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Robust neural additive models for location scale and shape

Tobias Weckop, Friedrich-Alexander University of Erlangen-Nuremberg

Co-authors: Anton Thielmann, Technical University Clausthal; Benjamin Säfken, Technical University Clausthal; Andreas Mayr, University of Marburg; Tobias Hepp, Friedrich-Alexander University of Erlangen-Nuremberg

Abstract: Neural Additive Models for Location, Scale, and Shape (NAMLSS) allow researchers to flexibly model multiple parameters of a target distribution as functions of a set of covariates. However, they are highly sensitive to systematic outliers, which can distort parameter estimates, compromise model performance, and skew subsequent interpretation. In this work, we introduce a robust loss function for NAMLSS based on a recently proposed likelihood penalization strategy that limits the impact of deviations from distributional assumptions. We propose a method for appropriately calibrating the severity of penalization when the data of interest follow a normal distribution and demonstrate its effectiveness in a simulation study. Finally, we illustrate the practical utility of the approach by modeling reference intervals for healthy hemoglobin levels in children.