Bayesian Non-parametric Quantile Process Regression and Estimation of Marginal Quantile Effects

TL;DR

This paper introduces a flexible Bayesian non-parametric method combining splines and neural networks to estimate all conditional quantiles simultaneously, ensuring non-crossing and capturing complex relationships in high-dimensional data.

Contribution

It presents a novel model that estimates the entire conditional quantile function using splines and neural networks, improving flexibility, scalability, and uncertainty quantification over existing methods.

Findings

Better recovery of quantiles in sparse data scenarios

Effective estimation of marginal quantile effects

Scalable to high-dimensional covariate spaces

Abstract

Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to simultaneously estimate non-crossing, non-linear quantile curves. We expand the conditional distribution function of the response in I-spline basis functions where the covariate-dependent coefficients are modeled using neural networks. By leveraging the approximation power of splines and neural networks, our model can approximate any continuous quantile function. Compared to existing models, our model estimates all rather than a finite subset of quantiles, scales well to high dimensions, and accounts for estimation uncertainty. While the model is arbitrarily flexible, interpretable marginal quantile effects are estimated using accumulative local effect plots and variable importance measures. A simulation study shows that our model can better recover quantiles of the response distribution when the data is sparse, and an analysis of birth weight data is presented.