提出新方法实现部分分布匹配，提升对异常数据的鲁棒性。
Partial Distribution Matching via Partial Wasserstein Adversarial Networks
- 基于部分Wasserstein距离的对偶形式设计对抗网络
- 在3D点云和高维特征空间中实现高效部分匹配
- 适合存在噪声或缺失数据的配准与迁移学习任务
本文研究分布匹配（DM）问题，旨在稳健地对齐两个概率分布。提出一种松弛形式——部分分布匹配（PDM），仅需匹配分布的一部分而非全部。理论上推导了部分Wasserstein-1（PW）差异的Kantorovich-Rubinstein对偶形式，并据此开发了部分Wasserstein对抗网络（PWAN），通过该对偶形式高效近似PW差异。利用梯度下降优化网络即可实现部分匹配。在点集配准和部分域自适应两个实际任务中验证了方法的有效性，分别在3D空间和高维特征空间中完成分布部分匹配。实验结果表明，所提PWAN能产生高度鲁棒的匹配结果，在性能上优于或相当于现有最优方法。
原文摘要 · Abstract (English)
This paper studies the problem of distribution matching (DM), which is a fundamental machine learning problem seeking to robustly align two probability distributions. Our approach is established on a relaxed formulation, called partial distribution matching (PDM), which seeks to match a fraction of the distributions instead of matching them completely. We theoretically derive the Kantorovich-Rubinstein duality for the partial Wasserstain-1 (PW) discrepancy, and develop a partial Wasserstein adversarial network (PWAN) that efficiently approximates the PW discrepancy based on this dual form. Partial matching can then be achieved by optimizing the network using gradient descent. Two practical tasks, point set registration and partial domain adaptation are investigated, where the goals are to partially match distributions in 3D space and high-dimensional feature space respectively. The experiment results confirm that the proposed PWAN effectively produces highly robust matching results, performing better or on par with the state-of-the-art methods.
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