# Distributional Refinement Network: Distributional Forecasting via Deep Learning

arXiv: https://arxiv.org/abs/2406.00998 · HTML: https://mlsanity.com/paper/2406.00998/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities](https://mlsanity.com/paper/2002.05777/) (2020)
- [Explainability is NOT a Game](https://mlsanity.com/paper/2307.07514/) (2023)
- [Deep Distribution Regression](https://mlsanity.com/paper/1903.06023/) (2019)
- [LocalGLMnet: interpretable deep learning for tabular data](https://mlsanity.com/paper/2107.11059/) (2021)
- [Stochastic loss reserving with mixture density neural networks](https://mlsanity.com/paper/2108.07924/) (2021)
- [Deep Quantile and Deep Composite Model Regression](https://mlsanity.com/paper/2112.03075/) (2021)
- [Mixture composite regression models with multi-type feature selection](https://mlsanity.com/paper/2103.07200/) (2021)
- [Bivariate Distribution Regression with Application to Insurance Data](https://mlsanity.com/paper/2203.12228/) (2022)

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

- [An Interpretable Deep Learning Model for General Insurance Pricing](https://mlsanity.com/paper/2509.08467/) (2025)

## Abstract (arXiv)

A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but challenges remain in developing models that can (i) allow covariates to flexibly impact different aspects of the conditional distribution, (ii) integrate developments in machine learning and AI to maximise the predictive power while considering (i), and, (iii) maintain a level of interpretability in the model to enhance trust in the model and its outputs, which is often compromised in efforts pursuing (i) and (ii). We tackle this problem by proposing a Distributional Refinement Network (DRN), which combines an inherently interpretable baseline model (such as GLMs) with a flexible neural network-a modified Deep Distribution Regression (DDR; Li et al., 2019) method. Inspired by the Combined Actuarial Neural Network (CANN; Schelldorfer and W''uthrich, 2019), our approach flexibly refines the entire baseline distribution. As a result, the DRN captures varying effects of features across all quantiles, improving predictive performance while maintaining adequate interpretability. Using both synthetic and real-world data, we demonstrate the DRN's superior distributional forecasting capacity. The DRN has the potential to be a powerful distributional regression model in actuarial science and beyond.