Wasserstein Generative Regression

TL;DR

This paper introduces a unified deep learning framework for nonparametric regression and conditional distribution learning, leveraging Wasserstein distances to improve estimation accuracy and construct prediction intervals.

Contribution

It proposes a novel approach that jointly estimates regression functions and conditional generators using neural networks, with theoretical guarantees and practical advantages.

Findings

Outperforms existing methods in simulated data scenarios

Provides non-asymptotic error bounds and distributional consistency

Effective in multivariate outcome and covariate settings

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 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.