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

TL;DR

This paper introduces PCF-GAN, a novel generative adversarial network that uses the path characteristic function to effectively generate and reconstruct high-fidelity time series data, outperforming existing methods.

Contribution

The paper develops the PCF-GAN framework with theoretical foundations, efficient training schemes, and an auto-encoder integration for improved time series generation.

Findings

PCF-GAN achieves superior generation quality over state-of-the-art baselines.

Theoretical properties of the PCF distance ensure stable and feasible training.

Auto-encoder integration enhances reconstruction capabilities.

Abstract

Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards this goal, a key step is the development of an effective discriminator to distinguish between time series distributions. We propose the so-called PCF-GAN, a novel GAN that incorporates the path characteristic function (PCF) as the principled representation of time series distribution into the discriminator to enhance its generative performance. On the one hand, we establish theoretical foundations of the PCF distance by proving its characteristicity, boundedness, differentiability with respect to generator parameters, and weak continuity, which ensure the stability and feasibility of training the PCF-GAN. On the other hand, we design efficient initialisation and optimisation schemes for PCFs to strengthen the discriminative power and accelerate training efficiency. To further boost the capabilities of complex time series generation, we integrate the auto-encoder structure via sequential embedding into the PCF-GAN, which provides additional reconstruction functionality. Extensive numerical experiments on various datasets demonstrate the consistently superior performance of PCF-GAN over state-of-the-art baselines, in both generation and reconstruction quality. Code is available at https://github.com/DeepIntoStreams/PCF-GAN.