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