# Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes

arXiv: https://arxiv.org/abs/2210.11844 · HTML: https://mlsanity.com/paper/2210.11844/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications](https://mlsanity.com/paper/1708.02647/) (2017)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Deep Mixture Point Processes: Spatio-temporal Event Prediction with Rich Contextual Information](https://mlsanity.com/paper/1906.08952/) (2019)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Latent Network Structure Learning from High Dimensional Multivariate Point Processes](https://mlsanity.com/paper/2004.03569/) (2020)
- [PriorVAE: Encoding spatial priors with VAEs for small-area estimation](https://mlsanity.com/paper/2110.10422/) (2021)
- [Scalable Bayesian Inference for Excitatory Point Process Networks](https://mlsanity.com/paper/1507.03228/) (2015)
- [Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data](https://mlsanity.com/paper/1803.06070/) (2018)
- [Temporal Attention Augmented Transformer Hawkes Process](https://mlsanity.com/paper/2112.14472/) (2021)
- [A framework for studying synaptic plasticity with neural spike train data](https://mlsanity.com/paper/1411.4077/) (2014)
- [Flexible multivariate spatio-temporal Hawkes process models of terrorism](https://mlsanity.com/paper/2202.12346/) (2022)

## Built on by (most cited first, 1 of 1)

- [HawkesNest: A Multi-Axis Synthetic Benchmark for Spatiotemporal Pattern Complexity](https://mlsanity.com/paper/2606.16863/) (2026)

## Abstract (arXiv)

Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events. Here we develop a new class of spatiotemporal Hawkes processes that can capture both triggering and clustering behavior and we provide an efficient method for performing inference. We use a log-Gaussian Cox process (LGCP) as prior for the background rate of the Hawkes process which gives arbitrary flexibility to capture a wide range of underlying background effects (for infectious diseases these are called endemic effects). The Hawkes process and LGCP are computationally expensive due to the former having a likelihood with quadratic complexity in the number of observations and the latter involving inversion of the precision matrix which is cubic in observations. Here we propose a novel approach to perform MCMC sampling for our Hawkes process with LGCP background, using pre-trained Gaussian Process generators which provide direct and cheap access to samples during inference. We show the efficacy and flexibility of our approach in experiments on simulated data and use our methods to uncover the trends in a dataset of reported crimes in the US.