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 future, 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. Experiments on synthetics and real data show the effectiveness of our approach.

利用机器学习技术，通过对早期时间步骤的样本集的给定序列，嵌入概率分布进入再生核希尔伯特空间，学习操作符实现预测时间变化分布的下一步，解决了分类器在时间变化条件下的训练问题，实现了域自适应训练。

预测时间变化概率分布的未来行为