Statistical Guarantees for Unpaired Image-to-Image Cross-Domain Analysis using GANs

Saptarshi Chakraborty, Peter Bartlett
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2404-2412, 2025.

Abstract

The field of unpaired image-to-image translation has undergone a significant transformation with the introduction of Generative Adversarial Networks (GANs), with CycleGAN and DiscoGAN as prominent variants. While these models show impressive empirical performance, their statistical properties are under-studied. In this paper, we propose a framework for analyzing the generalization error in cross-domain deep generative models. Our findings reveal that when provided with independent and identically distributed (i.i.d.) samples from two domains, the translation error, measured under the Wasserstein-1 loss, scales as $\tilde{\mathcal{O}} \left(\min(n, m)^{-1/\max(d,\tilde{d})}\right)$, provided that the true model possesses sufficient smoothness and the network sizes are chosen appropriately. Here, $n$ and $m$ represent the sizes of the sample sets, while $d$ and $\tilde{d}$ denote the dimensions of the respective data domains. Furthermore, we highlight the importance of a cycle loss term for ensuring distributional cycle consistency. Additionally, we provide insights into the relationship between the network size and the number of data points. Notably, as the true model exhibits greater smoothness, it suffices to work with smaller networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-chakraborty25b, title = {Statistical Guarantees for Unpaired Image-to-Image Cross-Domain Analysis using GANs}, author = {Chakraborty, Saptarshi and Bartlett, Peter}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2404--2412}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/chakraborty25b/chakraborty25b.pdf}, url = {https://proceedings.mlr.press/v258/chakraborty25b.html}, abstract = {The field of unpaired image-to-image translation has undergone a significant transformation with the introduction of Generative Adversarial Networks (GANs), with CycleGAN and DiscoGAN as prominent variants. While these models show impressive empirical performance, their statistical properties are under-studied. In this paper, we propose a framework for analyzing the generalization error in cross-domain deep generative models. Our findings reveal that when provided with independent and identically distributed (i.i.d.) samples from two domains, the translation error, measured under the Wasserstein-1 loss, scales as $\tilde{\mathcal{O}} \left(\min(n, m)^{-1/\max(d,\tilde{d})}\right)$, provided that the true model possesses sufficient smoothness and the network sizes are chosen appropriately. Here, $n$ and $m$ represent the sizes of the sample sets, while $d$ and $\tilde{d}$ denote the dimensions of the respective data domains. Furthermore, we highlight the importance of a cycle loss term for ensuring distributional cycle consistency. Additionally, we provide insights into the relationship between the network size and the number of data points. Notably, as the true model exhibits greater smoothness, it suffices to work with smaller networks.} }
Endnote
%0 Conference Paper %T Statistical Guarantees for Unpaired Image-to-Image Cross-Domain Analysis using GANs %A Saptarshi Chakraborty %A Peter Bartlett %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-chakraborty25b %I PMLR %P 2404--2412 %U https://proceedings.mlr.press/v258/chakraborty25b.html %V 258 %X The field of unpaired image-to-image translation has undergone a significant transformation with the introduction of Generative Adversarial Networks (GANs), with CycleGAN and DiscoGAN as prominent variants. While these models show impressive empirical performance, their statistical properties are under-studied. In this paper, we propose a framework for analyzing the generalization error in cross-domain deep generative models. Our findings reveal that when provided with independent and identically distributed (i.i.d.) samples from two domains, the translation error, measured under the Wasserstein-1 loss, scales as $\tilde{\mathcal{O}} \left(\min(n, m)^{-1/\max(d,\tilde{d})}\right)$, provided that the true model possesses sufficient smoothness and the network sizes are chosen appropriately. Here, $n$ and $m$ represent the sizes of the sample sets, while $d$ and $\tilde{d}$ denote the dimensions of the respective data domains. Furthermore, we highlight the importance of a cycle loss term for ensuring distributional cycle consistency. Additionally, we provide insights into the relationship between the network size and the number of data points. Notably, as the true model exhibits greater smoothness, it suffices to work with smaller networks.
APA
Chakraborty, S. & Bartlett, P.. (2025). Statistical Guarantees for Unpaired Image-to-Image Cross-Domain Analysis using GANs. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2404-2412 Available from https://proceedings.mlr.press/v258/chakraborty25b.html.

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