题　目：Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions

嘉　宾：王文佳，助理教授，香港科技大学（广州）

主持人：罗俊 教授 上海交通大学安泰经济与管理学院

时　间：2023年8月23日（周三）14:00-15:30pm

地　点：安泰经济与管理学院B207

内容简介:

Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this work, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification. This is a joint work with Yanyuan Wang and Xiaowei Zhang.

演讲人简介：

王文佳是香港科技大学（广州）信息枢纽数据科学与分析学域的助理教授；2018年8月获得佐治亚理工学院工业工程系博士学位。王文佳的研究方向包括不确定性量化、随机仿真、机器学习、非参数统计和计算机实验。目前已在统计学、机器学习顶级期刊、会议Journal of the American Statistical Association，Journal of Machine Learning Research，Technometrics，NeurIPS，ICLR等发表多篇文章。

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