  The power and flexibility of Optimal Transport (OT) have pervaded a wide
spectrum of problems, including recent Machine Learning challenges such as
unsupervised domain adaptation. Its essence of quantitatively relating two
probability distributions by some optimal metric, has been creatively exploited
and shown to hold promise for many real-world data challenges. In a related
theme in the present work, we posit that domain adaptation robustness is rooted
in the intrinsic (latent) representations of the respective data, which are
inherently lying in a non-linear submanifold embedded in a higher dimensional
Euclidean space. We account for the geometric properties by refining the $l^2$
Euclidean metric to better reflect the geodesic distance between two distinct
representations. We integrate a metric correction term as well as a prior
cluster structure in the source data of the OT-driven adaptation. We show that
this is tantamount to an implicit Bayesian framework, which we demonstrate to
be viable for a more robust and better-performing approach to domain
adaptation. Substantiating experiments are also included for validation
purposes.
