Extracting PAC Decision Trees from Black Box Binary Classifiers: The Gender Bias Case Study on BERT-based Language Models
Ana Ozaki, Roberto Confalonieri, Ricardo Guimarães, Anders Imenes
TL;DR
This work introduces PAC-based guarantees for extracting decision-tree surrogates from binary black-box classifiers, addressing fidelity between the surrogate and the target model. It combines theoretical developments (definitions, sample-size bounds, and PAC guarantees) with practical algorithms (TopDown and TrePAC) to produce interpretable trees. The authors validate the approach on a gender-bias case study using BERT/RoBERTa models, showing feasible data requirements and surrogate trees that reveal bias signals, while highlighting model complexity effects. The results demonstrate both the theoretical viability of PAC-guaranteed tree extraction and its practical utility for bias analysis and explainability, with future directions toward multi-class settings and alternative sampling strategies.
Abstract
Decision trees are a popular machine learning method, known for their inherent explainability. In Explainable AI, decision trees can be used as surrogate models for complex black box AI models or as approximations of parts of such models. A key challenge of this approach is determining how accurately the extracted decision tree represents the original model and to what extent it can be trusted as an approximation of their behavior. 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. Based on theoretical results from the PAC framework, we adapt a decision tree algorithm to ensure a PAC guarantee under certain 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.