Deep Neyman-Scott Processes

Abstract

A Neyman-Scott process is a special case of a Cox process. The latent and observable stochastic processes are both Poisson processes. We consider a deep Neyman-Scott process in this paper, for which the building components of a network are all Poisson processes. We develop an efficient posterior sampling via Markov chain Monte Carlo and use it for likelihood-based inference. Our method opens up room for the inference in sophisticated hierarchical point processes. We show in the experiments that more hidden Poisson processes brings better performance for likelihood fitting and events types prediction. We also compare our method with state-of-theart models for temporal real-world datasets and demonstrate competitive abilities for both data fitting and prediction, using far fewer parameters.

Spatiotemporal Clustering with Neyman-Scott Processes via Connections to Bayesian Nonparametric Mixture Models

“…5]. Likewise, recent work on deep NSPs offers an alternative way of constructing rich point process models by stacking Neyman-Scott processes hierarchically [Hong and Shelton, 2021]. Ultimately, Neyman-Scott processes connect the world of doubly-stochastic point processes to Bayesian nonparametric mixture models, and we suspect there are many fruitful possibilities at this intersection.…”