Multi-Output Robust and Conjugate Gaussian Processes

Joshua Rooijakkers; Leiv Rønneberg; François-Xavier Briol; Jeremias Knoblauch; Matias Altamirano

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arXiv · 2510.26401

Multi-Output Robust and Conjugate Gaussian Processes

Joshua Rooijakkers·Leiv Rønneberg·François-Xavier Briol·Jeremias Knoblauch·Matias Altamirano

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Abstract

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.

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Joshua Rooijakkers, Leiv Rønneberg, François-Xavier Briol, Jeremias Knoblauch, Matias Altamirano. 2025-10-30. Multi-Output Robust and Conjugate Gaussian Processes. https://arxiv.org/abs/2510.26401

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