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

arXiv: https://arxiv.org/abs/2201.05044 · HTML: https://mlsanity.com/paper/2201.05044/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 114 references that are in the map.
- First posted on arXiv 13 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Patterns of Scalable Bayesian Inference](https://mlsanity.com/paper/1602.05221/) (2016)
- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [TiDeH: Time-Dependent Hawkes Process for Predicting Retweet Dynamics](https://mlsanity.com/paper/1603.09449/) (2016)
- [Poisson-Randomized Gamma Dynamical Systems](https://mlsanity.com/paper/1910.12991/) (2019)
- [Point process models for sequence detection in high-dimensional neural spike trains](https://mlsanity.com/paper/2010.04875/) (2020)
- [The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation](https://mlsanity.com/paper/1707.04928/) (2017)
- [Deep Neyman-Scott Processes](https://mlsanity.com/paper/2111.03949/) (2021)
- [Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updates](https://mlsanity.com/paper/1907.00139/) (2019)

## Built on by (most cited first, 3 of 3)

- [Asymptotic Classification Error for Heavy-Tailed Renewal Processes](https://mlsanity.com/paper/2408.10502/) (2024)
- [A Criterion for Extending Continuous-Mixture Identifiability Results](https://mlsanity.com/paper/2503.03536/) (2025)
- [Scalable spatial point process models for forensic footwear analysis](https://mlsanity.com/paper/2602.07006/) (2026)

## Abstract (arXiv)

Neyman-Scott processes (NSPs) are point process models that generate clusters of points in time or space. They are natural models for a wide range of phenomena, ranging from neural spike trains to document streams. The clustering property is achieved via a doubly stochastic formulation: first, a set of latent events is drawn from a Poisson process; then, each latent event generates a set of observed data points according to another Poisson process. This construction is similar to Bayesian nonparametric mixture models like the Dirichlet process mixture model (DPMM) in that the number of latent events (i.e. clusters) is a random variable, but the point process formulation makes the NSP especially well suited to modeling spatiotemporal data. While many specialized algorithms have been developed for DPMMs, comparatively fewer works have focused on inference in NSPs. Here, we present novel connections between NSPs and DPMMs, with the key link being a third class of Bayesian mixture models called mixture of finite mixture models (MFMMs). Leveraging this connection, we adapt the standard collapsed Gibbs sampling algorithm for DPMMs to enable scalable Bayesian inference on NSP models. We demonstrate the potential of Neyman-Scott processes on a variety of applications including sequence detection in neural spike trains and event detection in document streams.