Xiaoyu Chen: Distribution-in-distribution-out Regression

Abstract

Regression analysis with probability measures as input predictors and output response has recently drawn great attention. However, it is challenging to handle multiple input probability measures due to the non-flat Riemannian geometry of the Wasserstein space, hindering the definition of arithmetic operations, hence additive linear structure is not well-defined. In this talk, a distribution-in-distribution-out regression model is proposed by introducing parallel transport to achieve provable commutativity and additivity of newly defined arithmetic operations in Wasserstein space. The appealing properties of the DIDO regression model can serve as a foundation for model estimation, prediction, and inference. Specifically, the Fréchet least squares estimator is employed to obtain the best linear unbiased estimate, supported by the newly established Fréchet Gauss-Markov Theorem. Furthermore, we investigate a special case when predictors and response are all univariate Gaussian measures, leading to a simple close-form solution of linear model coefficients and R²metric. A simulation study and real case study in intra-operative cardiac output prediction are performed to evaluate the performance of the proposed method. Broader opportunities will be discussed.

Speaker: 

Dr. Xiaoyu Chen is an Assistant Professor of Industrial and Systems Engineering at the University at Buffalo. He received his Ph.D. from the Grado Department of Industrial and Systems Engineering and earned his M.Eng. degree in Computer Science from Virginia Tech in 2021. His research focused on statistical learning methodologies with applications to cybermanufacturing systems and perioperative medicine. Dr. Chen is a member of the Institute for Operations Research and the Management Sciences (INFORMS), the Institute of Industrial and Systems Engineering (IISE), and the Association for Computing Machinery (ACM). His ongoing research projects are funded by National Science Foundation, American Heart Association, America Makes, state government agency, and industry partners.

https://www.acsu.buffalo.edu/~xchen325/