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有效的现代假设测试来弥合两个基本领域 - 统计假设检验和深度学习。这种桥梁的好处是双向的：一方面，它将能够利用深度学习来开发高维和复杂数据的高效和强大的测试工具；另一方面，它支持使用测试方法为机器学习模型开发主要验证工具，并为深层模型本身提供理论基础。这项工作将解决在从数据中发现的基于深度学习的算法和可信赖的算法方面的关键挑战，类似于假设测试在过去几十年中所扮演的角色。调查人员将为研究生和本科生提供研究机会，并开发有关机器学习和数据科学的研究生级和本科课程的教学材料。该项目的理论和计算结果有望使工业，政府和国家实验室的研发有益。该研究项目针对统计假设检验的尖端研究领域的基本挑战。主题包括可靠的假设检验，非参数测试（高维设置），拟合优点，顺序测试（包括顺序更改点检测）以及非本质上独立分区的测试（I.I.D.）数据。研究计划由四个高度集成的推力组成：（1）开发基于深度学习的强大假设检验，提供绩效保证，并开发有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，以利用数据中的低维结构。 （3）为深度学习模型（例如合适性测试）开发模型诊断工具。 （4）为顺序和观察数据开发基于学习的假设检验（non-i.i.d。）。研究中的问题的答案还将使几个紧密相关的领域受益，包括强大的机器学习和域适应性。预计这项研究将为广泛的应用提供强大的工具，并在其他科学和工程领域（例如单细胞RNA测序数据分析），监测关键的国家基础设施，例如电网和网络，智能逻辑网络以及疾病爆发发现。该研究组件将与教育活动紧密整合。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响标准来评估，被认为是宝贵的支持。

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