High-dimensional Multimodal Bayesian Learning

High-dimensional datasets are fast becoming a cornerstone across diverse domains, fueled by advancements in data-capturing technology like DNA sequencing, medical imaging techniques, and social media. This dissertation delves into the inherent opportunities and challenges posed by these types of datasets. We develop three Bayesian methods: (1) Multilevel Network Recovery for Genomics, (2) Network Recovery for Functional data, and (3) Bayesian Inference in Transformer-based Models. Chapter 2 in our work examines a two-tiered data structure; to simultaneously explore the variable selection and identify dependency structures among both higher and lower-level variables, we propose a multi-level nonparametric kernel machine approach, utilizing variational inference to jointly identify multi-level variables as well as build the network. Chapter 3 addresses the development of a simultaneous selection of functional domain subsets, selection of functional graphical nodes, and continuous response modeling given both scalar and functional covariates under semiparametric, nonadditive models, which allow us to capture unknown, possibly nonlinear, interaction terms among high dimensional functional variables. In Chapter 4, we extend our investigation of leveraging structure in high dimensional datasets to the relatively new transformer architecture; we introduce a new penalty structure to the Bayesian classification transformer, leveraging the multi-tiered structure of the transformer-based model. This allows for increased, likelihood-based regularization, which is needed given the high dimensional nature of our motivating dataset. This new regularization approach allows us to integrate Bayesian inference via variational approximations into our transformer-based model and improves the calibration of probability estimates.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Salem, Mohamed Mahmoud

Chair dc:contributor.committeechair

• Kim, Inyoung

Committee members dc:contributor.committeemember

• Franck, Christopher Thomas
• Van Mullekom, Jennifer Huffman
• Gramacy, Robert B.

• Gaussian Process
• High Dimensional Data
• Variable Selection
• Variational Inference
• Uncertainty Quantification

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:42169

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/123788