Piecewise deterministic generative models
Bertazzi, Andrea Shariatian, Dario Simsekli, Umut Moulines, Eric Durmus, Alain
Bertazzi, Andrea
Shariatian, Dario
Simsekli, Umut
Moulines, Eric
Durmus, Alain
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Department
Machine Learning
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Conference proceeding
Date
2024
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Language
English
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Abstract
We introduce 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.
Citation
A. Bertazzi, D. Shariatian, U. Simsekli, E. Moulines, and A. Durmus, “Piecewise deterministic generative models,” Adv Neural Inf Process Syst, vol. 37, pp. 93336–93373, Dec. 2024.
Source
Advances in Neural Information Processing Systems (NeurIPS 2024)
Conference
Keywords
Piecewise deterministic Markov processes (PDMPs), Generative models, Zig-Zag process, Bouncy Particle Sampler (BPS), R, omised Hamiltonian Monte Carlo (RHMC)
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NEURIPS