# Heterogeneous Multi-output Gaussian Process Prediction

arXiv: https://arxiv.org/abs/1805.07633 · HTML: https://mlsanity.com/paper/1805.07633/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2018.

## Built on by (most cited first, 26 of 26)

- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features](https://mlsanity.com/paper/2106.05960/) (2021)
- [Leveraging Probabilistic Circuits for Nonparametric Multi-Output Regression](https://mlsanity.com/paper/2106.08687/) (2021)
- [Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains](https://mlsanity.com/paper/2202.12636/) (2022)
- [Bayesian Gaussian Process ODEs via Double Normalizing Flows](https://mlsanity.com/paper/2309.09222/) (2023)
- [Physics-Informed Variational State-Space Gaussian Processes](https://mlsanity.com/paper/2409.13876/) (2024)
- [Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling](https://mlsanity.com/paper/2111.06173/) (2021)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [Heterogeneous Multi-Task Gaussian Cox Processes](https://mlsanity.com/paper/2308.15364/) (2023)
- [JoLT: Joint Probabilistic Predictions on Tabular Data Using LLMs](https://mlsanity.com/paper/2502.11877/) (2025)
- [Latent Variable Multi-output Gaussian Processes for Hierarchical Datasets](https://mlsanity.com/paper/2308.16822/) (2023)
- [Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes](https://mlsanity.com/paper/2407.16935/) (2024)
- [Regularized Multi-output Gaussian Convolution Process with Domain Adaptation](https://mlsanity.com/paper/2409.02778/) (2024)
- [A Variational Autoencoder for Heterogeneous Temporal and Longitudinal Data](https://mlsanity.com/paper/2204.09369/) (2022)
- [Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification](https://mlsanity.com/paper/2402.04582/) (2024)
- [Scalable Multi-Output Gaussian Processes with Stochastic Variational Inference](https://mlsanity.com/paper/2407.02476/) (2024)
- [Mixed Likelihood Variational Gaussian Processes](https://mlsanity.com/paper/2503.04138/) (2025)
- [Modular Gaussian Processes for Transfer Learning](https://mlsanity.com/paper/2110.13515/) (2021)
- [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)
- [Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorization](https://mlsanity.com/paper/2305.14543/) (2023)
- [Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty](https://mlsanity.com/paper/2603.17271/) (2026)
- [Transformed Latent Variable Multi-Output Gaussian Processes](https://mlsanity.com/paper/2605.05133/) (2026)
- [Elicitation-Augmented Bayesian Optimization](https://mlsanity.com/paper/2605.12079/) (2026)
- [Forecasting Multiple Observables with SCROLL: Score-Trained Uncertainty for Stochastic Dynamics](https://mlsanity.com/paper/2608.25898/) (2026)
- [Residual Correlation as a Diagnostic for Joint-Uncertainty Gains from GP Coregionalisation](https://mlsanity.com/paper/2609.30085/) (2026)

## Abstract (arXiv)

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in all likelihoods as latent functions. Our multi-output Gaussian process uses a covariance function with a linear model of coregionalisation form. Assuming conditional independence across the underlying latent functions together with an inducing variable framework, we are able to obtain tractable variational bounds amenable to stochastic variational inference. We illustrate the performance of the model on synthetic data and two real datasets: a human behavioral study and a demographic high-dimensional dataset.