| Summary: | Transfer covariance functions, which can model domain similarities and adaptively control the knowledge transfer across domains, are widely used in Gaussian process (GP) based transfer learning. We focus on regression problems in a black-box learning scenario, and study a family of rather general transfer covariance functions, T_*, that can model the similarity heterogeneity of domains through multiple kernel learning. A necessary and sufficient condition that (i) validates GPs using T_* for any data and (ii) provides semantic interpretations is given. Moreover, building on this condition, we propose a computationally inexpensive model learning rule that can explicitly capture different sub-similarities of domains. Extensive experiments on one synthetic dataset and four real-world datasets demonstrate the effectiveness of the learned GP on the sub-similarity capture and the transfer performance.
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