用梯度流方法实现可扩展且带标签信息的最优传输平均计算
Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation
- 基于概率测度空间的梯度流，通过时间离散化实现高效求解
- 支持小批量最优传输与任务感知正则化，精度优于现有方法
- 适合需要标签信息融合的跨领域数据聚合场景
Wasserstein barycenter 提供了一种在保留其所在空间几何结构的前提下聚合概率分布的合理方法。现有离散方法受限于必须获取输入分布的全部样本，而神经网络方法虽可扩展但依赖复杂优化且难以融入标签信息。本文通过概率测度空间中的梯度流解决上述问题。经时间离散化后，提出的方法具备三方面优势：（i）依赖小批量最优传输；（ii）可通过任务感知函数灵活引入正则化；（iii）可自然地将监督信息嵌入基础代价函数中。我们在涵盖计算机视觉、神经科学和化学工程的域适应基准上进行了实证验证。结果表明，该方法建立了 Wasserstein barycenter 求解的新标杆，带有标签信息的 barycenter 始终优于无标签版本。
原文摘要 · Abstract (English)
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not because as they assume access to the complete set of samples from the input measures. Meanwhile, neural network approaches do scale well, but rely on complex optimization problems and cannot easily incorporate label information. We address these limitations through gradient flows in the space of probability measures. Through time discretization, we achieve a scalable algorithm that i) relies on mini-batch optimal transport, ii) accepts modular regularization through task-aware functions, and iii) seamlessly integrates supervised information into the ground-cost. We empirically validate our approach on domain adaptation benchmarks that span computer vision, neuroscience, and chemical engineering. Our method establishes a new state-of-the-art Wasserstein barycenter solver, with labeled barycenters consistently outperforming unlabeled ones. Our code at https://github.com/SigmaNova/barycentric-gradient-flows
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