Domain Adaptation under Target and Conditional Shift

Let X denote the feature and Y the target. We consider domain adaptation under three possible scenarios: (1) the marginal PY changes, while the conditional PX|Y stays the same (target shift), (2) the marginal PY is fixed, while the conditional PX|Y changes with certain constraints (conditional shift), and (3) the marginal PY changes, and the conditional PX|Y changes with constraints (generalized target shift). Using background knowledge, causal interpretations allow us to determine the correct situation for a problem at hand. We exploit importance reweighting or sample transformation to find the learning machine that works well on test data, and propose to estimate the weights or transformations by reweighting or transforming training data to reproduce the covariate distribution on the test domain. Thanks to kernel embedding of conditional as well as marginal distributions, the proposed approaches avoid distribution estimation, and are applicable for high-dimensional problems. Numerical evaluations on synthetic and realworld data sets demonstrate the effectiveness of the proposed framework.