Wasserstein generative regression

• 成果类型: Article; Early Access
• 署名作者: Song, Shanshan; Wang, Tong; Shen, Guohao; Lin, Yuanyuan; Huang, Jian
• 署名单位: Tongji University; Tongji University; Chinese University of Hong Kong; Hong Kong Polytechnic University; Hong Kong Polytechnic University; Hong Kong Polytechnic University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf053
• 发表日期: 2025
• 关键词: CONDITIONAL DISTRIBUTION; Nonparametric Regression; neural-networks; dimensionality; models

摘要

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning framework, where a conditional generator is a function that can generate samples from a conditional distribution. The main idea is to estimate a conditional generator satisfying the constraint that it produces a good regression function estimator. We use deep neural networks to model the conditional generator. Our approach can handle problems with multivariate outcomes and covariates, and can be used to construct prediction intervals. We provide theoretical guarantees by deriving nonasymptotic error bounds and the distributional consistency of our approach under suitable assumptions. We perform numerical experiments to demonstrate the effectiveness and superiority of our approach over some existing approaches in various scenarios.