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SUMMARY:Metropolis Adjusted Langevin Trajectories: a robust alternative to
  Hamiltonian Monte Carlo  - Lionel Riou-Durand (University of Warwick)
DTSTART:20220511T130000Z
DTEND:20220511T140000Z
UID:TALK173504@talks.cam.ac.uk
CONTACT:Randolf Altmeyer
DESCRIPTION:Hamiltonian Monte Carlo (HMC) is a widely used sampler\, known
  for its efficiency on high dimensional distributions. Yet HMC remains qui
 te sensitive to the choice of integration time. Randomizing the length of 
 Hamiltonian trajectories (RHMC) has been suggested to smooth the Auto-Corr
 elation Functions (ACF)\, ensuring robustness of tuning. We present the La
 ngevin diffusion as an alternative to control these ACFs by inducing rando
 mness in Hamiltonian trajectories through a continuous refreshment of the 
 velocities. We connect and compare the two processes in terms of quantitat
 ive mixing rates for the 2-Wasserstein and L2 distances. The Langevin diff
 usion is presented as a limit of RHMC achieving the fastest mixing rate fo
 r strongly log-concave targets. We introduce a robust alternative to HMC b
 uilt upon these dynamics\, named Metropolis Adjusted Langevin Trajectories
  (MALT). Studying the scaling limit of MALT\, we obtain optimal tuning gui
 delines similar to HMC\, and recover the same scaling with respect to the 
 dimension without additional assumptions. We illustrate numerically the ef
 ficiency of MALT compared to HMC and RHMC.
LOCATION:Centre for Mathematical Sciences\, MR14
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