Paper: arXiv 2301.12710

Authors: Benjamin Avanzi, Greg Taylor, Melantha Wang, Bernard Wong

Abstract

High-cardinality categorical features are pervasive in actuarial data (e.g. occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings. In this work, we present a novel Generalised Linear Mixed Model Neural Network (“GLMMNet”) approach to the modelling of high-cardinality categorical features. The GLMMNet integrates a generalised linear mixed model in a deep learning framework, offering the predictive power of neural networks and the transparency of random effects estimates, the latter of which cannot be obtained from the entity embedding models. Further, its flexibility to deal with any distribution in the exponential dispersion (ED) family makes it widely applicable to many actuarial contexts and beyond. We illustrate and compare the GLMMNet against existing approaches in a range of simulation experiments as well as in a real-life insurance case study. Notably, we find that the GLMMNet often outperforms or at least performs comparably with an entity embedded neural network, while providing the additional benefit of transparency, which is particularly valuable in practical applications. Importantly, while our model was motivated by actuarial applications, it can have wider applicability. The GLMMNet would suit any applications that involve high-cardinality categorical variables and where the response cannot be sufficiently modelled by a Gaussian distribution.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel architecture (GLMMNet) combining neural networks with Generalised Linear Mixed Models for high-cardinality features, bridging classical actuarial theory and modern deep learning. Its performance is rigorously validated across both synthetic simulations and a real-world insurance dataset, providing strong interpretability alongside predictive power.

Research Flowchart

  flowchart TD
    A["Research Goal: Effectively model high-cardinality categorical features in non-Gaussian actuarial data"] --> B["Develop GLMMNet: Integrate GLMM random effects into a Deep Learning framework"]
    B --> C["Supported Inputs: High-cardinality categoricals & Exponential Dispersion family distributions"]
    C --> D["Benchmarking & Evaluation: Test GLMMNet against One-Hot and Entity Embedding models"]
    D --> E["Data Applications: Synthetic Simulation Experiments & Real-life Insurance Case Study"]
    E --> F["Key Outcomes: Superior/comparable predictive power with enhanced model transparency"]