Statistical Optimal Transport and Geometric Data Analysis
Current approaches to Big Data (or high-dimensional and massive data) and associated computational tools have left behind modern applications, such as image processing and computer vision, where data are not collected and expressed as vectors of real numbers or points in Euclidean space. Thus, there is a pressing need for transferring the success of traditional data processing resources and developing new statistical techniques to accommodate more general types of data. Although there has been recent promising progress in computational optimal transport, understanding its fundamental strengths and limitations as a statistical tool is currently in its infancy. Professor Chen’s overarching research goal is to develop new computational and statistical techniques to analyze data that is more complex than the Euclidean space valued data via the optimal transport theory, and to provide strong theoretical support for the statistical optimal transport with applications to geometric data analysis.The proposed research is expected to provide key enabling technologies for high-impact applications in machine learning and data science such as brain image scans based on magnetic resonance imaging (MRI) data.