  Transfer learning is a machine learning paradigm where knowledge from one
problem is utilized to solve a new but related problem. While conceivable that
knowledge from one task could be useful for solving a related task, if not
executed properly, transfer learning algorithms can 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 into the effect of prior knowledge for
transfer learning, at least with respect to our Bayesian formulation of the
transfer learning problem. 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,
one of which does not require the parametric assumption. We demonstrate the
effectiveness of our algorithms with real data sets, focusing primarily on when
the source and target data have strong similarities.
