Approximate posterior inference for Bayesian nonparametrics with total variation error bounds
department or school: Science, Faculty of
department or school: Statistics, Department of
data provider: DSpace
degree campus: UBCV
creator: Li, Xinglong
issued: 2025-04-17T16:05:02Z
issued: 2025
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: Bayesian nonparametric (BNP) models provide a flexible and powerful framework for statistical modeling by allowing the number of features or subgroups within a population to grow with the data volume. However, posterior inference in BNP models is challenging due to the infinite parameters involved, and the lack of general and efficient inference procedures impedes their practical application. Exact posterior inference methods either analytically marginalize out the infinitely many parameters, or introduce auxiliary variables to adaptively adjust the model size during inference. The former approach relies on conjugacy relationships between priors and likelihoods and suffers from high computational costs. Similarly, the latter approach is also computationally demanding, as it requires numerical integration during sampling for nonconjugate models. An alternative common practice in fitting BNP models involves approximating the nonparametric model with a parametric one, and subsequently applying a standard inference algorithm. While this is practical, parametric truncation can lead to significant unknown posterior approximation errors, particularly for BNP models with heavy tails that support the power-law behavior of the population. Previous work on truncated inference in BNP models has determined the truncation level via analysis of the forward generative model, which does not accurately reflect the error of approximation of the target posterior distribution. This thesis aims to develop approximate inference algorithms that can be directly used for posterior inference for general BNP models. We propose truncated inference methods and provide estimates of the posterior truncation error. Rather than setting the truncation level based on prior approximation error, we establish a desired posterior truncation error level, allowing the algorithm to adapt the truncation level until the desired truncation error is reached. The proposed algorithms are general in that they can b…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/90683
note: Approximate posterior inference forBayesian nonparametrics with totalvariation error boundsbyXinglong LiB.Sc., China University of Petroleum (East China), 2015M.Sc., Yunnan University, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Statistics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2025© Xinglong Li, 2025The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Approximate posterior inference for Bayesian nonparametrics withtotal variation error boundssubmitted by Xinglong Li in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in Statistics.Examining Committee:Trevor Campbell, Associate Professor, Department of Statistics, Universityof British ColumbiaSupervisorAlexandre Bouchard-CoËte´, Professor, Department of Statistics, University ofBritish ColumbiaSupervisory Committee MemberBen Bloem-Reddy, Assistant Professor, Department of Statistics, Universityof British ColumbiaSupervisory Committee MemberPaul Gustafson, Professor, Department of Statistics, University of BritishColumbiaUniversity ExaminerFrank Wood, Professor, Department of Computer Science, University ofBritish ColumbiaUniversity ExaminerSinead Williamson, Associate Professor, Department of Statistics and DataSciences , The University of Texas at AustinExternal ExamineriiAbstractBayesian nonparametric (BNP) models provide a flexible and powerful frame-work for statistical modeling by allowing the number of features or subgroupswithin a population to grow with the data volume. However, posteriorinference in BNP models is challenging due to the infinite parameters in-volved, and the lack of general and efficient inference procedures impedestheir practical application. Exact posterior inference methods either analyti-cally marginalize out the infinitely many parameter…
has type: Thesis/Dissertation
date issued: 2025-05
is shown at: 10.14288/1.0448446
language: eng
degree discipline: Statistics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Campbell, Trevor (Professor of statistics)
type: Text
identifier URI: http://hdl.handle.net/2429/90683