# Model-aware Quantile Regression for Discrete Data

arXiv: https://arxiv.org/abs/1804.03714 · HTML: https://mlsanity.com/paper/1804.03714/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [The Earth Mover's Pinball Loss: Quantiles for Histogram-Valued Regression](https://mlsanity.com/paper/2106.02051/) (2021)

## Abstract (arXiv)

Quantile regression relates the quantile of the response to a linear predictor. For a discrete response distributions, like the Poission, Binomial and the negative Binomial, this approach is not feasible as the quantile function is not bijective. We argue to use a continuous model-aware interpolation of the quantile function, allowing for proper quantile inference while retaining model interpretation. This approach allows for proper uncertainty quantification and mitigates the issue of quantile crossing. Our reanalysis of hospitalisation data considered in Congdon (2017) shows the advantages of our proposal as well as introducing a novel method to exploit quantile regression in the context of disease mapping.