Preference Banzhaf: A Game-Theoretic Index with Feature-wise Probabilities

Junho Choi, Jaesik Choi

Keywords: XAI, Game Theory, Banzhaf Value, Feature Attribution

TL;DR: We show theoretically and empirically that Banzhaf values with feature-wise probability is equivalent to centered linear regression.

Abstract: Game-theoretic feature attribution methods are popular in XAI because they satisfy several desirable axioms. Approximating a model as a game with input features as players, these methods measure the weighted average contribution of each feature to a model's prediction across different feature subsets. However, these techniques also make strict assumptions that may affect the quality of the explanations. One common assumption is that all features can join or leave a subset with probability of 0.5, i.e., all subsets are equally likely to form. However, in real games, each player can have different preference for joining a coalition, shifting the probability of the subsets and thus the attribution values. Following this notion, we introduce Preference Banzhaf, which calculates Banzhaf-like value with adjusted probabilities using centered linear regression. We theoretically show the convergence of Preference Banzhaf and empirically demonstrate the effect of probability adjustment on explanation quality and sensitivity.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 11475