Stochastic Bouncy Particle Sampler
This provides an incremental improvement for Bayesian inference in large-scale data settings.
The authors tackled the problem of efficiently sampling Bayesian posteriors in big datasets by introducing a stochastic version of the Bouncy Particle Sampler that allows a controllable bias for faster mixing, outperforming both unbiased slow-mixing versions and biased stochastic gradient-based samplers in several examples.
We introduce a novel stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear. The algorithm is based on simulating first arrival times in a doubly stochastic Poisson process using the thinning method, and allows efficient sampling of Bayesian posteriors in big datasets. We prove that in the BPS no bias is introduced by noisy evaluations of the log-likelihood gradient. On the other hand, we argue that efficiency considerations favor a small, controllable bias in the construction of the thinning proposals, in exchange for faster mixing. We introduce a simple regression-based proposal intensity for the thinning method that controls this trade-off. We illustrate the algorithm in several examples in which it outperforms both unbiased, but slowly mixing stochastic versions of BPS, as well as biased stochastic gradient-based samplers.