Generative Quantile Bayesian Prediction

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.