Machine Learning with High-Cardinality Categorical Features in Actuarial Applications

TL;DR

It is found that the GLMMNet often outperforms or at least performs comparably with an entity-embedded neural network in these settings, while providing the additional benefit of transparency, which is particularly valuable in practical applications.

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.

Figures (13)

• Figure 2.1: Architecture of GLMMNet
• Figure 3.1: Boxplots of out-of-sample performance metrics of the different models; GLMMNet highlighted in green. Each experiment is repeated 50 times, with 5,000 training observations and 2,500 testing observations each.
• Figure 3.2: True versus predicted densities for (selected) categories on the test set in experiment 1
• Figure 3.3: Boxplots of out-of-sample performance metrics of the different models in experiment 5 (middle; high noise Gaussian), shown with an $\ell_2$-regularised GLMMNet. Each experiment is repeated 50 times, with 5,000 training observations and 2,500 testing observations each.
• Figure 4.1: Histogram of claim amounts (on log scale). The $x$-axis numbers have been deliberately removed for confidentiality reasons.