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

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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.