提出三种新方法增强跨域对齐的鲁棒性，有效抵御数据污染。
On Robust Cross Domain Alignment
- 基于稳健统计学设计三种新方法提升GW距离抗干扰能力。
- 在真实机器学习任务中显著优于现有最先进方法。
- 适用于存在异常数据的跨域对齐场景，如图像、网络分析。
Gromov-Wasserstein (GW) 距离是衡量不同空间分布间对齐的有效度量，通过计算彼此偏离等距的程度，在领域迁移和网络分析中广泛应用。然而，它长期受底层分布污染的影响。现有提升鲁棒性的尝试多借鉴最优传输（OT）中的部分质量传输或不平衡策略。但跨域对齐问题与OT本质不同，需针对多样化应用场景和污染模式设计专门解决方案。本文基于稳健统计学，提出三种情境上新颖的技术来增强GW及其变体的鲁棒性。对每种方法，我们分析其度量性质、鲁棒性保障，以及相互间的依赖关系与与GW距离的关系。为全面评估，我们在真实机器学习任务中实证验证了其对污染的优越抗性，性能超越当前最先进的方法。
原文摘要 · Abstract (English)
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation and network analysis. It has long been shown to be vulnerable to contamination in the underlying measures. All efforts to introduce robustness in GW have been inspired by similar techniques in optimal transport (OT), which predominantly advocate partial mass transport or unbalancing. In contrast, the cross-domain alignment problem being fundamentally different from OT, demands specific solutions to tackle diverse applications and contamination regimes. Deriving from robust statistics, we discuss three contextually novel techniques to robustify GW and its variants. For each method, we explore metric properties and robustness guarantees along with their co-dependencies and individual relations with the GW distance. For a comprehensive view, we empirically validate their superior resilience to contamination under real machine learning tasks against state-of-the-art methods.
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