Theoretical Insights into CycleGAN: Analyzing Approximation and Estimation Errors in Unpaired Data Generation

TL;DR

This paper provides a theoretical analysis of CycleGAN, decomposing its excess risk into approximation and estimation errors, and explores how its architecture and training influence performance.

Contribution

It offers a novel theoretical framework for understanding the errors in CycleGAN, focusing on the impact of model complexity and cycle-consistency.

Findings

Decomposition of excess risk into approximation and estimation errors.

Upper bounds on estimation error using Rademacher complexity.

Insights into trade-offs between model complexity and training procedures.

Abstract

In this paper, we focus on analyzing the excess risk of the unpaired data generation model, called CycleGAN. Unlike classical GANs, CycleGAN not only transforms data between two unpaired distributions but also ensures the mappings are consistent, which is encouraged by the cycle-consistency term unique to CycleGAN. The increasing complexity of model structure and the addition of the cycle-consistency term in CycleGAN present new challenges for error analysis. By considering the impact of both the model architecture and training procedure, the risk is decomposed into two terms: approximation error and estimation error. These two error terms are analyzed separately and ultimately combined by considering the trade-off between them. Each component is rigorously analyzed; the approximation error through constructing approximations of the optimal transport maps, and the estimation error through establishing an upper bound using Rademacher complexity. Our analysis not only isolates these errors but also explores the trade-offs between them, which provides a theoretical insights of how CycleGAN's architecture and training procedures influence its performance.