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Postdoctoral Applicants
Monte Carlo and Machine Learning for High Dimensions and Rare Events
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Speaker: Xiaoou Cheng (NYU) PhD Candidate New York University Monday, February 2, 2026 10:30AM - 11:30AM and via Webcast: https://yale.zoom.us/j/94198022300?pwd=Bc3l38eVJI7eWUle5Isc3IpRcHDtcQ.1 |
Zoom Password: 123
Abstract: High dimensions and rare events are ubiquitous in scientific applications, yet they present significant challenges for probabilistic inference. In this talk, I will share theoretical insights into algorithm scalability in these demanding settings. First, I will discuss how certain Markov chain Monte Carlo (MCMC) methods efficiently sample low-dimensional marginals of high-dimensional distributions. While finite step sizes in samplers like unadjusted Hamiltonian Monte Carlo (HMC) and underdamped Langevin dynamics incur a bias, we demonstrate that controlling the error for low-dimensional marginals requires the step size to scale only with the target marginal’s dimension rather than the full state space under certain assumptions. This allows for significantly larger step sizes and lower iteration complexity than their Metropolized counterparts. We introduce a matrix polynomial framework to address the technical challenges. Second, I will show how a workhorse algorithm in reinforcement learning called “temporal difference learning” can estimate rare event statistics with relative accuracy, using time-series data much shorter than the natural timescale of the rare event. Finally, I will mention how to collect informational data to provably reduce computational burden in high dimensions, framing the active learning task as a problem in randomized numerical linear algebra.
Speaker bio: Xiaoou Cheng is a final-year PhD Candidate in mathematics at NYU Courant, working with Prof. Jonathan Weare. Her work focuses on the analysis, design, and application of Monte Carlo methods and probabilistic machine learning, particularly in the context of high dimensions and rare events. She earned her B.S. in Computational Mathematics from Peking University in 2020. Her research is supported in part by a Dean’s Dissertation Fellowship from NYU Graduate School of Arts & Science.
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