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

该项目旨在通过开发可靠的机器学习和计算效率高的现代假设检验，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，它将使深度学习能够为高维和复杂的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为机器学习模型开发有原则的验证工具，并为深度模型本身提供理论基础。这项工作将解决关键挑战，使基于深度学习的算法适用于从数据中发现，并值得信赖，类似于假设检验在过去几十年所扮演的角色。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发展。该研究项目针对统计假设检验的前沿研究领域的基本挑战。主题包括稳健假设检验、非参数检验（高维设置）、拟合优度检验、序列检验（包括序列变化点检测）和非同独立分布（i.i.d）数据的检验。该研究计划包括四个高度集成的重点：(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双样本测试，利用数据中的低维结构。(3)开发深度学习模型的模型诊断工具，如拟合优度检验。(4)为顺序数据和观察数据（非i.i.d）制定基于学习的假设检验。正在研究的问题的答案也将有利于几个密切相关的领域，包括强大的机器学习和领域适应。该研究预计将为其他科学和工程领域的广泛应用提供强大的工具，并推进知识，如单细胞RNA测序数据分析，监测关键的国家基础设施，如电网和网络，智能物流网络，以及疾病爆发检测。研究部分将与教育活动紧密结合。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.