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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Robust adaptation of integrator snippet sampling a
 lgorithms - Christophe Andrieu (University of Bris
 tol)
DTSTART;TZID=Europe/London:20241126T154000
DTEND;TZID=Europe/London:20241126T163000
UID:TALK221569AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/221569
DESCRIPTION:Assume interest is in sampling from a probability 
 distribution &mu\; defined on Z. We develop a fram
 ework to construct sampling algorithms taking full
  advantage of numerical integrators of ODEs\, say 
 &psi\;:Z&rarr\;Z for one integration step\, to exp
 lore &mu\; efficiently and robustly. The popular H
 ybrid/Hamiltonian Monte Carlo (HMC) algorithm [Dua
 ne et al.\, 1987\, Neal\, 2011] and its derivative
 s are examples of the use of numerical integrators
  in sampling algorithms. A key idea developed here
  is that of sampling integrator snippets\, that is
  fragments of the orbit of an ODE numerical integr
 ator &psi\; \, and the definition of an associated
  probability distribution &mu\; such that expectat
 ions with respect to &mu\; can be estimated from i
 ntegrator snippets sampled from &mu\; . The integr
 ator snippet &mu\; takes the form of a mixture of 
 pushforward distributions which suggests numerous 
 generalisations beyond mappings arising from numer
 ical integrators\, e.g. normalising flows. Very im
 portantly this structure also suggests new princip
 led and robust strategies to tune the parameters o
 f integrators\, such as the discretisation stepsiz
 e and effective integration time\, or number of in
 tegration steps\, in a Leapfrog integrator.\nWe fo
 cus here primarily on Sequential Monte Carlo (SMC)
  algorithms\, but the approach can be used in the 
 context of Markov chain Monte Carlo algorithms. We
  illustrate performance and\, in particular\, robu
 stness through numerical experiments and provide p
 reliminary theoretical results supporting observed
  performance.\n&nbsp\;\nJoint work with Mauro Cama
 ra Escudero and Chang Zhang\n&nbsp\;\nReport: arXi
 v:2404.13302
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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