FairTree: Subgroup Fairness Auditing of Machine Learning Models with Bias-Variance Decomposition

The evaluation of machine learning models typically relies mainly on performance metrics based on loss functions, which risk to overlook changes in performance in relevant subgroups. Auditing tools such as SliceFinder and SliceLine were proposed to detect such groups, but usually have conceptual disadvantages, such as the inability to directly address continuous covariates. In this paper, we introduce FairTree, a novel algorithm adapted from psychometric invariance testing. Unlike SliceFinder and related algorithms, FairTree directly handles continuous, categorical, and ordinal features without discretization. It further decomposes performance disparities into systematic bias and variance, allowing a categorization of changes in algorithm performance. We propose and evaluate two variations of the algorithm: a permutation-based approach, which is conceptually closer to SliceFinder, and a fluctuation test. Through simulation studies that include a direct comparison with SliceLine, we demonstrate that both approaches have a satisfactory rate of false-positive results, but that the fluctuation approach has relatively higher power. We further illustrate the method on the UCI Adult Census dataset. The proposed algorithms provide a flexible framework for the statistical evaluation of the performance and aspects of fairness of machine learning models in a wide range of applications even in relatively small data.