TY - JOUR
T1 - Spatiotemporal Clustering with Neyman-Scott Processes via Connections to Bayesian Nonparametric Mixture Models
AU - Wang, Yixin
AU - Degleris, Anthony
AU - Williams, Alex
AU - Linderman, Scott W.
N1 - Publisher Copyright:
© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.
PY - 2024
Y1 - 2024
N2 - 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. Supplementary materials for this article are available online.
AB - 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. Supplementary materials for this article are available online.
KW - Collapsed Gibbs
KW - Dirichlet process
KW - Mixture of finite mixture model
KW - Neyman-Scott process
UR - http://www.scopus.com/inward/record.url?scp=85176381678&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85176381678&partnerID=8YFLogxK
U2 - 10.1080/01621459.2023.2257896
DO - 10.1080/01621459.2023.2257896
M3 - Article
AN - SCOPUS:85176381678
SN - 0162-1459
VL - 119
SP - 2382
EP - 2395
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 547
ER -