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SUMMARY:Convergence bounds for the Random Walk Metropolis algorithm - Pers
 pectives from Isoperimetry - Sam Power\, University of Bristol
DTSTART:20230511T100000Z
DTEND:20230511T110000Z
UID:TALK200650@talks.cam.ac.uk
CONTACT:Dr H Ge
DESCRIPTION:Abstract: When carrying out inference in probabilistic models\
 , a recurring task is to examine high-dimensional probability measures wit
 h complex structure and ‘make sense of’ them in a suitable way. By now
 \, a wide range of practical solutions for this task exist\, each offering
  their own tradeoffs between computational efficiency\, statistical accura
 cy\, practical robustness\, and beyond. By analogy with fields such as opt
 imisation\, we might now seek to answer questions like “which classes of
  probability measure can be understood efficiently?”\, as well as quanti
 tative\, algorithm-specific versions of this question. This encourages the
  rigorous comparison of existing methods\, and can guide the design of imp
 roved methods.\n\nIn recent work\, we study this question in the context o
 f the Random Walk Metropolis algorithm\, a simple Markov chain-based itera
 tive algorithm for sampling from probability measures\, given only access 
 to an unnormalised density. Our analysis highlights the key role of ‘iso
 perimetry’\, a geometric notion for probability measures which appears t
 o robustly capture the complexity of understanding probability measures wi
 th local algorithms.\n\nIn this talk\, I will present our theoretical resu
 lts about the convergence behaviour of the Random Walk Metropolis algorith
 m (as well as related results for the Preconditioned Crank-Nicolson algori
 thm for sampling from GP posteriors)\, and contextualise the role which is
 operimetry plays in enabling these results. If time permits\, I will also 
 offer high-level comments on some potential implications of isoperimetry f
 or related approximate inference methodologies (e.g. VI\, NFs\, DDMs).\n\n
 (joint work with Christophe Andrieu\, Anthony Lee\, and Andi Wang\; prepri
 nt available at https://arxiv.org/abs/2211.08959)\n\nBio: Sam Power is a p
 ostdoctoral research associate at the University of Bristol. His research 
 centres around the design and analysis of stochastic algorithms\, with app
 lications to problems in modern statistics and machine learning. Some part
 icular interests include Markov chain Monte Carlo and Sequential Monte Car
 lo algorithms\, and how theoretical studies of these methods can enable th
 eir robust\, automatic\, and efficient deploymeent.\n
LOCATION:Cambridge University Engineering Department\, CBL Seminar room BE
 4-38.
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