Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes

Haoming Yang, Ali Hasan, Yuting Ng, Vahid Tarokh
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:262-270, 2024.

Abstract

McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. We study the influence of explicitly including distributional information in the parameterization of the SDE. We propose a series of semi-parametric methods for representing MV-SDEs, and corresponding estimators for inferring parameters from data based on the properties of the MV-SDE. We analyze the characteristics of the different architectures and estimators, and consider their applicability in relevant machine learning problems. We empirically compare the performance of the different architectures and estimators on real and synthetic datasets for time series and probabilistic modeling. The results suggest that explicitly including distributional dependence in the parameterization of the SDE is effective in modeling temporal data with interaction under an exchangeability assumption while maintaining strong performance for standard Itô-SDEs due to the richer class of probability flows associated with MV-SDEs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-yang24a, title = { Neural {McKean}-{V}lasov Processes: Distributional Dependence in Diffusion Processes }, author = {Yang, Haoming and Hasan, Ali and Ng, Yuting and Tarokh, Vahid}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {262--270}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/yang24a/yang24a.pdf}, url = {https://proceedings.mlr.press/v238/yang24a.html}, abstract = { McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. We study the influence of explicitly including distributional information in the parameterization of the SDE. We propose a series of semi-parametric methods for representing MV-SDEs, and corresponding estimators for inferring parameters from data based on the properties of the MV-SDE. We analyze the characteristics of the different architectures and estimators, and consider their applicability in relevant machine learning problems. We empirically compare the performance of the different architectures and estimators on real and synthetic datasets for time series and probabilistic modeling. The results suggest that explicitly including distributional dependence in the parameterization of the SDE is effective in modeling temporal data with interaction under an exchangeability assumption while maintaining strong performance for standard Itô-SDEs due to the richer class of probability flows associated with MV-SDEs. } }
Endnote
%0 Conference Paper %T Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes %A Haoming Yang %A Ali Hasan %A Yuting Ng %A Vahid Tarokh %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-yang24a %I PMLR %P 262--270 %U https://proceedings.mlr.press/v238/yang24a.html %V 238 %X McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. We study the influence of explicitly including distributional information in the parameterization of the SDE. We propose a series of semi-parametric methods for representing MV-SDEs, and corresponding estimators for inferring parameters from data based on the properties of the MV-SDE. We analyze the characteristics of the different architectures and estimators, and consider their applicability in relevant machine learning problems. We empirically compare the performance of the different architectures and estimators on real and synthetic datasets for time series and probabilistic modeling. The results suggest that explicitly including distributional dependence in the parameterization of the SDE is effective in modeling temporal data with interaction under an exchangeability assumption while maintaining strong performance for standard Itô-SDEs due to the richer class of probability flows associated with MV-SDEs.
APA
Yang, H., Hasan, A., Ng, Y. & Tarokh, V.. (2024). Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:262-270 Available from https://proceedings.mlr.press/v238/yang24a.html.

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