Partial Distribution Matching via Partial Wasserstein Adversarial Networks

2024-09-16

IEEE Transactions on Pattern Analysis and Machine Intelligence

AI Summary

This work addresses the Partial Distribution Matching (PDM) problem—robustly aligning salient subsets of two probability distributions without requiring full distributional alignment. To formalize PDM, we establish, for the first time, the Kantorovich–Rubinstein duality theory for the partial Wasserstein-1 distance. Leveraging this theoretical foundation, we propose PWAN, an adversarial network framework that enables efficient, differentiable partial matching via gradient-based optimization. Our method integrates partial Wasserstein metrics, adversarial training, and bilevel optimization. Evaluated on 3D point-set registration and partial-domain adaptation, PWAN achieves state-of-the-art or competitive performance, significantly improving matching robustness and generalization. It overcomes the strong assumption of complete distribution alignment inherent in conventional optimal transport–based methods.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

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.

Problem

• Partial matching of probability distributions for robust alignment
• Theoretical derivation of Kantorovich-Rubinstein duality for partial Wasserstein discrepancy
• Application in point set registration and partial domain adaptation tasks

Innovation

• Partial Wasserstein adversarial network for distribution matching
• Kantorovich-Rubinstein duality for partial Wasserstein discrepancy
• Gradient descent optimization for partial matching tasks