Proxy-informed Bayesian transfer learning with unknown sources

Generalization outside the scope of one's training data requires leveraging prior knowledge about the effects that transfer, and the effects that don't, between different data sources. Bayesian transfer learning is a principled paradigm for specifying this knowledge, and refining it on the basis of data from the source (training) and target (prediction) tasks. We address the challenging transfer learning setting where the learner (i) cannot fine-tune in the target task, and (ii) does not know which source data points correspond to the same task (i.e., the data sources are unknown). We propose a proxy-informed robust method for probabilistic transfer learning (PROMPT), which provides a posterior predictive estimate tailored to the structure of the target task, without requiring the learner have access to any outcome information from the target task. Instead, PROMPT relies on the availability of proxy information. PROMPT uses the same proxy information for two purposes: (i) estimation of effects specific to the target task, and (ii) construction of a robust reweighting of the source data for estimation of effects that transfer between tasks. We provide theoretical results on the effect of this reweighting on the risk of negative transfer, and demonstrate application of PROMPT in two synthetic settings.