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.

通过将度量空间从欧氏距离度量更改为测地距离度量，将先前的最优传输模型扩展到内在表示的领域自适应问题，并通过引入簇先验结构构建了一个隐式贝叶斯模型来提高数据的鲁棒性。

隐式贝叶斯自适应：一种协同传输方法