PhD Defense Tessa Steensgaard

Title: Transparent and Fair Statistical Learning in Non-Life Insurance

Abstract
  This thesis consists of three independent manuscripts and an introductory chapter that places their contributions in the context of non-life insurance. The manuscripts address model interpretability, fairness, and customer portfolio evolution. All contributions are illustrated using relevant simulated and real-world data sets.
  First, we consider partial dependence (PD) functions, which form the basis of widely used model interpretation methods such as PD plots and SHAP values. We discuss how these methods can obscure interaction effects and build on recent work that uses PD functions to construct a functional decomposition separating main and higher-order interaction effects. We propose an efficient and consistent algorithm, FastPD, for estimating arbitrary PD functions for tree-based models. At a complexity comparable to literature benchmarks estimating SHAP values, FastPD estimates PD functions from which PD plots, SHAP values, and the functional decomposition can be obtained with little additional computational effort.
  Second, we consider the problem of predicting a response Y using features X in the presence of an auxiliary attribute A, when the distribution of (A,X) should not determine the prediction target. We call a prediction functional AX-invariant if it depends on the underlying distribution P only through PY|A,X and is therefore unaffected by the joint distribution of (A,X). Under suitable causal assumptions, we show that AX-invariance is a necessary condition for functional-level path-specific and interventional fairness and, under stronger assumptions, is equivalent to these fairness notions. We characterise AX-invariant estimands and develop an asymptotic test for falsifying AX-invariance from observed data.
   Finally, we consider the evolution of an insurance customer’s product portfolio, where products are purchased and cancelled over time until the customer fully churns. Motivated by the assumption that these events cluster in time, we propose a fully parametric bivariate Hawkes process in which purchases and cancellations are modelled as mutually exciting counting processes. Customer and portfolio characteristics enter through covariates, while the specific products added or dropped are represented by marks. We further implement a simulation algorithm based on thinning that generates event histories from the fitted model parameters, allowing entire future portfolio trajectories to be simulated and evaluated.

Principal supervisor:, Associate Professor Munir Hiabu, University of Copenhagen
Co-supervisor: Professor Mogens Steffensen, University of Copenhagen
Co-supervisor: Associate Professor Christian Furrer, University of Copenhagen

Assessment committee:
Associate Professor Martin Bladt (Chair),University of Copenhagen
Professor Montserrat Guill´en, University of Barcelona
Associate Professor Mathias Lindholm, Stockholm University