Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to align datasets, but a key challenge in applying OT is that we need to specify a transport cost function that accurately captures how the two datasets are related. Reliable cost functions are typically not available and practitioners often resort to using hand-crafted or Euclidean cost even if it may not be appropriate. In this work, we investigate how to learn the cost function using a small amount of side information which is often available. The side information we consider captures subset correspondence---i.e. certain subsets of points in the two data sets are known to be related. For example, we may have some images labeled as cars in both datasets; or we may have a common annotated cell type in single-cell data from two batches. We develop an end-to-end optimizer (OT-SI) that differentiates through the Sinkhorn algorithm and effectively learns the suitable cost function from side information. On systematic experiments in images, marriage-matching and single-cell RNA-seq, our method substantially outperform state-of-the-art benchmarks.

本文研究了使用少量副信息来学习代价函数的方法，该信息能够捕获到数据集中的子集对应关系，并提出了一种基于 Sinkhorn 算法的端对端优化器，实现了代价函数的自适应学习，结果表明该方法在图片、婚姻匹配和单细胞 RNA 测序等数据集上取得了明显的性能优势。

从子集一一对应关系学习运输成本