Deep Neyman-Scott Processes

TL;DR

This paper introduces a deep Neyman-Scott process model that leverages hierarchical Poisson processes, enabling efficient inference and improved performance in modeling complex temporal point processes.

Contribution

It develops an MCMC-based inference method for deep Neyman-Scott processes, advancing hierarchical point process modeling capabilities.

Findings

Better likelihood fitting with more hidden Poisson processes

Improved event type prediction accuracy

Competitive performance with fewer parameters

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-the-art models for temporal real-world datasets and demonstrate competitive abilities for both data fitting and prediction, using far fewer parameters.