Extracting PAC Decision Trees from Black Box Binary Classifiers: The Gender Bias Study Case on BERT-based Language Models

Decision trees are a popular machine learning method, valued for their inherent explainability. In Explainable AI, decision trees serve as surrogate models for complex black box AI models or as approximations of parts of such models. A key challenge of this approach is assessing how accurately the extracted decision tree represents the original model and determining the extent to which it can be trusted as an approximation of its behaviour. In this work, we investigate the use of the Probably Approximately Correct (PAC) framework to provide a theoretical guarantee of fidelity for decision trees extracted from AI models. Leveraging the theoretical foundations of the PAC framework, we adapt a decision tree algorithm to ensure a PAC guarantee under specific conditions. We focus on binary classification and conduct experiments where we extract decision trees from BERT-based language models with PAC guarantees. Our results indicate occupational gender bias in these models, which confirm previous results in the literature. Additionally, the decision tree format enhances the visualization of which occupations are most impacted by social bias.