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UID:calendar.130832.field_date.0@www.tse-fr.eu
DTSTAMP:20240622T073314Z
CREATED:20230215T171001Z
DESCRIPTION:Lionel Riou-Durand (University of Warwick)\, “Metropolis Adjust
ed Langevin Trajectories: a robust alternative to Hamiltonian Monte Carlo”
\, Maths Job Market Seminar\, TSE\, Toulouse\, March 6\, 2023\, 09:30–10:4
5\, Auditorium 3.\n\nHamiltonian Monte Carlo (HMC) is a widely used sample
r\, known for its efficiency on high dimensional distributions. Yet HMC re
mains quite sensitive to the choice of integration time. Randomizing the l
ength of Hamiltonian trajectories (RHMC) has been suggested to smooth the
Auto-Correlation Functions (ACF)\, ensuring robustness of tuning. We prese
nt the Langevin diffusion as an alternative to control these ACFs by induc
ing randomness in Hamiltonian trajectories through a continuous refreshmen
t of the velocities. We connect and compare the two processes in terms of
quantitative mixing rates for the 2-Wasserstein and L2 distances. The Lang
evin diffusion is presented as a limit of RHMC achieving the fastest mixin
g rate for strongly log-concave targets. We introduce a robust alternative
to HMC built upon these dynamics\, named Metropolis Adjusted Langevin Tra
jectories (MALT). Studying the scaling limit of MALT\, we obtain optimal t
uning guidelines similar to HMC\, and recover the same scaling with respec
t to the dimension without additional assumptions. We illustrate numerical
ly the efficiency of MALT compared to HMC and RHMC.
DTSTART;TZID=Europe/Paris:20230306T093000
DTEND;TZID=Europe/Paris:20230306T104500
LAST-MODIFIED:20230303T011001Z
LOCATION:TSE\, Toulouse\, March 6\, 2023\, 09:30–10:45\, Auditorium 3
SUMMARY:Maths Job Market Seminar
URL;TYPE=URI:https://www.tse-fr.eu/seminars/2023-metropolis-adjusted-langev
in-trajectories-robust-alternative-hamiltonian-monte-carlo
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