# Heterogeneous Multi-Task Gaussian Cox Processes

arXiv: https://arxiv.org/abs/2308.15364 · HTML: https://mlsanity.com/paper/2308.15364/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 29 Aug 2023.

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

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Bayesian Few-Shot Classification with One-vs-Each P'olya-Gamma Augmented Gaussian Processes](https://mlsanity.com/paper/2007.10417/) (2020)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [A New Approach to Probabilistic Programming Inference](https://mlsanity.com/paper/1507.00996/) (2015)
- [Efficient Gaussian Process Classification Using Polya-Gamma Data Augmentation](https://mlsanity.com/paper/1802.06383/) (2018)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [Multi-Class Gaussian Process Classification Made Conjugate: Efficient Inference via Data Augmentation](https://mlsanity.com/paper/1905.09670/) (2019)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Scalable Joint Models for Reliable Uncertainty-Aware Event Prediction](https://mlsanity.com/paper/1708.04757/) (2017)
- [Non-linear process convolutions for multi-output Gaussian processes](https://mlsanity.com/paper/1810.04632/) (2018)
- [Efficient Inference of Gaussian Process Modulated Renewal Processes with Application to Medical Event Data](https://mlsanity.com/paper/1402.4732/) (2014)
- [Efficient Inference in Multi-task Cox Process Models](https://mlsanity.com/paper/1805.09781/) (2018)
- [Multi-output Gaussian Process Modulated Poisson Processes for Event Prediction](https://mlsanity.com/paper/2011.03172/) (2020)

## Built on by (most cited first, 4 of 4)

- [Federated Neural Nonparametric Point Processes](https://mlsanity.com/paper/2410.05637/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Task Diversity in Bayesian Federated Learning: Simultaneous Processing of Classification and Regression](https://mlsanity.com/paper/2412.10897/) (2024)
- [Real-time Multi-instrument Autonomous Discovery of Novel Phase-change Memory Materials](https://mlsanity.com/paper/2605.18033/) (2026)

## Abstract (arXiv)

This paper presents a novel extension of multi-task Gaussian Cox processes for modeling multiple heterogeneous correlated tasks jointly, e.g., classification and regression, via multi-output Gaussian processes (MOGP). A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks, while allowing for nonparametric parameter estimation. To circumvent the non-conjugate Bayesian inference in the MOGP modulated heterogeneous multi-task framework, we employ the data augmentation technique and derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters. We demonstrate the performance and inference on both 1D synthetic data as well as 2D urban data of Vancouver.