Generative Modelling via Quantile Regression

TL;DR

This paper introduces a novel approach to generative modeling by leveraging quantile regression, proposing a new loss function, analyzing convergence rates, and extending the framework to multivariate data generation.

Contribution

It establishes a theoretical connection between generative modeling and quantile regression, providing new loss functions and convergence analysis, and discusses multivariate extensions.

Findings

Derived minimax convergence rates under smoothness assumptions

Established a lower bound via nonparametric regression analogy

Discussed extensions to multivariate data generation

Abstract

We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To establish the lower bound, we show that nonparametric regression can be seen as a sub-problem of the considered generative modelling framework. Finally, we discuss extensions of our work to generate data from multivariate distributions.