# Efficient Inference in Multi-task Cox Process Models

arXiv: https://arxiv.org/abs/1805.09781 · HTML: https://mlsanity.com/paper/1805.09781/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

## Built on by (most cited first, 5 of 5)

- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [Heterogeneous Multi-Task Gaussian Cox Processes](https://mlsanity.com/paper/2308.15364/) (2023)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Scalable Multi-Output Gaussian Processes with Stochastic Variational Inference](https://mlsanity.com/paper/2407.02476/) (2024)

## Abstract (arXiv)

We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are also drawn from Gaussian processes and can incorporate additional dependencies. We derive closed-form expressions for the moments of the intensity functions and develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate LGCP, coregionalization models, and multi-task permanental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.