Wasserstein Generative Regression
This addresses the problem of flexible regression and conditional sampling for researchers and practitioners, offering a novel method but with incremental improvements over existing generative frameworks.
The paper tackles nonparametric regression and conditional distribution learning by proposing a unified approach that simultaneously estimates a regression function and a conditional generator using deep neural networks, with results including theoretical guarantees and demonstrated effectiveness in numerical experiments.
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.