深圳大学四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第六十一期

讲座题目: Green's matching: an efficient approach to parameter estimation in complex dynamic systems

主讲人：王学钦 教授(中国科学技术大学)

讲座时间：2023年12月12日（周二）16：30-17：30

讲座地点：深圳大学粤海校区汇星楼一楼一号教室

内容概述：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.

主讲人简介：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。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、高等教育出版社Lecture Notes: Data Science, Statistics and Probability系列丛书的副主编。

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2023年12月11日