Adapting to Shifts in Latent Confounders via Observed Concepts and Proxies

We address the problem of unsupervised domain adaptation when the source differs from the target because of a shift in the distribution of a latent confounder. In this case, neither covariate shift nor label shift assumptions apply. When all data is discrete, we show that the optimal target predictor can be non-parametrically identified with the help of concept and proxy variables, available only in the source, and unlabeled data from the target.