Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Among many successful applications of OT in machine learning (ML), domain adaptation (DA) -- a field of study where the goal is to transfer a classifier from one labelled domain to another similar, yet different unlabelled or scarcely labelled domain -- has been historically among the most investigated ones. This success is due to the ability of OT to provide both a meaningful discrepancy measure to assess the similarity of two domains' distributions and a mapping that can project source domain data onto the target one. In this paper, we propose a principally new OT-based approach applied to DA that uses the closed-form solution of the OT problem given by an affine mapping and learns an embedding space for which this solution is optimal and computationally less complex. We show that our approach works in both homogeneous and heterogeneous DA settings and outperforms or is on par with other famous baselines based on both traditional OT and OT in incomparable spaces. Furthermore, we show that our proposed method vastly reduces computational complexity.

翻译：最优传输（OT）是一种强大的几何工具，用于遵循最小努力原则比较和对齐概率测度。在机器学习（ML）中OT的众多成功应用中，领域适应（DA）——旨在将分类器从一个有标签领域迁移至另一个相似但无标签或标签稀缺领域的研究领域——历来是研究最为深入的方向之一。这一成功源于OT既能提供衡量两个领域分布相似性的有意义的差异测度，又能提供将源域数据投影至目标域的映射。本文提出了一种基于OT的全新领域适应方法，利用仿射映射给出的OT问题闭式解，并学习一个使该解达到最优且计算复杂度更低的嵌入空间。我们证明，该方法在同质和异质DA场景下均有效，且性能优于或持平于基于传统OT及不可比空间OT的其他经典基线方法。此外，我们提出的方法大幅降低了计算复杂度。