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UID:932@fds.yale.edu
DTSTART;TZID=America/New_York:20260202T103000
DTEND;TZID=America/New_York:20260202T113000
DTSTAMP:20260130T195848Z
URL:https://fds.yale.edu/events/fds-seminar-xiaoou-cheng/
SUMMARY:FDS Seminar: Xiaoou Cheng (NYU)\, "Monte Carlo and Machine Learning
  for High Dimensions and Rare Events "
DESCRIPTION:\nZoom Password: 123\n\n\n\nAbstract: High dimensions and rare
  events are ubiquitous in scientific applications\, yet they present signi
 ficant challenges for probabilistic inference. In this talk\, I will share
  theoretical insights into algorithm scalability in these demanding settin
 gs. First\, I will discuss how certain Markov chain Monte Carlo (MCMC) met
 hods efficiently sample low-dimensional marginals of high-dimensional dist
 ributions. While finite step sizes in samplers like unadjusted Hamiltonian
  Monte Carlo (HMC) and underdamped Langevin dynamics incur a bias\, we dem
 onstrate that controlling the error for low-dimensional marginals requires
  the step size to scale only with the target marginal's dimension rather t
 han the full state space under certain assumptions. This allows for signif
 icantly larger step sizes and lower iteration complexity than their Metrop
 olized 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 estima
 te rare event statistics with relative accuracy\, using time-series data m
 uch shorter than the natural timescale of the rare event. Finally\, I will
  mention how to collect informational data to provably reduce computationa
 l burden in high dimensions\, framing the active learning task as a proble
 m in randomized numerical linear algebra. \n\n\n\nSpeaker bio: Xiaoou Che
 ng is a final-year PhD Candidate in mathematics at NYU Courant\, working w
 ith Prof. Jonathan Weare. Her work focuses on the analysis\, design\, and 
 application of Monte Carlo methods and probabilistic machine learning\, pa
 rticularly in the context of high dimensions and rare events. She earned h
 er B.S. in Computational Mathematics from Peking University in 2020. Her r
 esearch is supported in part by a Dean's Dissertation Fellowship from NYU 
 Graduate School of Arts &amp\; Science.\n
CATEGORIES:FDS Events,Postdoctoral Applicants
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