Statistical Entropic Optimal Transport: Theory, Methods and Applications

Optimal transport provides a sensible mathematical framework to address the fundamental statistical question of how a statistician measures the distance between two distributions based on possibly large high-dimensional datasets. A variation of the original transportation problem featuring an entropic penalization has appeared as a more scalable alternative, fueling a wave of new results and successful applications in domains such as genomics, neuroscience, and economics, to name a few. Despite its practical success and the achieved understanding of some of its fundamental statistical properties, there is still a substantial gap between theory and practice in the entropic optimal transport framework. This project will bridge this gap through new methods grounded in an improved theoretical understanding of entropic optimal transport, potentially generating an innovative set of applications in the life sciences. Graduate students will be trained within the scope of this project. The core of this project focuses on two intimately related thrusts: first, to develop a foundation for inference in parametric models with entropic optimal transport and to identify the regimes for which this framework is best suited. This includes the problem of model-based clustering in high-dimensional, non-asymptotic regimes and a study of the robustness of entropic-optimal-transport estimators. Second, the PIs will develop statistical applications of entropic optimal transport in Alzheimer’s disease neuropathology and spatial transcriptomics. 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.