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 that satisfies 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 non-asymptotic error bounds and the distributional consistency of our approach under suitable assumptions. We also perform numerical experiments with simulated and real data to demonstrate the effectiveness and superiority of our approach over some existing approaches in various scenarios.

提出一种新的非参数回归和条件分布学习的统一方法，该方法可以通过生成学习框架同时估计回归函数和条件生成器，使用深度神经网络模型来构建条件生成器，并能够处理多元结果和协变量问题，可以用于构建预测区间，并提供了理论保证以及在模拟和真实数据上的数值实验结果。

Wasserstein生成回归