  We consider a transfer-learning problem by using the parameter transfer
approach, where a suitable parameter of feature mapping is learned through one
task and applied to another objective task. Then, we introduce the notion of
the local stability and parameter transfer learnability of parametric feature
mapping,and thereby derive a learning bound for parameter transfer algorithms.
As an application of parameter transfer learning, we discuss the performance of
sparse coding in self-taught learning. Although self-taught learning algorithms
with plentiful unlabeled data often show excellent empirical performance, their
theoretical analysis has not been studied. In this paper, we also provide the
first theoretical learning bound for self-taught learning.
