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

TL;DR

This work 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.

Abstract

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.

Figures (7)

• Figure 1: Distributions of the multimodal dataset, where $y=x_0 + x_1 + x_2$.
• Figure 2: The SHAP values and the main responsible scores of $x_0$, $x_1$ and $x_2$ explaining $y$'s deviation from the mean and the dominant mode.
• Figure 3: Time histories of river flow measurements.
• Figure 4: The first order ANOVA functions of the river flows of $ru_h$, $ru_{hp}$ and $ru_{ww}$, modeled by linear regression on the left and extreme gradient boosting on the right.
• Figure 5: Main responsible scores of $ru_h$ (upper-left), $ru_{hp}$ (upper-right) and $ru_{ww}$ (bottom).