CAREER: Robust and Efficient Algorithms for Statistical Estimation and Inference

职业：用于统计估计和推理的稳健且高效的算法

基本信息

批准号：
2045068
负责人：
Stanislav Minsker
金额：
$ 40万
依托单位：
University of Southern California
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2026-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2045068&HistoricalAwards=false
关键词：
CAREER Robust Efficient Algorithms Statistical

项目摘要

Statistical and machine learning methods are useful for making data-driven decisions. These methods are particularly advantageous in the presence of uncertainty originating from measurement errors or randomness inherent to the data collection process itself. The principal investigator (PI) will pursue a research program to develop statistical and machine learning methods possessing two important characteristics, robustness and efficiency. Robust algorithms are characterized by their ability to perform well even when some of the data are not accurate and clean but instead are "outliers," such as completely irrelevant or grossly corrupted measurements. Robust techniques can help to reduce the amount of resources spent on human-supervised data cleaning and preprocessing. On the other hand, methods that are efficient are able to extract most of the useful information contained in the data, therefore reducing the amount of uncertainty in the data-guided decision. This research program will be integrated with educational activities that, among other things, will expose undergraduate and graduate students to cutting edge approaches in statistics and machine learning, and give students an opportunity to serve as individual tutors and mentors at local K-12 schools.One part of the research program is devoted to investigation of the connections between self-normalized sums and robust statistical techniques. In particular, the PI will demonstrate that, unlike many existing approaches, algorithms based on the self-normalized sums often give rise to efficient methods, for instance in the context of univariate and multivariate mean estimation. Analysis of such algorithms is closely related to the theory self-normalized processes. Another part of the research focuses on the asymptotic properties of U-statistics of growing order, and the implications of these properties for robust and efficient empirical risk minimization (ERM), one of the key principles underlying modern mathematical statistics and machine learning algorithms. The PI will introduce a new approach to robust ERM and will relate questions about efficiency of resulting algorithms to purely mathematical questions in the theory of U-statistics. Finally, the research will address uncertainly quantification in robust statistics using Bayesian methods. Specifically, the PI aims to develop new robust analogues of the standard posterior distribution based on U-statistics of growing order, and will investigate the asymptotic behavior of these robust posteriors as well as the asymptotic frequentist properties of the corresponding credible sets.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.

统计和机器学习方法对于做出数据驱动的决策很有用。在存在数据收集过程本身固有的测量误差或随机性的情况下，这些方法尤其有利。首席研究员（PI）将遵循一项研究计划，以开发具有两个重要特征，鲁棒性和效率的统计和机器学习方法。强大的算法的特征是它们的表现能力即使某些数据不准确和清洁，但是“离群值”，例如完全无关紧要或严重损坏的测量值。强大的技术可以帮助减少在人类监督数据清洁和预处理上花费的资源数量。另一方面，有效的方法能够提取数据中包含的大多数有用信息，从而减少了数据引导决策中的不确定性数量。该研究计划将与教育活动融合，除其他外，这些活动将使本科生和研究生在统计和机器学习方面采用最先进的方法，并为学生提供一个在本地K-12学校的个人导师和导师的机会。研究计划的一部分致力于研究自我分类的总和和强大的统计技术之间的联系。特别是，PI将证明，与许多现有的方法不同，基于自称的总和通常会产生有效的方法，例如在单变量和多变量平均值估计的背景下，算法通常会产生有效的方法。这种算法的分析与理论自相应过程密切相关。研究的另一部分侧重于增长秩序的U统计量的渐近性质，以及这些特性对可靠和有效的经验风险最小化（ERM）的含义，这是现代数学统计和机器学习算法的基本关键原则之一。 PI将引入一种新的方法来进行鲁棒性ERM，并将有关导致算法的效率与U统计理论中的纯粹数学问题联系起来。最后，该研究将使用贝叶斯方法解决鲁棒统计数据中不确定的量化。具体而言，PI旨在基于增长的秩序的U统计数据来开发标准后部分布的新的鲁棒类似物，并将调查这些可靠的稳定后代的渐近行为以及相应可靠的集合的渐近频繁属性的渐近性频繁属性。这些奖项是NSF的法定任务，反映了通过评估的范围的范围，这是由构成构成的范围及其范围的范围。