Scalable Bayesian Inference for Generalized Multivariate Dynamic Linear Models
Open Access
- Author:
- Saxena, Manan
- Graduate Program:
- Informatics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- March 12, 2024
- Committee Members:
- Justin Silverman, Thesis Advisor/Co-Advisor
Romit Maulik, Committee Member
Dongwon Lee, Professor in Charge/Director of Graduate Studies
Aron Laszka, Committee Member - Keywords:
- Bayesian Statistics
Multinomial Time Series
Generalized Multivariate Dynamic Linear Models
Optimization
Microbiome - Abstract:
- Generalized Multivariate Dynamic Linear Models (GMDLMs) are a flexible class of multivariate time series models well-suited for non-Gaussian observations. They represent a special case within the more widely recognized multinomial logistic-normal (MLN) models. They are effective for analyzing sequence count data due to their ability to handle complex covariance structures and provide interpretability/control over the structure of the model. However, their current implementations are limited to small datasets, primarily because of computational inefficiency and increased variance in parameter estimates. Our work addresses the need for scalable Bayesian inference methods for these models. We develop an efficient method for obtaining a point estimate of our parameter by using the Kalman Filter and calculating closed-form gradients for our optimizer. Additionally, we provide uncertainty quantification of our parameter using Multinomial Dirichlet Bootstrap and refine these estimates further with Particle Refinement. We demonstrate that our inference scheme is considerably faster than STAN and provides a reliable approximation comparable to results obtained from MCMC.