主题：Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions
主讲人：王文佳 香港科技大学（广州）
主持人：刘一鸣 暨南大学
时间：2023年3月15日（周三）15:30-16:30
地点：暨南大学石牌校区经济学院（中惠楼）102室
摘要
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.
主讲人简介
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计算机实验与不确定性量化、机器学习与非参数统计。目前已在统计学、机器学习顶级期刊、会议《JASA》，《JMLR》，《NIPS》等发表多篇文章。
