Ph.D. Defense

Qinsheng Zhang

(Faculty Advisor: Yongxin Chen)

"Learning, sampling and inference with stochastic differential equations"

Thursday, Nov 30 2023

1:30 PM – 3:30 PM EST

Coda C1115 Druid Hills

Virtual: Meeting Link

Abstract:

Stochastic differential equations (SDEs) constitute a formidable tool for modeling the dynamics of continuous-time stochastic processes and offer a natural framework for the probabilistic modeling of high-dimensional data. Consequently, they have garnered increasing attention in generative machine learning. Despite their promise, the applications of SDEs in machine learning have been limited due to the lack of scalable learning approaches that can train flexible neural networks to approximate stochastic processes, and the difficulty of conducting tractable inference and sampling caused by inefficient SDE solvers. In this work, I outline my efforts to develop novel computational models capable of efficient and scalable learning, sampling, and inference from SDEs. Specifically, I introduce several approaches to learning SDEs for probabilistic modeling, including fitting non-linear forward and backward SDEs with neural networks and learning with limited data. Next, I present a novel deep model designed to learn SDE dynamics while satisfying given constraints on the marginal probability of the SDE. Furthermore, I developed an efficient algorithm for drawing samples from high-dimensional SDEs, which proves effective in generating. This thesis represents an advancement in scalable neural Stochastic Differential Equations (SDEs), extending their applicability to a range of high-dimensional probabilistic modeling tasks, including building large-scale text-to-image / text-to-3d generative models.

Committee:

Dr. Yongxin Chen (Advisor) – School of Aerospace Engineering, Georgia Institute of Technology

Dr. Humphrey Shi – School of Interactive Computing, Georgia Institute of Technology

Dr. Zsolt Kira – School of Interactive Computing, Georgia Institute of Technology

Dr. Danfei Xu – School of Interactive Computing, Georgia Institute of Technology

Dr. Molei Tao –  School of Mathematics, Georgia Institute of Technology