# Multi-Output Robust and Conjugate Gaussian Processes

arXiv: https://arxiv.org/abs/2510.26401 · HTML: https://mlsanity.com/paper/2510.26401/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 88 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 30 of 40)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods](https://mlsanity.com/paper/2305.15027/) (2023)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergences](https://mlsanity.com/paper/1806.02261/) (2018)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Estimating Density Models with Truncation Boundaries using Score Matching](https://mlsanity.com/paper/1910.03834/) (2019)
- [Bayesian Quadrature for Multiple Related Integrals](https://mlsanity.com/paper/1801.04153/) (2018)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Variational Inference based on Robust Divergences](https://mlsanity.com/paper/1710.06595/) (2017)
- [Multivariate Gaussian and Student-t Process Regression for Multi-output Prediction](https://mlsanity.com/paper/1703.04455/) (2017)
- [General Bayesian Loss Function Selection and the use of Improper Models](https://mlsanity.com/paper/2106.01214/) (2021)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Vector-Valued Control Variates](https://mlsanity.com/paper/2109.08944/) (2021)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [Financial Applications of Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/1903.04841/) (2019)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [Cross-Covariance Functions for Multivariate Geostatistics](https://mlsanity.com/paper/1507.08017/) (2015)
- [Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures](https://mlsanity.com/paper/2202.09233/) (2022)
- [Prediction-Centric Uncertainty Quantification via MMD](https://mlsanity.com/paper/2410.11637/) (2024)
- [Robust Gaussian Processes via Relevance Pursuit](https://mlsanity.com/paper/2410.24222/) (2024)

## Built on by (most cited first, 2 of 2)

- [Transformed Latent Variable Multi-Output Gaussian Processes](https://mlsanity.com/paper/2605.05133/) (2026)
- [Predictively Oriented Gaussian Process Posteriors](https://mlsanity.com/paper/2610.03201/) (2026)

## Abstract (arXiv)

Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes, MOGPs are sensitive to model misspecification and outliers, which can distort predictions within individual outputs. This situation can be further exacerbated by multiple anomalous response variables whose errors propagate due to correlations between outputs. To handle this situation, we extend and generalise the robust and conjugate Gaussian process (RCGP) framework introduced by Altamirano et al. (2024). This results in the multi-output RCGP (MO-RCGP): a provably robust MOGP that is conjugate, and jointly captures correlations across outputs. We thoroughly evaluate our approach through applications in finance and cancer research.