Bridging Statistical Hypothesis Tests and Deep Learning for Reliability and Computational Efficiency

连接统计假设检验和深度学习以提高可靠性和计算效率

• 批准号: 2134037
• 负责人: Yao Xie
• 金额: $ 110万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2134037&HistoricalAwards=false
• 关键词: Bridging; Statistical; Hypothesis; Tests; Deep

This project aims to bridge two fundamental areas — statistical hypothesis testing and deep learning — through developing reliable machine learning and computationally efficient modern hypothesis tests. The benefit of such a bridge goes both ways: on the one hand, it will enable the leveraging of deep learning to develop efficient and powerful testing tools for high-dimensional and complex data; on the other hand, it supports the use of testing methodologies to develop principled validation tools for machine learning models and provide a theoretical foundation of deep models themselves. The work will address critical challenges in making deep learning-based algorithms applicable and trustworthy for making discoveries from data, akin to the role that hypothesis testing has played in the past decades. The investigators will provide research opportunities for graduate and undergraduate students and develop pedagogical materials for graduate-level and undergraduate-level courses on machine learning and data science. The theoretical and computational outcomes of the project are expected to benefit research and development in industry, government, and national labs. The research project targets fundamental challenges in the cutting-edge research areas of statistical hypothesis tests. The topics include robust hypothesis tests, non-parametric tests (high-dimensional setting), goodness-of-fit tests, sequential tests (including sequential change-point detection), and tests for non-identically-independently-districtbuted (i.i.d.) data. The research plan consists of four highly integrated thrusts: (1) Develop deep learning-based robust hypothesis tests, provide performance guarantees, and develop efficient computational methods to leverage modern optimization. (2) Develop deep-learning-based non-parametric two-sample tests that exploit low-dimensional structure in data. (3) Develop model diagnosis tools for deep learning models such as goodness-of-fit tests. (4) Develop learning-based hypothesis tests for sequential and observational data (non-i.i.d.). The answers to the questions under study will also benefit several closely related areas, including robust machine learning and domain adaptation. The research is expected to result in powerful tools for a wide range of applications and advance knowledge in other scientific and engineering domains such as single-cell RNA sequencing data analysis, monitoring critical national infrastructures such as power grids and networks, smart logistic networks, and disease outbreak detection. The research components will be tightly integrated with educational activities.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.

该项目旨在通过开发可靠的机器学习和计算高效的现代假设测试，在统计假设检验和深度学习这两个基本领域之间架起一座桥梁。这种桥梁的好处是双向的：一方面，它将使深度学习能够利用深度学习为高维和复杂数据开发高效而强大的测试工具；另一方面，它支持使用测试方法来开发机器学习模型的原则性验证工具，并为深度模型本身提供理论基础。这项工作将解决基于深度学习的算法在从数据中发现时适用和值得信赖的关键挑战，类似于假设检验在过去几十年中所发挥的作用。研究人员将为研究生和本科生提供研究机会，并为研究生和本科生水平的机器学习和数据科学课程开发教学材料。该项目的理论和计算结果预计将有利于工业、政府和国家实验室的研究和开发。该研究项目针对的是统计假设检验前沿研究领域的根本挑战。主题包括稳健假设检验、非参数检验(高维设置)、拟合度检验、序贯检验(包括序贯变点检测)和非相同-独立分区(I.I.D.)检验。数据。该研究计划包括四个高度集成的推进：(1)开发基于深度学习的稳健假设检验，提供性能保证，并开发高效的计算方法来利用现代优化。(2)开发基于深度学习的非参数两样本测试，利用数据中的低维结构。(3)开发适合深度学习模型的模型诊断工具，如拟合度检验。(4)为序贯数据和观测数据(非I.I.D.)开发基于学习的假设检验。正在研究的问题的答案也将使几个密切相关的领域受益，包括稳健的机器学习和领域适应。预计这项研究将产生广泛应用的强大工具，并促进其他科学和工程领域的知识，如单细胞RNA测序数据分析、监测电网和网络等关键国家基础设施、智能物流网络和疾病爆发检测。研究部分将与教育活动紧密结合。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets

• DOI: 10.1109/isit50566.2022.9834367
• 发表时间: 2022-02
• 期刊: 2022 IEEE International Symposium on Information Theory (ISIT)
• 作者: Jie Wang;Yao Xie

Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories

• DOI: 10.48550/arxiv.2306.14859
• 发表时间: 2023-06
• 期刊: ArXiv
• 作者: Zixuan Zhang;Minshuo Chen;Mengdi Wang;Wenjing Liao;Tuo Zhao

Non-stationary spatio-temporal point process modeling for high-resolution COVID-19 data

• DOI: 10.1093/jrsssc/qlad013
• 发表时间: 2023-03-28
• 期刊: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS
• 影响因子: 1.6
• 作者: Dong，Zheng;Zhu，Shixiang;Rodriguez-Cortes，Francisco J.
• 通讯作者: Rodriguez-Cortes，Francisco J.

Spatio-temporal point processes with deep non-stationary kernels

• DOI: 10.48550/arxiv.2211.11179
• 发表时间: 2022-11
• 期刊: ArXiv
• 作者: Zheng Dong;Xiuyuan Cheng;Yao Xie

Neural Spectral Marked Point Processes

• 发表时间: 2021-06
• 期刊: ArXiv
• 作者: Shixiang Zhu;Haoyun Wang;Xiuyuan Cheng;Yao Xie