  Existing domain adaptation focuses on transferring knowledge between domains
with categorical indices (e.g., between datasets A and B). However, many tasks
involve continuously indexed domains. For example, in medical applications, one
often needs to transfer disease analysis and prediction across patients of
different ages, where age acts as a continuous domain index. Such tasks are
challenging for prior domain adaptation methods since they ignore the
underlying relation among domains. In this paper, we propose the first method
for continuously indexed domain adaptation. Our approach combines traditional
adversarial adaptation with a novel discriminator that models the
encoding-conditioned domain index distribution. Our theoretical analysis
demonstrates the value of leveraging the domain index to generate invariant
features across a continuous range of domains. Our empirical results show that
our approach outperforms the state-of-the-art domain adaption methods on both
synthetic and real-world medical datasets.
