CRII: III: Efficient and Robust Statistical Estimation from Nonlinear Compressed Measurements

CRII：III：通过非线性压缩测量进行高效且稳健的统计估计

基本信息

批准号：
1948133
负责人：
Jie Shen
金额：
$ 17.5万
依托单位：
Stevens Institute of Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-09-01 至 2023-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1948133&HistoricalAwards=false
关键词：
CRII III Efficient Robust Statistical

项目摘要

This project advances the nation's development in science and engineering by providing new theory and algorithms for knowledge discovery from high-dimensional data. High-dimensional estimation, a computational procedure that extracts the most useful information from a large pool of redundant or irrelevant features, has played fundamental roles in various areas such as medical imaging, biology, and climatology. However, the well-established estimation schemes degrade dramatically when the data have complex structures, or when they are contaminated due to hardware failures, programming errors, or cyber-attacks. The goal of this project is to significantly broaden the understanding of the fundamental limits of learning algorithms against different types of structures and data errors, to offer a complete guideline for robust algorithmic design, and to highlight the extent to which an intelligent system behaves reliably and consistently. Outputs, such as theoretical results, algorithm implementation, and reusable empirical data, are designed to support a wide range of researchers in machine learning, high-dimensional statistics, signal processing, biology, and other related fields.The project will be carried out by investigating the interplay of high-dimensional statistics, optimization, and learning theory. The investigator will develop a unified framework for nonlinear estimation in the high-dimensional regime, which uncovers parameter estimation from quantized measurements and learning with nonlinear activation functions in deep neural networks. In particular, to account for the nonlinear and possibly nonconvex nature, the investigator will develop efficient constrained optimization algorithms by leveraging inherent geometric structures into algorithmic design and theoretical analysis. Based on the unified framework and the established generic results, the investigator will revisit an ensemble of heuristic algorithms and will provide a theoretical justification on when and why they succeed in practice. Lastly, the investigator will design algorithms that are robust to various types of data corruption, such as adversarial noise, outlier, and malicious noise. To obtain a near-optimal dependence on the noise rate and data dimension in the sample complexity, a series of new statistical results will be established by leveraging tools from, and enriching theory in learning theory and robust statistics.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.

该项目通过从高维数据中提供知识发现的新理论和算法来推动国家在科学和工程方面的发展。高维估计是一种计算程序，从大量冗余或无关的功能中提取最有用的信息，在各个领域（例如医学成像，生物学和气候学）中扮演了基本角色。但是，当数据具有复杂的结构或由于硬件故障，编程错误或网络攻击而污染时，良好的估计方案显着降低了估计方案。该项目的目的是显着扩大对不同类型的结构和数据错误学习算法的基本局限性的理解，为鲁棒算法设计提供完整的指导，并强调智能系统可靠，一致地行事的程度。诸如理论结果，算法实施和可重复使用的经验数据之类的输出旨在支持机器学习，高维统计，信号处理，生物学和其他相关领域的广泛研究人员。该项目将通过研究高维统计，优化，优化和学习理论的互动来实现。研究者将在高维度中开发一个统一的框架，用于非线性估计，该框架从量化的测量值中发现了参数估计，并通过深层神经网络中的非线性激活功能进行了学习。特别是，为了说明非线性和可能的非概念性质，研究者将通过将固有的几何结构利用固有的几何结构进行算法设计和理论分析来开发有效的约束优化算法。基于统一的框架和既定的通用结果，研究人员将重新审视启发式算法的合奏，并将提供理论上的理由，以实践何时以及为什么成功。最后，研究者将设计对各种类型的数据损坏（例如对抗噪声，异常值和恶意噪声）的算法。为了获得样本复杂性中对噪声速率和数据维度的近乎最佳依赖，通过利用工具的工具并丰富了学习理论和强大统计的理论，将建立一系列新的统计结果。这项奖项反映了NSF的法定任务，并通过使用基金会的知识优点和广泛影响来评估，这是NSF的法定任务。