Schuh, K. J. (2023, December 14). Nonlinear Hamiltonian Monte Carlo and its Particle Approximation [Conference Presentation]. Workshop: “‘Third workshop on Monte Carlo methods in Warsaw,’” Poland.
Workshop: ''Third workshop on Monte Carlo methods in Warsaw''
en
Event date:
13-Dec-2023 - 15-Dec-2023
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Event place:
Poland
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Keywords:
Hamiltonian Monte Carlo; McKean-Vlasov Process; Propagation of Chaos; Markov chain Monte Carlo; Couplings
en
Abstract:
In the talk, a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC)
termed nonlinear HMC (nHMC) is presented to sample from nonlinear probability measures of meanfield type. Provided the underlying confinement potential is L-gradient Lipschitz and asymptotically
K-strongly convex, we prove contraction in L
1
-Wasserstein distance. Further, we show that uniformly
in time nHMC can be approximated by unadjusted HMC for its corresponding mean-field particle
system in L
1
-Wasserstein distance. In particular, we analyse the number of gradient evaluations needed
for unadjusted HMC with randomized time integration to achieve an ϵ-accuracy of a d-dimensional
nonlinear probability measure in L
1
-Wasserstein distance. The talk is based on joint work with Nawaf
Bou-Rabee (arXiv:2308.11491).
