# Quantile Regression Neural Networks: A Bayesian Approach

arXiv: https://arxiv.org/abs/2009.13591 · HTML: https://mlsanity.com/paper/2009.13591/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2020.

## Built on by (most cited first, 5 of 5)

- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Uncertainty Quantification in Machine Learning for Biosignal Applications -- A Review](https://mlsanity.com/paper/2312.09454/) (2023)
- [Deep Huber quantile regression networks](https://mlsanity.com/paper/2306.10306/) (2023)
- [LogGENE: A smooth alternative to check loss for Deep Healthcare Inference Tasks](https://mlsanity.com/paper/2206.09333/) (2022)
- [Sequential sparse Gaussian process quantile regression](https://mlsanity.com/paper/2606.31284/) (2026)

## Abstract (arXiv)

This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) for the response variable. It is shown that the posterior distribution for feedforward neural network quantile regression is asymptotically consistent under a misspecified ALD model. This consistency proof embeds the problem from density estimation domain and uses bounds on the bracketing entropy to derive the posterior consistency over Hellinger neighborhoods. This consistency result is shown in the setting where the number of hidden nodes grow with the sample size. The Bayesian implementation utilizes the normal-exponential mixture representation of the ALD density. The algorithm uses Markov chain Monte Carlo (MCMC) simulation technique - Gibbs sampling coupled with Metropolis-Hastings algorithm. We have addressed the issue of complexity associated with the afore-mentioned MCMC implementation in the context of chain convergence, choice of starting values, and step sizes. We have illustrated the proposed method with simulation studies and real data examples.