  As a recent noticeable topic, domain generalization aims to learn a
generalizable model on multiple source domains, which is expected to perform
well on unseen test domains. Great efforts have been made to learn
domain-invariant features by aligning distributions across domains. However,
existing works are often designed based on some relaxed conditions which are
generally hard to satisfy and fail to realize the desired joint distribution
alignment. In this paper, we propose a novel domain generalization method,
which originates from an intuitive idea that a domain-invariant classifier can
be learned by minimizing the KL-divergence between posterior distributions from
different domains. To enhance the generalizability of the learned classifier,
we formalize the optimization objective as an expectation computed on the
ground-truth marginal distribution. Nevertheless, it also presents two obvious
deficiencies, one of which is the side-effect of entropy increase in
KL-divergence and the other is the unavailability of ground-truth marginal
distributions. For the former, we introduce a term named maximum in-domain
likelihood to maintain the discrimination of the learned domain-invariant
representation space. For the latter, we approximate the ground-truth marginal
distribution with source domains under a reasonable convex hull assumption.
Finally, a Constrained Maximum Cross-domain Likelihood (CMCL) optimization
problem is deduced, by solving which the joint distributions are naturally
aligned. An alternating optimization strategy is carefully designed to
approximately solve this optimization problem. Extensive experiments on four
standard benchmark datasets, i.e., Digits-DG, PACS, Office-Home and
miniDomainNet, highlight the superior performance of our method.
