  We propose Regularized Learning under Label shifts (RLLS), a principled and a
practical domain-adaptation algorithm to correct for shifts in the label
distribution between a source and a target domain. We first estimate importance
weights using labeled source data and unlabeled target data, and then train a
classifier on the weighted source samples. We derive a generalization bound for
the classifier on the target domain which is independent of the (ambient) data
dimensions, and instead only depends on the complexity of the function class.
To the best of our knowledge, this is the first generalization bound for the
label-shift problem where the labels in the target domain are not available.
Based on this bound, we propose a regularized estimator for the small-sample
regime which accounts for the uncertainty in the estimated weights. Experiments
on the CIFAR-10 and MNIST datasets show that RLLS improves classification
accuracy, especially in the low sample and large-shift regimes, compared to
previous methods.
