# Deep Quantile and Deep Composite Model Regression

arXiv: https://arxiv.org/abs/2112.03075 · HTML: https://mlsanity.com/paper/2112.03075/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2021.

## Built on by (most cited first, 3 of 3)

- [Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning](https://mlsanity.com/paper/2206.14666/) (2022)
- [Distributional Refinement Network: Distributional Forecasting via Deep Learning](https://mlsanity.com/paper/2406.00998/) (2024)
- [A Quantile Regression Approach for Remaining Useful Life Estimation with State Space Models](https://mlsanity.com/paper/2506.17018/) (2025)

## Abstract (arXiv)

A main difficulty in actuarial claim size modeling is that there is no simple off-the-shelf distribution that simultaneously provides a good distributional model for the main body and the tail of the data. In particular, covariates may have different effects for small and for large claim sizes. To cope with this problem, we introduce a deep composite regression model whose splicing point is given in terms of a quantile of the conditional claim size distribution rather than a constant. To facilitate M-estimation for such models, we introduce and characterize the class of strictly consistent scoring functions for the triplet consisting a quantile, as well as the lower and upper expected shortfall beyond that quantile. In a second step, this elicitability result is applied to fit deep neural network regression models. We demonstrate the applicability of our approach and its superiority over classical approaches on a real accident insurance data set.