Low-rank regularization of Fréchet regression models for distribution function response

Music City Center 

Fréchet regression has emerged as a promising approach for modeling non-Euclidean response variables associated with Euclidean covariates. In this talk, we propose an estimation method with low-rank regularization for global Fréchet regression models. Specifically focusing on distribution function responses, we demonstrate how this framework employs low-rank regularization to enhance the efficiency and accuracy of the model fit. The proposed method enables more robust modeling and estimation, particularly in high-dimensional settings. We present a detailed theoretical analysis of the large-sample properties of the proposed estimator. Numerical experiments further validate these theoretical results.

Fréchet regression

Low-rank regularization

Distribution function responses

Quantile function responses

Wasserstein space

Optimal transport 

Section on Statistical Computing