  Bayesian transfer learning (BTL) is defined in this paper as the task of
conditioning a target probability distribution on a transferred source
distribution. The target globally models the interaction between the source and
target, and conditions on a probabilistic data predictor made available by an
independent local source modeller. Fully probabilistic design is adopted to
solve this optimal decision-making problem in the target. By successfully
transferring higher moments of the source, the target can reject unreliable
source knowledge (i.e. it achieves robust transfer). This dual-modeller
framework means that the source's local processing of raw data into a
transferred predictive distribution -- with compressive possibilities -- is
enriched by (the possible expertise of) the local source model. In addition,
the introduction of the global target modeller allows correlation between the
source and target tasks -- if known to the target -- to be accounted for.
Important consequences emerge. Firstly, the new scheme attains the performance
of fully modelled (i.e. conventional) multitask learning schemes in (those
rare) cases where target model misspecification is avoided. Secondly, and more
importantly, the new dual-modeller framework is robust to the model
misspecification that undermines conventional multitask learning. We thoroughly
explore these issues in the key context of interacting Gaussian process
regression tasks. Experimental evidence from both synthetic and real data
settings validates our technical findings: that the proposed BTL framework
enjoys robustness in transfer while also being robust to model
misspecification.
