Wasserstein generative regression
提出一种统一方法，同时估计回归函数和条件生成器，用深度神经网络建模，适用于多变量结果和协变量，能构建预测区间，并提供理论保证。
Abstract 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.