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SUMMARY:Breaking symmetry to save symmetry: asymmetric momentum sampling i
 n event-chain Monte Carlo - Michael Faulkner (University of Warwick)
DTSTART:20241126T112500Z
DTEND:20241126T121500Z
UID:TALK221488@talks.cam.ac.uk
DESCRIPTION:Sampling algorithms are commonplace in statistics and machine 
 learning &ndash\; in particular\, in Bayesian computation &ndash\; and hav
 e been used for decades to enable inference\, prediction and model compari
 son in many different settings.&nbsp\; They are also widely used in statis
 tical physics\, where many popular sampling algorithms first originated\, 
 including the famous Metropolis algorithm [1].&nbsp\; The algorithm has le
 d to huge success in both fields\, but typically exhibits slow mixing when
  faced with broken symmetry in statistical physics &mdash\; as well as str
 ong autocorrelations in the broad regions of probability mass found at tra
 nsitions into symmetry-broken thermodynamic phases.&nbsp\; More recent dev
 elopments in both fields [2\, 3] have led\, however\, to state-of-the-art 
 sampling algorithms that augment the state space with auxiliary momenta\, 
 which leads to ballistic-style dynamics that drive the system through the 
 original state space.&nbsp\; Event-chain Monte Carlo is the main such algo
 rithm in statistical physics\, where symmetry-broken momentum sampling rec
 overed symmetry on the original state space of an important model system [
 4]. &nbsp\;The concept also accelerated mixing in the seminal work that so
 lved the two-dimensional melting transition [5].&nbsp\; This talk gives a 
 brief introduction to broken symmetry in statistical physics\, before movi
 ng on to Metropolis and event-chain sampling of smooth probability distrib
 utions.&nbsp\; We then explain the (non-proven!) freedom to break symmetry
  on event-chain momentum space\, before showcasing its recovery of symmetr
 y on the original state space of the important model system [4].&nbsp\; We
  finish by discussing the implications for dealing with strong autocorrela
 tions at symmetry-broken phase transitions.&nbsp\; This talk uses concepts
  developed in a recent paper on the shared structure of the two research f
 ields [6].\n&nbsp\;\n[1] Metropolis et al.\, J. Chem. Phys. 21 1087 (1953)
 \n[2] Bierkens & Roberts\, Ann. Appl. Probab. 27\, 846 (2017)\n[3] Bernard
 \, Krauth & Wilson\, Phys. Rev. E 80 056704 (2009)\n[4] Faulkner\, Phys. R
 ev. B 109\, 085405 (2024)\n[5] Bernard & Krauth\, Phys. Rev. Lett. 107\, 1
 55704 (2011)\n[6] Faulkner & Livingstone\, Statist. Sci. 39\, 137 (2024)
LOCATION:Seminar Room 1\, Newton Institute
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