Partial Distribution Matching via Partial Wasserstein Adversarial Networks.

Area of Science:

• Machine Learning
• Probability Theory
• Optimization

Background:

• Distribution matching (DM) is crucial for aligning probability distributions in machine learning.
• Existing DM methods often struggle with robustness and partial alignment requirements.

Purpose of the Study:

• To introduce a relaxed formulation, partial distribution matching (PDM), for robust distribution alignment.
• To develop an efficient approximation for the partial Wasserstein-1 (PW) discrepancy.
• To demonstrate the efficacy of PDM in practical applications like point set registration and domain adaptation.

Main Methods:

• Theoretical derivation of the Kantorovich-Rubinstein duality for the partial Wasserstein-1 (PW) discrepancy.
• Development of a partial Wasserstein adversarial network (PWAN) for approximating the PW discrepancy.
• Optimization of the PWAN using gradient descent for partial matching.

Main Results:

• The PWAN efficiently approximates the PW discrepancy, enabling effective partial distribution matching.
• Experiments in point set registration and partial domain adaptation show robust matching results.
• The proposed PWAN performs comparably to or better than state-of-the-art methods.

Conclusions:

• Partial distribution matching (PDM) offers a robust alternative to complete distribution matching.
• The partial Wasserstein adversarial network (PWAN) is an efficient and effective tool for PDM.
• The proposed method shows significant promise for applications requiring partial distribution alignment.