Deep Neyman-Scott Processes
This addresses inference challenges in sophisticated hierarchical point processes for researchers in statistics and machine learning, though it appears incremental as an extension of existing Neyman-Scott processes.
The paper tackles inference in hierarchical point processes by developing a deep Neyman-Scott process with Poisson process components, using efficient MCMC sampling for likelihood-based inference. The method achieves competitive performance in data fitting and prediction on real-world temporal datasets while using far fewer parameters than state-of-the-art models.
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.