Multi-Output Robust and Conjugate Gaussian Processes

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.

Permutation invariant multi-output Gaussian Processes for drug combination prediction in cancer

Dose-response prediction in cancer is an active application field in machine learning. Using large libraries of \textit{in-vitro} drug sensitivity screens, the goal is to develop accurate predictive models that can be used to guide experimental design or inform treatment decisions. Building on previous work that makes use of permutation invariant multi-output Gaussian Processes in the context of dose-response prediction for drug combinations, we develop a variational approximation to these models. The variational approximation enables a more scalable model that provides uncertainty quantification and naturally handles missing data. Furthermore, we propose using a deep generative model to encode the chemical space in a continuous manner, enabling prediction for new drugs and new combinations. We demonstrate the performance of our model in a simple setting using a high-throughput dataset and show that the model is able to efficiently borrow information across outputs.