AF: Small: Faster Algorithms for High-Dimensional Robust Statistics

AF：小：用于高维稳健统计的更快算法

• 批准号: 2307106
• 负责人: Yu Cheng
• 金额: $ 39.1万
• 依托单位: Brown University
• 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: 2022-11-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307106&HistoricalAwards=false
• 关键词: AF; Small; Faster; Algorithms; Dimensional

As machine learning plays a more prominent role in our society, there is a need for learning algorithms that are reliable and robust. In modern machine learning, one often needs to work with data that are high-dimensional and noisy. Recent work gave the first efficient robust estimators for several basic statistical problems, and since then, there has been a flurry of research that obtained efficient robust algorithms for many machine-learning problems. However, one major drawback of existing algorithms in the literature is that they tend to be much slower when compared to their non-robust counterparts, or they often involve parameters that require careful tuning. To address these issues, this project aims to (i) design faster and provably robust algorithms for a wide range of high-dimensional statistical and learning tasks, and (ii) explore non-convex formulations of robust estimation and analyze their optimization landscape. This project will advance the fields of computer science and statistics, and also potentially lead to useful tools for other areas. The pursuit of faster and simpler algorithms will help accelerate technology transfer into practice, stimulate systematic approaches to robustness, and provide a positive societal impact in the long run. The education plan of this project includes incorporating the materials generated from this project into graduate-level courses at the University of Illinois at Chicago (UIC), as well as training graduate and undergraduate students at UIC, which is an urban university with a diverse student population.Designing robust algorithms in high dimensions is a very challenging task. Even for the basic problem of mean estimation, when a small fraction of the input is adversarially corrupted, no efficient algorithms were known until recently. The first polynomial-time estimators with dimension-independent error guarantees were discovered in 2016. However, given the amount of data available today, polynomial-time no longer translates to scalability in practice. Motivated by the need for faster and more practical algorithms, this project focuses on two main thrusts to expand the area of algorithmic high-dimensional robust statistics. First, the investigator would like to speed up existing algorithms and develop new robust algorithms for a broader range of problems and richer families of distributions, with the ultimate goal of matching the runtime of the fastest non-robust algorithms. Second, the investigator wants to design robust estimators that can be computed via standard first-order optimization methods. The main challenge is to find an objective function whose gradient can be evaluated using basic matrix operations while proving the structural result that this objective has no bad local optima. Concretely, the investigator plans to work on these two thrusts by targeting various aspects of the following problems: (1) robust stochastic optimization, (2) robust sparse mean estimation and sparse PCA, (3) robust covariance estimation, (4) list-decodable learning, and (5) robust learning of Bayesian networks. This project is interdisciplinary and will rely on intuition and techniques from statistics, probability, linear algebra, discrete and continuous optimization, and non-convex optimization.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.

随着机器学习在我们的社会中发挥着越来越重要的作用，需要可靠且稳健的学习算法。在现代机器学习中，人们经常需要处理高维且有噪声的数据。最近的工作为几个基本统计问题提供了第一个有效的鲁棒估计器，从那时起，出现了一系列的研究，为许多机器学习问题获得了有效的鲁棒算法。然而，文献中现有算法的一个主要缺点是，与非鲁棒算法相比，它们往往要慢得多，或者它们经常涉及需要仔细调整的参数。为了解决这些问题，该项目的目标是（i）为各种高维统计和学习任务设计更快且可证明稳健的算法，以及（ii）探索稳健估计的非凸公式并分析其优化前景。该项目将推动计算机科学和统计学领域的发展，并有可能为其他领域带来有用的工具。追求更快、更简单的算法将有助于加速技术转化为实践，激发系统方法的鲁棒性，并从长远来看产生积极的社会影响。该项目的教育计划包括将该项目产生的材料纳入伊利诺伊大学芝加哥分校（UIC）的研究生水平课程中，以及在UIC（一所学生多元化的城市大学）培训研究生和本科生。设计高维度的鲁棒算法是一项非常具有挑战性的任务。即使对于均值估计的基本问题，当一小部分输入被对抗性破坏时，直到最近才知道有效的算法。第一个具有维度无关误差保证的多项式时间估计器于 2016 年被发现。然而，考虑到当今可用的数据量，多项式时间在实践中不再转化为可扩展性。出于对更快、更实用算法的需求，该项目侧重于扩展算法高维鲁棒统计领域的两个主要目标。首先，研究人员希望加快现有算法的速度，并为更广泛的问题和更丰富的分布族开发新的鲁棒算法，最终目标是匹配最快的非鲁棒算法的运行时间。其次，研究人员希望设计可以通过标准一阶优化方法计算的稳健估计器。主要挑战是找到一个可以使用基本矩阵运算评估梯度的目标函数，同时证明该目标没有不良局部最优的结构结果。 具体来说，研究者计划通过针对以下问题的各个方面来研究这两个主旨：（1）鲁棒随机优化，（2）鲁棒稀疏均值估计和稀疏PCA，（3）鲁棒协方差估计，（4）列表-可解码学习，以及（5）贝叶斯网络的稳健学习。该项目是跨学科的，将依赖于统计学、概率、线性代数、离散和连续优化以及非凸优化的直觉和技术。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值进行评估，被认为值得支持以及更广泛的影响审查标准。

项目成果

Robust Matrix Sensing in the Semi-Random Model

半随机模型中的鲁棒矩阵传感

• 发表时间: 2023
• 期刊: Proceedings of the 37th Conference on Neural Information Processing Systems
• 作者: Gao, Xing;Cheng, Yu
• 通讯作者: Cheng, Yu

Outlier-Robust Sparse Estimation via Non-Convex Optimization

通过非凸优化的异常值稳健稀疏估计

• 发表时间: 2022
• 期刊: Conference on Neural Information Processing Systems
• 作者: Cheng, Yu;Diakonikolas, Ilias;Ge, Rong;Gupta, Shivam;Kane, Daniel M.;Soltanolkotabi, Mahdi
• 通讯作者: Soltanolkotabi, Mahdi

Robust Second-Order Nonconvex Optimization and Its Application to Low Rank Matrix Sensing

• DOI: 10.48550/arxiv.2403.10547
• 发表时间: 2024-03
• 期刊: ArXiv
• 作者: Shuyao Li;Yu Cheng;Ilias Diakonikolas;Jelena Diakonikolas;Rong Ge;Stephen J. Wright

Tight Lower Bounds for Directed Cut Sparsification and Distributed Min-Cut

定向切割稀疏化和分布式最小切割的严格下界

• 发表时间: 2024
• 期刊: Proceedings of the 43rd ACM Symposium on Principles of Database Systems
• 作者: Cheng, Yu;Li, Max;Lin, Honghao;Tai, Zi-Yi;Woodruff, David P.;Zhang, Jason
• 通讯作者: Zhang, Jason

Efficiently Solving Turn-Taking Stochastic Games with Extensive-Form Correlation

有效解决具有广泛形式相关性的轮流随机博弈

• DOI: 10.1145/3580507.3597665
• 发表时间: 2023
• 期刊: Proceedings of the 24th ACM Conference on Economics and Computation
• 作者: Zhang, Hanrui;Cheng, Yu;Conitzer, Vincent
• 通讯作者: Conitzer, Vincent