无需访问原始数据即可高效计算多分布的最优运输中位数。
Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decomposition
- 通过单循环对偶分解实现联邦化计算，仅需聚合信息
- 每次迭代复杂度极低，支持大规模分布式应用
- 适用于保护隐私的多源分布融合任务
我们提出一种高效的联邦对偶分解算法，用于计算多个分布的Wasserstein中位数，并可自动选择解的支持集。该算法不访问本地数据，仅依赖高度聚合的信息，且无需反复求解质量运输问题。由于避免了矩阵-向量运算，每次迭代的计算复杂度极低，具有显著的可扩展性。我们在多种混合模型实例上验证了其有效性，并与当前最先进方法进行了对比。
原文摘要 · Abstract (English)
We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only highly aggregated information. It also does not require repeated solutions to mass transportation problems. Because of the absence of any matrix-vector operations, the algorithm exhibits a very low complexity of each iteration and significant scalability. We illustrate its virtues and compare it to the state-of-the-art methods on several examples of mixture models.
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