BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Robust adaptation of integrator snippet sampling algorithms - Chri stophe Andrieu (University of Bristol) DTSTART:20241126T154000Z DTEND:20241126T163000Z UID:TALK221569@talks.cam.ac.uk DESCRIPTION:Assume interest is in sampling from a probability distribution &mu\; defined on Z. We develop a framework to construct sampling algorith ms taking full advantage of numerical integrators of ODEs\, say &psi\;:Z&r arr\;Z for one integration step\, to explore &mu\; efficiently and robustl y. The popular Hybrid/Hamiltonian Monte Carlo (HMC) algorithm [Duane et al .\, 1987\, Neal\, 2011] and its derivatives are examples of the use of num erical integrators in sampling algorithms. A key idea developed here is th at of sampling integrator snippets\, that is fragments of the orbit of an ODE numerical integrator &psi\; \, and the definition of an associated pro bability distribution &mu\; such that expectations with respect to &mu\; c an be estimated from integrator snippets sampled from &mu\; . The integrat or 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 importantly this structure also suggests new principled and robust strategies to tune the parameters of integrators\, such as the discretisation stepsize and effective integr ation time\, or number of integration steps\, in a Leapfrog integrator.\nW e focus here primarily on Sequential Monte Carlo (SMC) algorithms\, but th e approach can be used in the context of Markov chain Monte Carlo algorith ms. We illustrate performance and\, in particular\, robustness through num erical experiments and provide preliminary theoretical results supporting observed performance.\n \;\nJoint work with Mauro Camara Escudero and Chang Zhang\n \;\nReport: arXiv:2404.13302 LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR