Generalizing knowledge beyond source domains is a crucial prerequisite for
many biomedical applications such as drug design and molecular property
prediction. To meet this challenge, researchers have used optimal transport
(OT) to perform representation alignment between the source and target domains.
Yet existing OT algorithms are mainly designed for classification tasks.
Accordingly, we consider regression tasks in the unsupervised and
semi-supervised settings in this paper. To exploit continuous labels, we
propose novel metrics to measure domain distances and introduce a posterior
variance regularizer on the transport plan. Further, while computationally
appealing, OT suffers from ambiguous decision boundaries and biased local data
distributions brought by the mini-batch training. To address those issues, we
propose to couple OT with metric learning to yield more robust boundaries and
reduce bias. Specifically, we present a dynamic hierarchical triplet loss to
describe the global data distribution, where the cluster centroids are
progressively adjusted among consecutive iterations. We evaluate our method on
both unsupervised and semi-supervised learning tasks in biochemistry.
Experiments show the proposed method significantly outperforms state-of-the-art
baselines across various benchmark datasets of small molecules and material
crystals.

本文提出使用最优传输算法（OT）进行表示对齐，解决生物医学应用中的连续标签回归任务问题。通过提出新的测度域距离和引入后验方差正则化的方法，进一步为拓展任务提供了支持。此外，提出了将 OT 与度量学习相结合的方法，通过动态层次三重损失函数来描述全局数据分布，试验证明该方法在未监督和半监督学习任务的小分子和材料晶体数据上显著优于现有方法。