Gaussian Process Regression (GPR) is a powerful non-parametric statistical modelling approach, widely valued for its flexibility and strong uncertainty quantification. However, its predictive performance can deteriorate substantially in data-scarce settings, such as applications involving expensive or time-intensive data collection. A promising solution to this problem is the integration of transfer learning (TL) with GPR, which leverages knowledge from the source task to enhance target task predictions. Existing GPR with TL methods based on adaptive transfer kernel learning have several limitations, including: optimising the conditional probability while ignoring the source domain distribution, lacking a shift correction mechanism to address shifts in feature distributions, and high computational complexity on large-scale datasets. To address these issues, this paper proposes an efficient GPR with TL model, namely JPNKN, which has three distinctive advantages: (1) joint probability likelihood maximization instead of conditional probability, which improves target-domain prediction performance while simultaneously preserving accurate inference capability on the source domain; (2) multi-layer Neural Kernel Network (NKN), with Maximum Mean Discrepancy (MMD) as a regularization term, enabling the model to better adapt to nonlinear relationships and distribution shifts; (3) a novel Wasserstein-based data distillation, reducing computational time for NKN training while preserving source-domain distribution characteristics, making the JPNKN model more efficient for deployment on large-scale datasets. Extensive experimental results on both synthetic and real-world datasets demonstrate that JPNKN significantly outperforms existing methods in terms of prediction accuracy and computational efficiency, and provides a new solution for prediction tasks with scarce target samples and domain shift.
Cao et al. (Fri,) studied this question.