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.

这个教师早期职业发展（职业）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，以有效地将数据整合到随机和模拟分析中。这些分析通常在决策和许多行业的绩效评估，风险分析和决策任务中常规出现。由于高保真模拟模型的重大计算负担，随机问题的内在高维度以及数据系统集成的结构并发症，因此工业系统的最新扩展挑战了传统统计方法在吸收数据中的使用挑战。该研究计划将将计算模拟的使用与非参数统计和现代优化工具相结合，以生成既准确又有效率的方法。如果成功，研究结果将有助于开发基于数据驱动的模拟工具，以评估自动化车辆安全性。这些工具将通过机构协作网络和在线公共渠道传播到相关的政府和工业单位。该研究还将提供可靠的，数据驱动的方法来评估风险并校准对国内经济至关重要的各个行业中使用的模拟平台。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，并就工程专业的社会角色提供实用的案例研究。该教育计划还将为研究生提供培训并创造本科研究机会，尤其是针对代表性不足的工程和数据科学少数群体。具体的研究目标将在随机和模拟分析中四个基本问题中开发统计不确定性量化方法：1）罕见的预测和计算； 2）在模拟分析中传播输入模型误差； 3）从输出数据中校准随机输入模型； 4）在数据驱动的随机优化中获得的溶液的可行性定量和丰富。 每个问题都列出了由小样本偏见，巨大的计算负担，高维度或过度保存的不同挑战，从而阻碍了现有方法的有效性。 这项研究将强调一个统一的框架，以使用新的公式和优化程序的分析来生成绩效估计，该计划通过非参数统计方法得出或合理地提出或合理的优化程序。 这项研究将涵盖置信界的发展以及对模型错误指定的鲁棒性的量化以及算法分析，以确保根据优化和仿真效率来确保计算障碍性。 开发的技术将跨蒙特卡洛模拟，随机和强大的优化以及统计数据进行交叉施用。 研究结果还将为下一代工程师提供多方面的观点，即使用将使他们未来职业的计算和统计工具。

项目成果

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

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

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

Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization

• DOI: 10.1287/opre.2018.1786
• 发表时间: 2016-05
• 期刊: Oper. Res.
• 作者: H. Lam

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