Transfer Kernel Learning for Multi-Source Transfer Gaussian Process Regression

Multi-source transfer regression is a practical and challenging problem where capturing the diverse relatedness of different domains is the key of adaptive knowledge transfer. In this article, we propose an effective way of explicitly modeling the domain relatedness of each domain pair through transfer kernel learning. Specifically, we first discuss the advantages and disadvantages of existing transfer kernels in handling the multi-source transfer regression problem. To cope with the limitations of the existing transfer kernels, we further propose a novel multi-source transfer kernel k_ms. The proposed k_ms assigns a learnable parametric coefficient to model the relatedness of each inter-domain pair, and simultaneously regulates the relatedness of the intra-domain pair to be 1. Moreover, to capture the heterogeneous data characteristics of multiple domains, k_ms exploits different standard kernels for different domain pairs. We further provide a theorem that not only guarantees the positive semi-definiteness of k_ms but also conveys a semantic interpretation to the learned domain relatedness. Moreover, the theorem can be easily used in the learning of the corresponding transfer Gaussian process model with k_ms. Extensive empirical studies show the effectiveness of our proposed method on domain relatedness modelling and transfer performance.