Reproduce “Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains” on OpenResearch

About this paper

Haitao Liu, Kai Wu, Yew-Soon Ong, Chao Bian, Xiaomo Jiang, Xiaofang Wang

A Multi-Task Gaussian Process framework was developed to learn across heterogeneous input domains by employing Bayesian calibration and a residual modeling strategy. The proposed HSVLMC model consistently achieved superior prediction accuracy and uncertainty quantification compared to baseline methods across synthetic and real-world datasets, including a multi-fidelity steam turbine exhaust design problem.

Key insights

• The flexible Bayesian calibration method effectively aligns heterogeneous input domains while accounting for dimensionality reduction, which reduces information loss compared to fixed prior mappings.
• Formulating posterior domain mapping as a residual of prior mappings provides an inductive bias that guides model inference, potentially accelerating convergence and enhancing robustness.
• Stochastic variational inference allows for a scalable MTGP framework, making it practical for large datasets and complex multi-task scenarios despite the inherent computational complexity of GPs.

Summary by alphaXiv.