Recent work has suggested using Monte Carlo methods based on piecewise
deterministic Markov processes (PDMPs) to sample from target distributions of
interest. PDMPs are non-reversible continuous-time processes endowed with
momentum, and hence can mix better than standard reversible MCMC samplers.
Furthermore, they can incorporate exact sub-sampling schemes which only require
access to a single (randomly selected) data point at each iteration, yet
without introducing bias to the algorithm's stationary distribution. However,
the range of models for which PDMPs can be used, particularly with
sub-sampling, is limited. We propose approximate simulation of PDMPs with
sub-sampling for scalable sampling from posterior distributions. The
approximation takes the form of an Euler approximation to the true PDMP
dynamics, and involves using an estimate of the gradient of the log-posterior
based on a data sub-sample. We thus call this class of algorithms
stochastic-gradient PDMPs. Importantly, the trajectories of stochastic-gradient
PDMPs are continuous and can leverage recent ideas for sampling from measures
with continuous and atomic components. We show these methods are easy to
implement, present results on their approximation error and demonstrate
numerically that this class of algorithms has similar efficiency to, but is
more robust than, stochastic gradient Langevin dynamics.

通过近似模拟带有子抽样的分段确定性马尔可夫过程（PDMPs）的方法，可以从后验分布中进行可扩展的抽样。这种方法的效率类似于随机梯度 Langevin 动力学，但更为稳健。