Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data
Statistics Theory
2021-04-13 v2 Probability
Methodology
Statistics Theory
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.
Cite
@article{arxiv.2007.11048,
title = {Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data},
author = {Xiaohui Chen},
journal= {arXiv preprint arXiv:2007.11048},
year = {2021}
}