CAREER: Optimization-based Quantification of Statistical Uncertainty in Stochastic and Simulation Analysis

职业：随机和仿真分析中基于优化的统计不确定性量化

• 批准号: 1834710
• 负责人: Henry Lam
• 金额: $ 49.43万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-01 至 2023-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1834710&HistoricalAwards=false
• 关键词: CAREER; Optimization; based; Quantification; Statistical

This Faculty Early Career Development (CAREER) Program research project will create a systematic framework for designing, analyzing, and implementing statistical methods for uncertainty quantification that effectively integrate data into stochastic and simulation analyses. These analyses arise routinely in performance evaluations, risk analytics, and decision-making tasks in policymaking and many industries. The recent expansion of industrial system complexities challenges the use of conventional statistical methods in assimilating data, due to the heavy computational burden of high-fidelity simulation models, the intrinsic high dimensionality of stochastic problems, and the structural complications of data-system integration. The research program will blend the use of computational simulation with nonparametric statistics and modern optimization tools to produce methodologies that are both statistically accurate and computationally efficient. If successful, the research outcomes will aid in developing data-driven simulation-based tools for evaluating automated vehicle safety. The tools will be disseminated to relevant governmental and industrial units through institutional collaborative networks and online public channels. The research will also provide reliable, data-driven methodologies to assess risks and calibrate the simulation platforms used in various industries vital to the domestic economy. The education program will expand the undergraduate simulation curriculum, develop a new interdisciplinary graduate course, and provide practical case studies on the societal roles of the engineering profession. The education program will also provide training for graduate students and create undergraduate research opportunities, especially for under-represented minorities in engineering and data science.The specific research objectives will develop statistical uncertainty quantification methods in four fundamental problems in stochastic and simulation analyses: 1) Rare-event prediction and computation; 2) Propagation of input model errors in simulation analysis; 3) Calibration of stochastic input models from output data; and 4) Quantification and enrichment of the feasibility of obtained solutions in data-driven stochastic optimization. Each problem presents distinct challenges arising from small-sample bias, immense computational burden, high dimensionality, or over-conservativeness that impedes the effectiveness of existing methods. The research will emphasize a unified framework to generate performance estimates using new formulations and analyses of optimization programs posited over stochastic spaces, with constraints derived or justified via nonparametric statistical methods. The research will encompass the development of confidence bounds and the quantification of robustness to model misspecification, and the algorithmic analyses that ensure computational tractability in terms of optimization and simulation efficiencies. The techniques developed will cross-fertilize areas across Monte Carlo simulation, stochastic and robust optimization, and statistics. The research outcomes will also equip next-generation engineers with multi-faceted perspectives in using computational and statistical tools that will benefit their future careers.

该教师早期职业发展（CAREER）计划研究项目将创建一个系统的框架，用于设计，分析和实施不确定性量化的统计方法，有效地将数据集成到随机和模拟分析中。这些分析经常出现在政策制定和许多行业的绩效评估、风险分析和决策任务中。最近工业系统的复杂性的扩展挑战使用传统的统计方法在同化数据，由于高保真仿真模型，随机问题的内在高维的沉重的计算负担，和数据系统集成的结构复杂性。该研究计划将结合使用计算模拟与非参数统计和现代优化工具，以产生统计准确和计算效率高的方法。如果成功，研究成果将有助于开发基于数据驱动的仿真工具，以评估自动驾驶汽车的安全性。这些工具将通过机构合作网络和在线公共渠道传播给相关的政府和行业单位。该研究还将提供可靠的数据驱动方法，以评估风险并校准对国内经济至关重要的各个行业所使用的模拟平台。该教育计划将扩大本科模拟课程，开发新的跨学科研究生课程，并提供有关工程专业社会角色的实际案例研究。该教育计划还将为研究生提供培训，并为本科生创造研究机会，特别是为工程和数据科学领域代表性不足的少数民族创造机会。具体研究目标将在随机和模拟分析中的四个基本问题中发展统计不确定性量化方法：1）稀有事件预测和计算; 2）模拟分析中输入模型误差的传播; 3）根据输出数据校准随机输入模型;以及4）量化和丰富数据驱动随机优化中获得的解决方案的可行性。 每个问题都提出了不同的挑战，小样本偏差，巨大的计算负担，高维，或过度保守，阻碍了现有方法的有效性。 该研究将强调一个统一的框架，以产生性能估计使用新的配方和分析的优化程序假设在随机空间，通过非参数统计方法导出或证明的约束。 该研究将包括发展的置信界限和量化的鲁棒性模型的误设定，并在优化和仿真效率方面的算法分析，以确保计算的易处理性。 开发的技术将交叉施肥领域在蒙特卡洛模拟，随机和强大的优化，统计。 研究成果还将使下一代工程师在使用计算和统计工具方面具有多方面的观点，这将有利于他们未来的职业生涯。

项目成果

SAMPLING UNCERTAIN CONSTRAINTS UNDER PARAMETRIC DISTRIBUTIONS

• DOI: 10.1109/wsc.2018.8632432
• 发表时间: 2018-12
• 期刊: 2018 Winter Simulation Conference (WSC)
• 作者: H. Lam;Fengpei Li

Doubly Robust Stein-Kernelized Monte Carlo Estimator: Simultaneous Bias-Variance Reduction and Supercanonical Convergence

• 发表时间: 2021-10
• 期刊: J. Mach. Learn. Res.
• 作者: H. Lam;Haofeng Zhang

Calibrating Input Parameters via Eligibility Sets

通过资格集校准输入参数

• DOI: 10.1109/wsc48552.2020.9383885
• 发表时间: 2020
• 期刊: Winter Simulation Conference
• 作者: Bai, Yuanlu;Lam, Henry
• 通讯作者: Lam, Henry

ON EFFICIENCIES OF STOCHASTIC OPTIMIZATION PROCEDURES UNDER IMPORTANCE SAMPLING

• DOI: 10.1109/wsc.2018.8632321
• 发表时间: 2018-12
• 期刊: 2018 Winter Simulation Conference (WSC)
• 作者: H. Lam;Guangxin Jiang;M. Fu

Batching on biased estimators

对有偏估计量进行批处理

• 发表时间: 2022
• 期刊: Proceedings of the Winter Simulation Conference (WSC
• 作者: He, Shengyi;Lam, Henry
• 通讯作者: Lam, Henry