Blind Domain Adaptation: An RKHS Approach

We study the problem of domain adaptation: our goal is to learn a classifier, but the data distribution at training time (source) differs from the data distribution at prediction time (target). In contrast to existing work, we do not assume any samples from the target distribution to be available already at training time, not even unlabeled ones. Instead, we assume that the distribution mismatch is due to an underlying time-evolution of the data distribution, and that we have access to sample sets from more than one earlier time steps. Our main contribution is a method for learning an operator that can extrapolate the dynamics of the data distribution. For this we rely on two recent techniques: the embedding of probability distributions into a reproducing kernel Hilbert space, and vector-valued regression. By extrapolating the learned dynamics into the fu-ture, we obtain an estimate of the target distribution, based on which we can either directly learn a classifier for the target situation, or create a new sample set. Ex-periments on synthetics and real data show the effectiveness of our approach.