Collaborative Research: III: Medium: Conditional Transport: Theory, Methods, Computation, and Applications

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Measuring the difference between probability distributions is a fundamental problem in statistics and machine learning (ML). It plays essential roles in many critical ML and artificial intelligence (AI) tasks, such as building deep generative models to synthesize realistic data and training deep reinforcement learning agents. The project’s novelties are 1) establishing Conditional Transport (CT) as a new statistical distance between probability distributions to address several key limitations of existing methods, 2) developing a new distribution-based learning framework with efficient approximate computation algorithms, and 3) applying CT to better solve modern ML/AI problems involving large-scale and high-dimensional data and models. The project’s impacts are 1) advancing distribution-based ML/AI fundamental research, and 2) enabling efficient and robust methods for the ML/AI applications in science, engineering, and bio-medicine, in particular in inverse materials design and multi-omics data analysis. The investigators will integrate the proposed research with training, education, and outreach activities for next-generation workforce development, by developing new ML/AI course materials to better prepare students and researchers at all levels with a diversified educational background, promoting diversity, equity, and inclusion with the emphasis on attracting talents from under-represented groups, with a special emphasis on broadening participation in interdisciplinary computing. This project aims to establish CT and its enabled distribution-based learning framework, which has the paradigm-shift potential to further advance ML/AI research with new models and inference algorithms. In particular, 1) theoretical understanding of CT will provide the foundation of this new learning framework with desired model representation power as well as learning stability. 2) Maximum likelihood estimation, Bayesian inference, and entropy regularized optimal transport will be revisited based on CT, enabling efficient Bayesian computation and optimization taking advantage of modern deep network models and stochastic gradient descent tools. 3) New and improved ML/AI models and inference algorithms will be developed for deep generative modeling, contrastive representation learning, and deep reinforcement learning to advance the state of the art. 4) Inverse materials design and multi-omics data analysis, two real-world applications that require reliable uncertainty quantification for consequent critical decision making, will showcase the advantages of the CT-based methods.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.