報告題目：Green’s matching: an efficient approach to parameter estimation in complex dynamic systems
報 告 人：王學欽 教授 中國科學技術大學
報告時間：2024年04月16日 下午 14:00-15:00
報告地點：騰訊會議 ID：881-762-247
或點擊鍊接直接加入會議：https://meeting.tencent.com/dm/mTWYSWZGNmqs
校内聯系人：趙世舜 zhaoss@jlu.edu.cn
報告摘要：
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.
報告人簡介：
王學欽，中國科學技術大學講席教授，2003年畢業于賓漢姆頓大學，教育部高層次人才入選者，ISI當選會員。現擔任教育部高等學校統計學類專業教學指導委員會委員、中國現場統計研究會副理事長、中國現場統計研究會教育統計與管理分會理事長、統計學國際期刊JASA等的Associate Editor。主要研究方向為大規模複雜數據的統計學理論、方法與算法；統計機器學習；精準醫療；醫療政策；風險管理和政策評估。
