HOT-GAN: Hilbert Optimal Transport for Generative Adversarial Network

Area of Science:

• Machine Learning
• Artificial Intelligence
• Data Science

Background:

• Generative Adversarial Networks (GANs) excel at synthetic data generation by learning data distributions.
• Optimal Transport (OT) has been used to address GAN training instability and gradient vanishing.
• Existing OT-GANs in Euclidean space struggle with high-order statistics.

Purpose of the Study:

• To propose a novel computational framework, Hilbert Optimal Transport GAN (HOT-GAN), for improved synthetic data generation.
• To generalize OT-based GANs from Euclidean space to Reproducing Kernel Hilbert Space (RKHS).
• To enable GANs to capture more informative, high-order statistics for enhanced data generation.

Main Methods:

• Developed HOT-GAN by embedding data into RKHS using a Hilbert embedding.
• Proved a closed-form kernel reformulation for HOT-GAN in RKHS, ensuring a tractable objective.
• Leveraged theoretical differentiability guarantees for adversarial kernel learning in generator training.

Main Results:

• HOT-GAN effectively captures higher-order statistics in RKHS.
• The proposed framework demonstrates improved stability and performance in GAN training.
• Experimental results show HOT-GAN outperforms existing representative GAN methods.

Conclusions:

• HOT-GAN offers a theoretically sound and practically effective approach for advanced synthetic data generation.
• Generalizing OT-GANs to RKHS unlocks the potential for learning richer data representations.
• The framework provides a pathway for developing more powerful and stable generative models.