Robust domain-adaptive discriminant analysis

Consider a domain-adaptive supervised learning setting, where a classifier learns from labeled data in a source domain and unlabeled data in a target domain to predict the corresponding target labels. If the classifier’s assumption on the relationship between domains (e.g. covariate shift, common subspace, etc.) is valid, then it will usually outperform a non-adaptive source classifier. If its assumption is invalid, it can perform substantially worse. Validating assumptions on domain relationships is not possible without target labels. We argue that, in order to make domain-adaptive classifiers more practical, it is necessary to focus on robustness; robust in the sense that an adaptive classifier will still perform at least as well as a non-adaptive classifier without having to rely on the validity of strong assumptions. With this objective in mind, we derive a conservative parameter estimation technique, which is transductive in the sense of Vapnik and Chervonenkis, and show for discriminant analysis that the new estimator is guaranteed to achieve a lower risk on the given target samples compared to the source classifier. Experiments on problems with geographical sampling bias indicate that our parameter estimator performs well.