  Many machine learning methods assume that the training and test data follow
the same distribution. However, in the real world, this assumption is very
often violated. In particular, the phenomenon that the marginal distribution of
the data changes is called covariate shift, one of the most important research
topics in machine learning. We show that the well-known family of covariate
shift adaptation methods is unified in the framework of information geometry.
Furthermore, we show that parameter search for geometrically generalized
covariate shift adaptation method can be achieved efficiently. Numerical
experiments show that our generalization can achieve better performance than
the existing methods it encompasses.
