迈向通过流匹配实现的通用Wasserstein重心
Towards Universal Wasserstein Barycenters through Flow Matching
- Sigma Nova
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出BaryFM流匹配模型，实现Wasserstein单纯形中任意重心的通用逼近，在域适应等4个任务上验证，平均排名优于15种方法。
AI中文摘要：
在概率度量下定义概率测度的加权平均是概率机器学习中的核心工具。在Wasserstein度量下，这些被称为Wasserstein重心。虽然大多数方法针对固定的权重向量计算重心，但近似整个单纯形上的重心族（我们称之为Wasserstein单纯形）仍未得到充分探索。我们将此问题称为通用重心逼近，并提出BaryFM，一种流匹配模型，将边缘测度传输到Wasserstein单纯形中的任意重心。一旦训练完成，该网络可以通过常微分方程从Wasserstein单纯形中的测度中采样。我们在4个下游任务上验证了我们的方法：域适应、泛化、贝叶斯后验聚合和算法公平性。BaryFM在10个域适应基准测试中，在15个竞争方法中取得了最佳平均排名，匹配或超越了非通用求解器。
英文摘要：
Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstein metric, these are called \emph{Wasserstein barycenters}. While most approaches compute barycenters for a fixed weight vector, approximating the whole family of barycenters over the simplex, which we call the \emph{Wasserstein simplex}, remains underexplored. We refer to this problem as \emph{Universal Barycenter Approximation}, and propose \texttt{BaryFM}, a flow matching model transporting the marginal measures into any barycenter in the Wasserstein simplex. Once trained, the network can draw samples from measures in the Wasserstein simplex through an ordinary differential equation. We validate our method on 4 downstream tasks: domain adaptation, generalization, Bayesian posterior aggregation and algorithmic fairness. \texttt{BaryFM} achieves the best average rank among 15 competing methods across 10 domain adaptation benchmarks, matching or surpassing non-universal solvers.
