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.

翻译：本文提出了一种用于非参数回归和条件分布学习的新颖统一方法。该方法通过生成学习框架同时估计回归函数和条件生成器，其中条件生成器是一个能够从条件分布中生成样本的函数。核心思想是估计一个满足约束条件（即能产生良好回归函数估计量）的条件生成器。我们采用深度神经网络对条件生成器进行建模。该方法可处理多变量结果和协变量问题，并能用于构建预测区间。我们在适当假设下推导出非渐近误差界和分布一致性，提供了理论保证。此外，通过模拟数据和真实数据的数值实验，证明该方法在多种场景下相较于现有方法具有有效性和优越性。