In practice, the data distribution at test time often differs, to a smaller or larger extent, from that of the original training data. Consequentially, the so-called source classifier, trained on the available labelled data, deteriorates on the test, or target, data. Domain adaptive classifiers aim to combat this problem, but typically assume some particular form of domain shift. Most are not robust to violations of domain shift assumptions and may even perform worse than their non-adaptive counterparts. We construct robust parameter estimators for discriminant analysis that guarantee performance improvements of the adaptive classifier over the non-adaptive source classifier.

Domain adaptation has become a prominent problem setting in machine learning and related fields. This review asks the question: How can a classifier learn from a source domain and generalize to a target domain We present a categorization of approaches, divided into, what we refer to as, sample-based, feature-based, and inference-based methods. Sample-based methods focus on weighting individual observations during training based on their importance to the target domain. Feature-based methods revolve around on mapping, projecting, and representing features such that a source classifier performs well on the target domain and inference-based methods incorporate adaptation into the parameter estimation procedure, for instance through constraints on the optimization procedure. Additionally, we review a number of conditions that allow for formulating bounds on the cross-domain generalization error. Our categorization highlights recurring ideas and raises questions important to further research.