Numerical Construction of Optimal Estimators Using Machine Learning Tools

使用机器学习工具数值构建最优估计器

• 批准号: 2210216
• 负责人: Alex Luedtke
• 金额: $ 17.5万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-15 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210216&HistoricalAwards=false
• 关键词: Numerical; Construction; Optimal; Estimators; Using

Optimal statistical procedures make maximal use of available data, making it possible to answer pressing scientific questions more precisely and cost-effectively. These procedures are traditionally derived via analytic calculations that require expert knowledge achieved over many years of training. In this project, the investigators will study two novel strategies for deriving optimal procedures. Compared to existing approaches, these strategies require more expertise in computational methods and less expertise in statistical theory. As a result, this project will broaden the pool of researchers who can develop optimal statistical procedures. If preliminary results support the strong performance of the new methods, the investigators will incorporate them into vaccine clinical trial data analyses. Through this project, the investigators will engage undergraduates in statistical research and advance the understanding of mentored graduate students.The investigators will consider both local and global notions of optimality. The first strategy will use novel representations of the efficient influence function (EIF). The EIF is a critical ingredient for constructing asymptotically efficient estimators, particularly in nonparametric and semiparametric models. It also provides a principled approach to debias machine learning-based estimators to recover valid statistical inference. Unfortunately, the conventional approach for deriving the EIF involves advanced theory that is often not taught in statistical curricula. Additionally, in some problems, the EIF does not have a closed form, rendering its use difficult even for experts. The investigators will derive a novel representation of the EIF that lends itself to computerization and study how it can be used to derive novel asymptotically efficient estimators. The second strategy will use ideas from deep reinforcement learning, as used recently to build self-learning game playing algorithms with super-human performance, to adversarially learn (globally and locally) minimax optimal statistical procedures with computational tools. Except in simple cases, analytic calculations have thus far only been successfully used to derive estimators that are asymptotically minimax optimal. However, asymptotic optimality does not generally guarantee optimality in small samples. Existing works on numerically learning minimax optimal estimators use a Bayesian formulation of the minimax problem. This formulation results in learning schemes that are too computationally prohibitive to be applicable to most problems. This project will develop and study an alternative means to construct these estimators that can readily leverage massively parallel computing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

最佳统计程序可以最大程度地使用可用的数据，从而可以更精确，更具成本效益地回答科学问题。这些程序在传统上是通过分析计算得出的，这些计算需要多年的培训中实现的专家知识。在该项目中，研究人员将研究两种新的策略，以得出最佳程序。与现有方法相比，这些策略在计算方法方面需要更多的专业知识，并且在统计理论方面的专业知识较少。结果，该项目将扩大可以制定最佳统计程序的研究人员库。如果初步结果支持新方法的强劲性能，则研究人员将将其纳入疫苗临床试验数据分析中。通过该项目，调查人员将吸引本科生参与统计研究，并促进对受过指导研究生的理解。研究人员将考虑本地和全球最佳概念。第一个策略将使用有效影响函数（EIF）的新颖表示。 EIF是构建渐近高效估计器的关键要素，尤其是在非参数和半参数模型中。它还为基于Debias机器学习的估计器提供了一种原则性的方法，以恢复有效的统计推断。不幸的是，得出EIF的常规方法涉及经常在统计课程中教授的高级理论。此外，在某些问题中，EIF没有封闭的形式，即使对于专家来说也很难使用。研究人员将得出EIF的新型表示，该表示将其自身用于计算机化，并研究如何使用它来推导新型的渐近高效估计器。第二种策略将使用深度强化学习的想法，最近用来构建具有超人性能的自学习游戏玩算法，以对抗（全球和本地）使用计算工具来学习（全球和本地）最佳最佳统计过程。除了简单的情况外，迄今为止，分析计算仅被成功地用于得出渐近最小值的估计器。但是，渐近最优性通常不能保证小样本中的最佳性。现有的关于最小值最佳估计器的作品使用了最小问题的贝叶斯公式。这种表述导致学习方案在计算上过于刺激，无法适用于大多数问题。该项目将开发和研究一种替代手段，以构建这些估计值，这些估计值可以很容易地利用大规模平行的计算。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子优点和更广泛的影响评估标准，被认为值得通过评估。