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Tuesday, February 17, 2026
Speaker: Aki Nishimura (Johns Hopkins University) [Zoom Link]
Title: Zigzag path connects two Monte Carlo paradigms: Hamiltonian counterparts to piecewise deterministic Markov processes
Abstract: Zigzag and other piecewise deterministic Markov process samplers have attracted significant interest for their non-reversibility and other appealing properties for Bayesian computation. Hamiltonian Monte Carlo is another state-of-the-art sampler, exploiting fictitious momentum to guide Markov chains through complex target distributions.
In this talk, we first establish a remarkable connection between the zigzag sampler and a variant of Hamiltonian Monte Carlo based on Laplace-distributed momentum. The position-velocity component of the corresponding Hamiltonian dynamics travels along a zigzag path paralleling the Markovian zigzag process; however, the dynamics is non-Markovian as the momentum component encodes non-immediate pasts. In the limit of increasingly frequent momentum refreshments in which we preserve its direction but re-sample magnitude, we prove that Hamiltonian zigzag converges strongly to its Markovian counterpart. This theoretical insight in particular explains the two zigzags' relative performance on target distributions with highly correlated parameters, which we demonstrate on a 11,235-dimensional truncated Gaussian target arising from Bayesian phylogenetic multivariate probit model applied to an HIV virus dataset. We then proceed to construct a Hamiltonian counterpart to the bouncy particle sampler (BPS), further strengthening the connection between the two paradigms. We achieve this by turning BPS's Poisson schedule for velocity switch events into a deterministic one dictated by an auxiliary "inertia" parameter. The resulting Hamiltonian BPS constitutes an efficient sampler on log-concave targets and straightforwardly accommodates parameter constraints. We demonstrate its competitive performance in the posterior computation under Bayesian sparse logistic regression model applied to a large-scale observational study consisting of 72,489 patients and 22,175 clinical covariates.
Format and Rules
The seminars are held on Zoom and last 60 minutes.
A moderator collects audience questions in Q&A section.
Moderators may ask you to unmute yourself to participate in the discussion. Please note that you may be recorded if you activate your audio or video during the seminar.
Organizers
Valentin De Bortoli (Google DeepMind)
Yang Chen (University of Michigan)
Nianqiao Ju (Dartmouth College)
Sifan Liu (Duke University)
Sam Power (University of Bristol)
Qian Qin (University of Minnesota)
Guanyang Wang (Rutgers University)
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Acknowledgements
Sincerely thank Ying Jin for the patient guidance
Gratefully inspired by the Online Causal Inference Seminar