Stochastic Gradient Piecewise Deterministic Monte Carlo Samplers

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• Paul Fearnhead (Lancaster University)
• Thursday 28 November 2024, 10:05-10:55
• Seminar Room 1, Newton Institute.

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SSDW04 - Monte Carlo sampling: beyond the diffusive regime

Recently it has been shown that piecewise deterministic Markov processes (PDMPs) can be used as an alternative to MCMC . The idea is to simulate a PDMP that has been designed to have the posterior distribution as its stationary distribution, with there being simple rules for specifying the dynamics of the PDMP to enable this. Furthermore, the PDMP samplers are non-reversible, and thus can mix better than reversible MCMC in high-dimensions, and they can be implemented with sub-sampling ideas to reduce the per-iteration cost. Unfortunately, whilst the dynamics of these PDM Ps are easy to define, simulating a continuous-time realisation is challenging in general. To overcome this, we will show we can approximately simulate the dynamics of a PDMP with subsampling. The resulting algorithm is easy to implement, and is computationally efficient as it involves just accessing one or two data points per iteration. The resulting algorithm can be viewed as an alternative to the popular stochastic-gradient Langevin dynamics (SGLD) algorithm, but with a PDMP replacing the Langevin dynamics. The resulting stochastic gradient PDMP algorithm has a number of advantages over SGLD : the underlying dynamics are non-reversible; the algorithm is more stable and can have a higher order of accuracy; and we can leverage its continuous trajectories to more naturally incorporate model selection. This is joint work with Sebastiano Grazzi, Chris Nemeth, Estevao Prado and Gareth Roberts

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

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