HDI and TFAIM Lab Seminar: Piecewise Deterministic Generative Models

On April 24, 2025 HDI & TFAIM Lab will be held at HSE University. Alain Durmus (Ecole Polytechnique) will speak on 'Piecewise Deterministic Generative Models'.

Abstract: 

We will introduce in this talk a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to diffusions, such 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 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. Promising numerical simulations support further investigations into this class of models.

Start time: 16:20

The seminar will be held online. For more details, please, contact ealyamovskaya@hse.ru.