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SUMMARY:Piecewise deterministic generative models - Andrea Bertazzi (Écol
 e Polytechnique)
DTSTART:20241129T100500Z
DTEND:20241129T105500Z
UID:TALK221494@talks.cam.ac.uk
DESCRIPTION:In this talk we introduce a novel class of generative models b
 ased on piecewise deterministic Markov processes (PDMPs). Similarly to dif
 fusions\, these Markov processes admit time reversals that turn out to be 
 PDMPs as well. We apply this observation to three PDMPs considered in the 
 literature: the Zig-Zag process\, Bouncy Particle Sampler\, and Randomised
  Hamiltonian Monte Carlo. For these three particular instances\, we show t
 hat the jump rates and kernels of the corresponding time reversals admit e
 xplicit expressions depending on some conditional densities of the PDMP un
 der consideration before and after a jump. &nbsp\;Based on these results\,
  we propose efficient training procedures to learn these characteristics a
 nd consider methods to approximately simulate the reverse process. Finally
 \, we provide bounds in the total variation distance between the data dist
 ribution and the resulting distribution of our model in the case where the
  base distribution is the standard $d$-dimensional Gaussian distribution. 
 We conclude the talk with promising numerical simulations on toy datasets.
 \nJoint work with Alain Durmus\, Dario Shariatian\, Umut Simsekli\, Eric M
 oulines.
LOCATION:Seminar Room 1\, Newton Institute
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