Generative Modelling via Quantile Regression

2024/09/06 by Johannes Schmidt-Hieber, Petr Zamolodtchikov, Schmidt-Hieber, Johannes +1 · 2 citations
Computer Science · #62C20 (Secondary) #62G08 (Primary) #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2409.04231

openalex publication_date 2024/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Generative Quantile Bayesian Prediction
• Error Analysis of Neural-Network-Based Engression

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