissertations & Theses, 2016 - 123 p.
Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Thesis (Ph.D.)--North Carolina State University, 2016.
High-dimensional data arises in multiple fields, such as genetics, finance, medicine, etc. A number of statistical methods have been developed to deal with variable selection in highdimensional linear models. In this thesis, we propose several new Bayesian methods to address such problems. Chapter 1 presents a selective literature review of existing statistical methods with a main focus on Bayesian variable selection methodologies. A selective review of recommender systems are also given in this chapter.
ISBN: 9781369622966Subjects--Topical Terms:
517247
Statistics.
Bayesian Methods for High-dimensional Data.
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High-dimensional data arises in multiple fields, such as genetics, finance, medicine, etc. A number of statistical methods have been developed to deal with variable selection in highdimensional linear models. In this thesis, we propose several new Bayesian methods to address such problems. Chapter 1 presents a selective literature review of existing statistical methods with a main focus on Bayesian variable selection methodologies. A selective review of recommender systems are also given in this chapter.
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Chapter 2 proposes a Bayesian variable selection method by incorporating global-local priors into the credible region selection framework, which separates model fitting and variable selection, to search for the sparsest solution within the joint posterior credible regions. The Dirichlet-Laplace (DL) prior is adapted to linear regression. Posterior consistency for the normal and DL priors is shown, along with variable selection consistency. We also introduce a new method to tune hyperparameters in prior distributions for linear regression. We propose to choose the hyperparameters to minimize a discrepancy between the induced distribution on R-square and a prespecified target distribution. Prior elicitation on R-square is more natural, particularly when there are a large number of predictor variables in which elicitation on that scale is not feasible. For a normal prior, these hyperparameters are available in closed form to minimize the Kullback-Leibler divergence between the distributions.
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Chapter 3 proposes a new class of priors for linear regression, the R-square induced Dirichlet Decomposition (R2-D2) prior. The prior is induced by a Beta prior on the coefficient of determination, and then the total prior variance of the regression coefficients is decomposed through a Dirichlet prior. We demonstrate both theoretically and empirically the advantages of the R2-D2 prior over a number of common shrinkage priors, including the Horseshoe, Horseshoe+, and Dirichlet-Laplace priors. The R2-D2 prior possesses the fastest concentration rate around zero and heaviest tails among these common shrinkage priors, which is established based on its marginal density, a Meijer G-function. We show that its Bayes estimator converges to the truth at a Kullback-Leibler super-efficient rate, attaining a sharper information theoretic bound than existing common shrinkage priors. We also demonstrate that the R2-D2 prior yields a consistent posterior. The R2-D2 prior permits straightforward Gibbs sampling and thus enjoys computational tractability. The proposed prior is further investigated in a mouse gene expression application.
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Chapter 4 is motivated by a movie rating system. This chapter proposes a full Bayesian hybrid recommender system, using a shared-variable approach for matrix completion to coerce informative missingness into a regression-based model to improve prediction performance. We jointly model the movie rating and the probability of each movie being rated as a function of the expected rating. The proposed model is fitted through MCMC sampling. The computation is stable, accurate and easy to implement. We apply our model on a movie rating system, particularly the MovieLens data. Our method illustrates significant improvement in prediction by adding informative missingness into the model.
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