用黎曼几何联合学习最优传输的度量与距离，提升域自适应性能。
A Riemannian Approach to Ground Metric Learning for Optimal Transport
- 基于对称正定矩阵的黎曼几何，学习潜在空间中的最优传输度量。
- 在域自适应任务中，所学度量显著提升最优传输距离的有效性。
- 适合需要精确分布对齐的迁移学习场景，如图像域适应。
最优传输（OT）理论在机器学习与信号处理中受到广泛关注。OT定义了源数据与目标数据点概率分布之间的距离。影响基于OT距离的关键因素是嵌入空间中的基础度量。本文提出一种方法，通过参数化为对称正定矩阵的潜在基础度量来学习合适的度量，并利用对称正定矩阵丰富的黎曼几何特性，联合优化最优传输距离与基础度量。实验结果表明，所学习的度量在基于最优传输的域自适应任务中具有显著有效性。
原文摘要 · Abstract (English)
Optimal transport (OT) theory has attracted much attention in machine learning and signal processing applications. OT defines a notion of distance between probability distributions of source and target data points. A crucial factor that influences OT-based distances is the ground metric of the embedding space in which the source and target data points lie. In this work, we propose to learn a suitable latent ground metric parameterized by a symmetric positive definite matrix. We use the rich Riemannian geometry of symmetric positive definite matrices to jointly learn the OT distance along with the ground metric. Empirical results illustrate the efficacy of the learned metric in OT-based domain adaptation.
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