Derivation of Output Correlation Inferences for Multi-Output (aka Multi-Task) Gaussian Process
This work offers incremental improvements by making MTGP derivations more accessible for practitioners in Bayesian optimization and related fields.
The paper provides clear derivations of the formulations and gradients for Multi-task Gaussian Processes (MTGP), addressing the challenge of understanding these from existing literature.
Gaussian process (GP) is arguably one of the most widely used machine learning algorithms in practice. One of its prominent applications is Bayesian optimization (BO). Although the vanilla GP itself is already a powerful tool for BO, it is often beneficial to be able to consider the dependencies of multiple outputs. To do so, Multi-task GP (MTGP) is formulated, but it is not trivial to fully understand the derivations of its formulations and their gradients from the previous literature. This paper serves friendly derivations of the MTGP formulations and their gradients.