# Variational Inference for Neyman-Scott Processes

arXiv: https://arxiv.org/abs/2303.03701 · HTML: https://mlsanity.com/paper/2303.03701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Joint Stochastic Approximation and Its Application to Learning Discrete Latent Variable Models](https://mlsanity.com/paper/2005.14001/) (2020)
- [Point process models for sequence detection in high-dimensional neural spike trains](https://mlsanity.com/paper/2010.04875/) (2020)
- [Deep Neyman-Scott Processes](https://mlsanity.com/paper/2111.03949/) (2021)
- [An Interaction Neyman-Scott Point Process Model for Coronavirus Disease-19](https://mlsanity.com/paper/2102.02999/) (2021)

## Abstract (arXiv)

Neyman-Scott processes (NSPs) have been applied across a range of fields to model points or temporal events with a hierarchy of clusters. Markov chain Monte Carlo (MCMC) is typically used for posterior sampling in the model. However, MCMC's mixing time can cause the resulting inference to be slow, and thereby slow down model learning and prediction. We develop the first variational inference (VI) algorithm for NSPs, and give two examples of suitable variational posterior point process distributions. Our method minimizes the inclusive Kullback-Leibler (KL) divergence for VI to obtain the variational parameters. We generate samples from the approximate posterior point processes much faster than MCMC, as we can directly estimate the approximate posterior point processes without any MCMC steps or gradient descent. We include synthetic and real-world data experiments that demonstrate our VI algorithm achieves better prediction performance than MCMC when computational time is limited.