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SUMMARY:Convergence of kinetic Langevin samplers for non-convex potentials
  - Katharina Schuh (Technische Universität Wien)
DTSTART:20241126T100500Z
DTEND:20241126T105500Z
UID:TALK221485@talks.cam.ac.uk
DESCRIPTION:In this talk we study three kinetic Langevin samplers includin
 g the Euler discretization\, the BU and the UBU splitting scheme. We are i
 nterested in how efficiently they sample a given probability distribution 
 with non-convex potential. We show contraction results in L^1 -Wasserstein
  distance for all three samplers. These results are based on a carefully t
 ailored distance function and an appropriate coupling construction. Additi
 onally\, we analyse the error in the L^1 -Wasserstein distance between the
  target measure and the invariant measure of the discretization scheme. To
  get an &epsilon\;-accuracyin L^1-Wasserstein distance\, we show complexit
 y guarantees of order O( d^{1/2}/&epsilon\;) for the Euler scheme and O(d^
 {1/4} / &epsilon\;) for the UBU scheme under appropriate regularity assump
 tions on the target measure. The results can also be applied to interactin
 g particle systems and provide bounds for sampling probability measures of
  mean-field type.\nThe talk is based on a joint work with Peter A. Whalley
 .
LOCATION:Seminar Room 1\, Newton Institute
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