报告时间：2024年4月17日（周三）16:00-17:00

报告地点：中国人民大学明德主楼1016

报告嘉宾：王学钦

报告主题：Green’s matching: an efficient approach to parameter estimation in complex dynamic systems

报告摘要

Green’s matching: an efficient approach to parameter estimation in complex dynamic systems

Parameters of differential equations are essential to characterize the intrinsic behaviors of dynamic systems. Many scientific challenges are hindered by a lack of computational and statistical efficiency in parameter estimation of dynamic systems, especially for complex systems with general-order differential operators, such as motion dynamics. Aiming at discovering these dynamic systems behind noisy data, we develop a computationally tractable and statistically efficient two-step method called Green’s matching via estimating equations. Particularly, we avoid time-consuming numerical integration by the pre-smoothing of trajectories in the estimating equations, and the pre-smoothing of curve derivatives is generally not involved in the estimating equations due to the inversion of differential operators by Green’s functions. These appealing features improve both computational and statistical efficiency for parameter estimation. We prove that Green’s matching attains statistically optimal convergence for general-order systems. While for the other two widely used two-step methods, their estimation biases may dominate the estimation errors, resulting in poor convergence rates for high-order systems. We conduct extensive simulations to examine the estimation behaviors of two-step methods and other competitive approaches. Our results show that Green’s matching outperforms other methods for parameter estimation, which also supports Green’s matching in more complicated statistical inferences, such as equation discovery or causal network inference, for general-order dynamic systems.

作者简介

王学钦，中国科学技术大学讲席教授，2003年毕业于宾汉姆顿大学，教育部高层次人才入选者，ISI当选会员。现担任教育部高等学校统计学类专业教学指导委员会委员、中国现场统计研究会副理事长、中国现场统计研究会教育统计与管理分会理事长、统计学国际期刊JASA等的Associate Editor。主要研究方向为大规模复杂数据的统计学理论、方法与算法；统计机器学习；精准医疗；医疗政策；风险管理和政策评估。