  Neyman-Scott processes (NSPs) have been applied across a range of fields to
model points or temporal events with a hierarchy of clusters. Markov chain
Monte Carlo (MCMC) is typically used for posterior sampling in the model.
However, MCMC's mixing time can cause the resulting inference to be slow, and
thereby slow down model learning and prediction. We develop the first
variational inference (VI) algorithm for NSPs, and give two examples of
suitable variational posterior point process distributions. Our method
minimizes the inclusive Kullback-Leibler (KL) divergence for VI to obtain the
variational parameters. We generate samples from the approximate posterior
point processes much faster than MCMC, as we can directly estimate the
approximate posterior point processes without any MCMC steps or gradient
descent. We include synthetic and real-world data experiments that demonstrate
our VI algorithm achieves better prediction performance than MCMC when
computational time is limited.
