Title:
Learning, sampling and inference with stochastic differential equations
Learning, sampling and inference with stochastic differential equations
Author(s)
Zhang, Qinsheng
Advisor(s)
Chen, Yongxin
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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 dissertation, 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 develop an efficient algorithm for drawing samples from high-dimensional SDEs, which proves effective in generating diverse and high-fidelity data, such as realistic images and videos.
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Date Issued
2023-12-06
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Text
Resource Subtype
Dissertation