  In this paper, we provide a new framework to obtain the generalization bounds
of the learning process for domain adaptation, and then apply the derived
bounds to analyze the asymptotical convergence of the learning process. Without
loss of generality, we consider two kinds of representative domain adaptation:
one is with multiple sources and the other is combining source and target data.
  In particular, we use the integral probability metric to measure the
difference between two domains. For either kind of domain adaptation, we
develop a related Hoeffding-type deviation inequality and a symmetrization
inequality to achieve the corresponding generalization bound based on the
uniform entropy number. We also generalized the classical McDiarmid's
inequality to a more general setting where independent random variables can
take values from different domains. By using this inequality, we then obtain
generalization bounds based on the Rademacher complexity. Afterwards, we
analyze the asymptotic convergence and the rate of convergence of the learning
process for such kind of domain adaptation. Meanwhile, we discuss the factors
that affect the asymptotic behavior of the learning process and the numerical
experiments support our theoretical findings as well.
