Bayesian-AIME: Quantifying Uncertainty and Enhancing Stability in Approximate Inverse Model Explanations

Explainable artificial intelligence (XAI), which provides the rationale behind machine learning decisions, is essential for deploying AI in high-risk domains. However, most XAI methods provide only single-point explanations without indicating their reliability and are often unstable, i.e., small changes in training data can lead to significantly different explanations. This study addresses these limitations by proposing a Bayesian-approximate inverse model explanation method, an extension of AIME that incorporates a Bayesian framework. By modeling the inverse operator of a black-box model probabilistically, Bayesian-AIME estimates feature importance as a posterior distribution. This enables the assignment of 95% credible intervals (CIs) to feature importance scores, facilitating quantitative assessment of explanation reliability. Using the posterior mean also improves explanation stability. The effectiveness of the method was evaluated via three experiments: (1) stability analysis via bootstrapping, (2) validation of CIs on synthetic data with known importance, and (3) case studies on Titanic survival prediction and breast cancer diagnosis. The results showed that Bayesian-AIME outperformed existing methods in terms of stability and conveyed meaningful uncertainty, thus enhancing model interpretability. This study contributes to strengthening the reliability of XAI for practical applications.