Distributional Refinement Network: Distributional Forecasting via Deep Learning

Paper: arXiv 2406.00998

Authors: Benjamin Avanzi, Eric Dong, Patrick J. Laub, Bernard Wong

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.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel Distributional Refinement Network (DRN) that effectively bridges interpretable parametric models (GLMs) with flexible deep learning architectures (DDR/CANN) for probabilistic forecasting. It features strong empirical validation using both synthetic and real-world actuarial claims data, balancing statistical rigour with practical interpretability.

Research Flowchart

  flowchart TD
    A[Research Goal: Flexible, Interpretable Distributional Forecasting] --> B[Inputs: Features/Covariates & Synthetic/Real-world Data]
    B --> C[Baseline Model: Interpretable GLMs]
    B --> D[Refinement Model: Modified Deep Distribution Regression]
    C & D --> E[Computational Process: Distributional Refinement Network Hybrid Engine]
    E --> F[Outputs: Quantile-varying Effects & Refined Loss Distributions]
    F --> G[Key Outcomes: Superior Predictive Power + Preserved Model Interpretability]