Multi-Output Robust and Conjugate Gaussian Processes

TL;DR

This paper introduces MO-RCGP, a robust, conjugate multi-output Gaussian process model that effectively handles outliers and model misspecification, capturing correlations across multiple outputs in complex applications.

Contribution

The paper extends the RCGP framework to multi-output settings, creating a robust, conjugate MOGP that models output dependencies and improves prediction reliability.

Findings

Effective in finance and cancer research applications.

Handles outliers and model misspecification robustly.

Captures correlations across multiple outputs.

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.