Piecewise deterministic generative models

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• Andrea Bertazzi (École Polytechnique)
• Friday 29 November 2024, 10:05-10:55
• Seminar Room 1, Newton Institute.

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SSDW04 - Monte Carlo sampling: beyond the diffusive regime

In this talk we introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs). Similarly to diffusions, these Markov processes admit time reversals that turn out to be PDM Ps as well. We apply this observation to three PDM Ps considered in the literature: the Zig-Zag process, Bouncy Particle Sampler, and Randomised Hamiltonian Monte Carlo. For these three particular instances, we show that the jump rates and kernels of the corresponding time reversals admit explicit expressions depending on some conditional densities of the PDMP under consideration before and after a jump.  Based on these results, we propose efficient training procedures to learn these characteristics and consider methods to approximately simulate the reverse process. Finally, we provide bounds in the total variation distance between the data distribution 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. Joint work with Alain Durmus, Dario Shariatian, Umut Simsekli, Eric Moulines.

This talk is part of the Isaac Newton Institute Seminar Series series.

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