A Bayesian Approach to (Online) Transfer Learning: Theory and Algorithms

Transfer learning is a machine learning paradigm where knowledge from one problem is utilized to solve a new but related problem. On the one hand, it is conceivable that knowledge from one task could be useful for solving a related task. On the other hand, it is also recognized that if not executed properly, transfer learning algorithms can in fact impair the learning performance instead of improving it - commonly known as negative transfer. In this paper, we study transfer learning from a Bayesian perspective, where a parametric statistical model is used. Specifically, we study three variants of transfer learning problems, instantaneous, online, and time-variant transfer learning. For each problem, we define an appropriate objective function, and provide either exact expressions or upper bounds on the learning performance using information-theoretic quantities, which allow simple and explicit characterizations when the sample size becomes large. Furthermore, examples show that the derived bounds are accurate even for small sample sizes. The obtained bounds give valuable insights on the effect of prior knowledge for transfer learning in our formulation. In particular, we formally characterize the conditions under which negative transfer occurs. Lastly, we devise two (online) transfer learning algorithms that are amenable to practical implementations. Specifically, one algorithm does not require the parametric assumption, thus extending our results to more general models. We demonstrate the effectiveness of our algorithms with real data set, especially when the source and target data have a strong similarity.