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2021 Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data
Xiaohui Chen
Author Affiliations +
Electron. Commun. Probab. 26: 1-13 (2021). DOI: 10.1214/21-ECP416

Abstract

This paper concerns the parameter estimation problem for the quadratic potential energy in interacting particle systems from continuous-time and single-trajectory data. Even though such dynamical systems are high-dimensional, we show that the vanilla maximum likelihood estimator (without regularization) is able to estimate the interaction potential parameter with optimal rate of convergence simultaneously in mean-field limit and in long-time dynamics. This to some extend avoids the curse-of-dimensionality for estimating large dynamical systems under symmetry of the particle interaction.

Funding Statement

Research was supported in part by NSF CAREER Award DMS-1752614 and a Simons Fellowship.

Acknowledgments

Part of this research was carried out in the Institute for Data, System, and Society (IDSS) at Massachusetts Institute of Technology. The author would like to thank Philippe Rigollet (MIT) and Yun Yang (UIUC) for helpful comments.

Citation

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Xiaohui Chen. "Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP416

Information

Received: 21 July 2020; Accepted: 30 June 2021; Published: 2021
First available in Project Euclid: 14 July 2021

Digital Object Identifier: 10.1214/21-ECP416

Subjects:
Primary: 60H15, 62M05

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