Abstract: Recent research showed that Piecewise Deterministic Markov Processes (PDMP) may be exploited to design efficient MCMC algorithms . The Zig-Zag sampler is an example of this: it is based on the simulation of a PDMP whose switching rate λ(t) is governed by the derivative of a (minus log) target density.
While many theoretical properties of this sampler have been derived, less has been done to explore the applicability of the Zig-Zag sampler to solve Bayesian inference problems. In particular, the computation of the derivative of the log-density in the rate λ(t) might be challenging. To expand the applicability of the Zig-Zag sampler, we incorporate Automatic Differentiation tools in the Zig-Zag algorithm, to evaluate λ(t) from the functional form of the log-target density. Moreover, to allow the simulation of a PDMP via Poisson thinning, we use univariate optimization routines to find local upper bounds.
In this talk we introduce PDMPs and the Zig-Zag sampler; we expose our Automatic Zig-Zag sampler; we discuss the challenges that arise with the simulation via thinning and the need of a new tuning parameter; and we comment on efficiencies and bottlenecks of AD for Zig-Zag. We present many examples to compare our method to HMC, another widely used gradient-based method.
This is joint work with Simon Spencer and Gareth Roberts.
 Fearnhead, P., Bierkens, J., Pollock, M., and Roberts, G.O., 2018. Piecewise deterministic Markov processes for continuous-time Monte Carlo. Statistical Science, 33(3), pp.386-412.