arXiv:2510.26401v2 Announce Type: replace Abstract: Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes (GPs), MOGPs are sensitive to model misspecification and outliers, which can distort predictions within individual outputs. In the multi-output case, this situation can be further exacerbated as anomalous observations in one response can adversely influence predictions for other correlated outputs. To handle this situation, we propose R-MOGP, an MOGP that is provably robust to outliers in any individual response. Our approach preserves conjugacy, achieving robustness without sacrificing computational efficiency, and integrates naturally with sparse variational inference for scalability. Empirically, we show that R-MOGP achieves performance comparable to existing state-of-the-art robust MOGPs at a fraction of their computational costs.