Temporal generative adversarial networks

July 11, 2024 — July 11, 2024

adversarial
AI
Bregman
game theory
generative
learning
likelihood free
Monte Carlo
optimization
probability
Figure 1

Turns out we can use GANs as time series predictors. How does this work? No idea.

1 GANs as SDEs

Should look into this (Yang, Zhang, and Karniadakis 2020; Kidger et al. 2021).

2 Connection to path signature methods

Not sure, but mentioned in (Salvi et al. 2024, 2021).

3 Incoming

4 References

Esteban, Hyland, and Rätsch. 2017. “Real-Valued (Medical) Time Series Generation with Recurrent Conditional GANs.”
Kidger, Foster, Li, et al. 2021. “Neural SDEs as Infinite-Dimensional GANs.” In Proceedings of the 38th International Conference on Machine Learning.
Kiraly, and Oberhauser. 2019. “Kernels for Sequentially Ordered Data.” Journal of Machine Learning Research.
Leznik, Lochner, Wesner, et al. 2022. “[SoK] The Great GAN Bake Off, An Extensive Systematic Evaluation of Generative Adversarial Network Architectures for Time Series Synthesis.” Journal of Systems Research.
Liao, Ni, Sabate-Vidales, et al. 2024. “Sig-Wasserstein GANs for Conditional Time Series Generation.” Mathematical Finance.
Liao, Ni, Szpruch, et al. 2023. “Conditional Sig-Wasserstein GANs for Time Series Generation.”
Lou, Li, and Ni. 2024. “PCF-GAN: Generating Sequential Data via the Characteristic Function of Measures on the Path Space.” In Proceedings of the 37th International Conference on Neural Information Processing Systems. NIPS ’23.
Ni, Szpruch, Sabate-Vidales, et al. 2022. “Sig-Wasserstein GANs for Time Series Generation.” In Proceedings of the Second ACM International Conference on AI in Finance. ICAIF ’21.
Rahman, Florez, Anandkumar, et al. 2022. “Generative Adversarial Neural Operators.”
Salvi, Cass, Foster, et al. 2021. “The Signature Kernel Is the Solution of a Goursat PDE.” SIAM Journal on Mathematics of Data Science.
Salvi, Lemercier, Liu, et al. 2024. “Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes.” In Advances in Neural Information Processing Systems. NIPS ’21.
Xu, Wenliang, Munn, et al. 2020. “COT-GAN: Generating Sequential Data via Causal Optimal Transport.” In Proceedings of the 34th International Conference on Neural Information Processing Systems. NIPS ’20.
Yang, Zhang, and Karniadakis. 2020. “Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations.” SIAM Journal on Scientific Computing.
Yoon, Jarrett, and van der Schaar. 2019. “Time-Series Generative Adversarial Networks.” In Proceedings of the 33rd International Conference on Neural Information Processing Systems.