Date on Master's Thesis/Doctoral Dissertation

8-2023

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Han, Dan

Committee Co-Chair (if applicable)

Gill, Ryan

Committee Member

Gill, Ryan

Committee Member

Biro, Csaba

Committee Member

Du-Caines, Jian

Author's Keywords

Bayesian; exponential; graph models

Abstract

Networks have the critical ability to represent the complex interconnectedness of social relationships, biological processes, and the spread of diseases and information. Exponential random graph models (ERGM) are one of the popular statistical methods for analyzing network data. ERGM, however, struggle with computational challenges and degeneracy issues, further exacerbated by their inability to handle high-dimensional network data. Bayesian techniques provide a promising avenue to overcome these two problems. This paper considers penalized Bayesian exponential random graph models with adaptive lasso and adaptive ridge penalties to perform variable selection and reduce multicollinearity on a variety of networks. The experimental results demonstrate their effectiveness in variable selection and reduction of multicollinearity across diverse networks, outperforming the widely used Bayesian exponential random graph model proposed by Caimo et al., which lacks regularization capabilities. This paper presents a valuable extension to network models for large-scale high-dimensional data and offers opportunities for advancing research in diverse fields.

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