Optimal Bayesian Transfer Regression

Abstract

Transfer learning studies effective ways to derive better predictors for a system of interest in a target domain, where there is lack of data, by utilizing data from other related systems as source domain(s). We define a Bayesian transfer learning framework for regression to integrate data between the domains through a joint prior distribution for the source and target parameters. We derive closed-form posteriors of the target parameters integrating both the source and target data, from which closed-form effective joint distributions in the target domain can be derived in terms of generalized hypergeometric functions of matrix argument to define the optimal Bayesian transfer regression (OBTR) operator. We show that the OBTR improves the mean squared error when the source and target domains are related on both synthetic and real-world data.