Reproduce “PCF-GAN: generating sequential data via the characteristic function of measures on the path space” on OpenResearch

About this paper

Hang Lou, Siran Li, Hao Ni

PCF-GAN introduces the Path Characteristic Function (PCF) to represent time series distributions, integrating this novel metric into a Generative Adversarial Network discriminator for sequential data generation. The model consistently outperforms existing methods in generating and reconstructing diverse time series, demonstrating enhanced training stability and fidelity.

Key insights

• Extending characteristic functions to the path space via Lie group-valued unitary features provides a mathematically principled and powerful metric (PCFD) to uniquely characterize and compare distributions of stochastic processes.
• The PCFD possesses inherent properties like characteristicity, boundedness, differentiability, and weak continuity, which collectively ensure stable GAN training, prevent vanishing/exploding gradients, and enable robust gradient-based optimization.
• The combined auto-encoder architecture with reconstruction and regularization losses helps the discriminator learn meaningful low-dimensional sequential embeddings, thereby mitigating mode collapse and improving both generation and reconstruction quality.

Summary by alphaXiv.