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CATEGORIES:CCIMI Seminars
SUMMARY:Metropolis Adjusted Langevin Trajectories: a robus
t alternative to Hamiltonian Monte Carlo - Lionel
Riou-Durand (University of Warwick)
DTSTART;TZID=Europe/London:20220511T140000
DTEND;TZID=Europe/London:20220511T150000
UID:TALK173504AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173504
DESCRIPTION:Hamiltonian Monte Carlo (HMC) is a widely used sam
pler\, known for its efficiency on high dimensiona
l distributions. Yet HMC remains quite sensitive t
o the choice of integration time. Randomizing the
length of Hamiltonian trajectories (RHMC) has been
suggested to smooth the Auto-Correlation Function
s (ACF)\, ensuring robustness of tuning. We presen
t the Langevin diffusion as an alternative to cont
rol these ACFs by inducing randomness in Hamiltoni
an trajectories through a continuous refreshment o
f the velocities. We connect and compare the two p
rocesses in terms of quantitative mixing rates for
the 2-Wasserstein and L2 distances. The Langevin
diffusion is presented as a limit of RHMC achievin
g the fastest mixing rate for strongly log-concave
targets. We introduce a robust alternative to HMC
built upon these dynamics\, named Metropolis Adju
sted Langevin Trajectories (MALT). Studying the sc
aling limit of MALT\, we obtain optimal tuning gui
delines similar to HMC\, and recover the same scal
ing with respect to the dimension without addition
al assumptions. We illustrate numerically the effi
ciency of MALT compared to HMC and RHMC.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Randolf Altmeyer
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