  What is the role of unlabeled data in an inference problem, when the presumed
underlying distribution is adversarially perturbed? To provide a concrete
answer to this question, this paper unifies two major learning frameworks:
Semi-Supervised Learning (SSL) and Distributionally Robust Learning (DRL). We
develop a generalization theory for our framework based on a number of novel
complexity measures, such as an adversarial extension of Rademacher complexity
and its semi-supervised analogue. Moreover, our analysis is able to quantify
the role of unlabeled data in the generalization under a more general condition
compared to the existing theoretical works in SSL. Based on our framework, we
also present a hybrid of DRL and EM algorithms that has a guaranteed
convergence rate. When implemented with deep neural networks, our method shows
a comparable performance to those of the state-of-the-art on a number of
real-world benchmark datasets.
