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報(bào)告題目：Green’s matching: an efficient approach to parameter estimation in complex dynamic systems

主講人：王學(xué)欽教授（中國(guó)科學(xué)技術(shù)大學(xué)）

時(shí)間：2025年4月28日（周一）10:00 a.m.

地點(diǎn)：北院卓遠(yuǎn)樓305會(huì)議室

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院

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.

主講人簡(jiǎn)介：

王學(xué)欽，中國(guó)科學(xué)技術(shù)大學(xué)講席教授，2003年畢業(yè)于賓漢姆頓大學(xué)，教育部高層次人才入選者，ISI當(dāng)選會(huì)員。現(xiàn)擔(dān)任教育部高等學(xué)校統(tǒng)計(jì)學(xué)類(lèi)專業(yè)教學(xué)指導(dǎo)委員會(huì)委員、中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)副理事長(zhǎng)、中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)教育統(tǒng)計(jì)與管理分會(huì)理事長(zhǎng)主要研究方向?yàn)榇笠?guī)模復(fù)雜數(shù)據(jù)的統(tǒng)計(jì)學(xué)理論、方法與算法；統(tǒng)計(jì)機(jī)器學(xué)習(xí)；精準(zhǔn)醫(yī)療；醫(yī)療政策；風(fēng)險(xiǎn)管理和政策評(píng)估。