Generative Quantile Bayesian Prediction

TL;DR

This paper introduces Generative Quantile Bayesian Prediction (GQBP), a novel approach that directly learns predictive quantiles using generative models, offering advantages over existing methods in large-scale prediction tasks.

Contribution

The paper presents GQBP, a new generative approach for predictive quantile estimation that improves scalability and theoretical properties compared to conformal, fiducial, and marginal likelihood methods.

Findings

GQBP effectively estimates predictive quantiles in normal-normal models.

The method demonstrates advantages in causal inference scenarios.

GQBP outperforms some existing approaches in large-scale prediction tasks.

Abstract

Prediction is a central task of machine learning. Our goal is to solve large scale prediction problems using Generative Quantile Bayesian Prediction (GQBP).By directly learning predictive quantiles rather than densities we achieve a number of theoretical and practical advantages. We contrast our approach with state-of-the-art methods including conformal prediction, fiducial prediction and marginal likelihood. Our distinguishing feature of our method is the use of generative methods for predictive quantile maps. We illustrate our methodology for normal-normal learning and causal inference. Finally, we conclude with directions for future research.