Mixup-Induced Domain Extrapolation for Domain Generalization

Domain generalization aims to learn a well-performed classifier on multiple source domains for unseen target domains under domain shift. Domain-invariant representation (DIR) is an intuitive approach and has been of great concern. In practice, since the targets are variant and agnostic, only a few sources are not sufficient to reflect the entire domain population, leading to biased DIR. Derived from PAC-Bayes framework, we provide a novel generalization bound involving the number of domains sampled from the environment (N) and the radius of the Wasserstein ball centred on the target (r), which have rarely been considered before. Herein, we can obtain two natural and significant findings: when N increases, 1) the gap between the source and target sampling environments can be gradually mitigated; 2) the target can be better approximated within the Wasserstein ball. These findings prompt us to collect adequate domains against domain shift. For seeking convenience, we design a novel yet simple Extrapolation Domain strategy induced by the Mixup scheme, namely EDM. Through a reverse Mixup scheme to generate the extrapolated domains, combined with the interpolated domains, we expand the interpolation space spanned by the sources, providing more abundant domains to increase sampling intersections to shorten r. Moreover, EDM is easy to implement and be plugged-and-played. In experiments, EDM has been plugged into several methods in both closed and open set settings, achieving up to 5.73% improvement.