Distributional Refinement Network: Distributional Forecasting via Deep Learning

TL;DR

The paper introduces the Distributional Refinement Network (DRN), a novel deep learning approach that enhances distributional forecasting by combining interpretable models with neural networks, improving accuracy while maintaining interpretability.

Contribution

It proposes the DRN, a new model that refines baseline distributional models with neural networks, balancing flexibility, predictive power, and interpretability in actuarial forecasting.

Findings

DRN outperforms traditional models in distributional forecasting.

The approach effectively captures feature effects across all quantiles.

Demonstrated superior performance on synthetic and real data.

Abstract

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{\''u}thrich, 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.