Bayesian generalized additive model selection

He, Virginia Xiaojun

Bayesian generalized additive model selection

He, Virginia Xiaojun

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Publication Type:: Thesis
Issue Date:: 2025

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Field	Value	Language
dc.contributor.author	He, Virginia Xiaojun
dc.date.accessioned	2026-01-15T02:11:36Z
dc.date.available	2026-01-15T02:11:36Z
dc.date.issued	2025
dc.identifier.uri	http://hdl.handle.net/10453/191847
dc.description	University of Technology Sydney. Faculty of Science.	en_US.UTF-8
dc.description.abstract	Generalized additive models (GAMs) offer a parsimonious, flexible and interpretable framework for regression, particularly when handling a large numbers of candidate predictors. This thesis addresses the GAM variable selection problem: categorizing each candidate predictor's effect type to be linear, non-linear or zero on the mean response. We use Bayesian model selection paradigms and group least absolute shrinkage and selection operator (LASSO) priors. Two types of priors are explored for the sparse fits. The first, Laplace-Zero and Grouped Lasso-Zero priors, is applied to Gaussian and binary responses. The second, (Grouped) Horseshoe priors, is used for Gaussian and count responses. For both prior types, tailored auxiliary variable representations enable the Markov chain Monte Carlo (MCMC) sampling reduce to the Gibbs sampling or to slice sampling. To improve computational scalability and speed, we also derive the mean field variational Bayes (MFVB) algorithms under the Laplace-Zero and Grouped Lasso-Zero priors. The GAM selection framework is further extended to generalized additive mixed model (GAMM) with random intercept. Finally, the properties of the Grouped Horseshoe distribution and its use in Bayesian GAM selection are investigated. While many characteristics of univariate Horseshoe distribution are carried over, some distinctions arise in the grouped case.	en_US.UTF-8
dc.format	Thesis (PhD)
dc.language.iso	en_US	en_US.UTF-8
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/191847/1/thesis.pdf
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.rights	© 2025 Virginia Xiaojun He
dc.rights	au.edu.uts.lib/cph
dc.title	Bayesian generalized additive model selection	en_US.UTF-8
dc.type	Thesis
utslib.copyright.status	open_access	*

Abstract:

Generalized additive models (GAMs) offer a parsimonious, flexible and interpretable framework for regression, particularly when handling a large numbers of candidate predictors. This thesis addresses the GAM variable selection problem: categorizing each candidate predictor's effect type to be linear, non-linear or zero on the mean response. We use Bayesian model selection paradigms and group least absolute shrinkage and selection operator (LASSO) priors. Two types of priors are explored for the sparse fits. The first, Laplace-Zero and Grouped Lasso-Zero priors, is applied to Gaussian and binary responses. The second, (Grouped) Horseshoe priors, is used for Gaussian and count responses. For both prior types, tailored auxiliary variable representations enable the Markov chain Monte Carlo (MCMC) sampling reduce to the Gibbs sampling or to slice sampling. To improve computational scalability and speed, we also derive the mean field variational Bayes (MFVB) algorithms under the Laplace-Zero and Grouped Lasso-Zero priors. The GAM selection framework is further extended to generalized additive mixed model (GAMM) with random intercept. Finally, the properties of the Grouped Horseshoe distribution and its use in Bayesian GAM selection are investigated. While many characteristics of univariate Horseshoe distribution are carried over, some distinctions arise in the grouped case.

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http://hdl.handle.net/10453/191847