# A Bayesian explanation of machine learning models based on modes and functional ANOVA

arXiv: https://arxiv.org/abs/2411.02746 · HTML: https://mlsanity.com/paper/2411.02746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 8 of 8)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [A Linearly-Convergent Stochastic L-BFGS Algorithm](https://mlsanity.com/paper/1508.02087/) (2015)
- [Anomaly Attribution with Likelihood Compensation](https://mlsanity.com/paper/2208.10679/) (2022)

## Abstract (arXiv)

Most methods in explainable AI (XAI) focus on providing reasons for the prediction of a given set of features. However, we solve an inverse explanation problem, i.e., given the deviation of a label, find the reasons of this deviation. We use a Bayesian framework to recover the ``true'' features, conditioned on the observed label value. We efficiently explain the deviation of a label value from the mode, by identifying and ranking the influential features using the ``distances'' in the ANOVA functional decomposition. We show that the new method is more human-intuitive and robust than methods based on mean values, e.g., SHapley Additive exPlanations (SHAP values). The extra costs of solving a Bayesian inverse problem are dimension-independent.