  We consider the Hypothesis Transfer Learning (HTL) problem where one
incorporates a hypothesis trained on the source domain into the learning
procedure of the target domain. Existing theoretical analysis either only
studies specific algorithms or only presents upper bounds on the generalization
error but not on the excess risk. In this paper, we propose a unified
algorithm-dependent framework for HTL through a novel notion of transformation
function, which characterizes the relation between the source and the target
domains. We conduct a general risk analysis of this framework and in
particular, we show for the first time, if two domains are related, HTL enjoys
faster convergence rates of excess risks for Kernel Smoothing and Kernel Ridge
Regression than those of the classical non-transfer learning settings.
Experiments on real world data demonstrate the effectiveness of our framework.
