The 40th Anniversary of Shenzhen University and the 40th Anniversary of Mathematics Department

Liyuan scholar Colloquiumsixty-one

Lecture Title: Green's matching: an efficient approach to parameter estimation in complex dynamic systems

Speaker：Prof. Xueqin Wang (University of Science and Technology of China)

Lecture time: Tuesday, December 12, 2023, 16:30-17:30

Lecture location:Classroom No. 1, 1/F, Hui Xing Building, Yuehai Campus, Shenzhen University, China

Overview：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.

Speaker Introduction：Xueqin Wang, Chair Professor of University of Science and Technology of China (USTC), graduated from Binghamton University in 2003, and is a selected candidate of Ministry of Education's high-level talents. He is currently a member of the Teaching Guidance Committee of Statistics in Higher Education of the Ministry of Education, vice president of China Field Statistics Research Society, president of China Field Statistics Research Society, associate editor of JASA, an international journal of statistics, and associate editor of Lecture Notes: Data Science, Statistics and Probability series of the Higher Education Publishing House. Associate Editor of Lecture Notes: Data Science, Statistics and Probability series of Higher Education Press.

Teachers and students are welcome to participate!

Invited by: School of Mathematical Sciences

School of Mathematical Sciences

December 11, 2023