Exact Shapley Attributions in Quadratic-time for FANOVA Gaussian Processes

TL;DR

This paper introduces a quadratic-time method to compute exact Shapley attributions for FANOVA Gaussian processes, enabling scalable, uncertainty-aware feature importance explanations for probabilistic models.

Contribution

It presents the first quadratic-time algorithms for exact local and global Shapley value computations in FANOVA Gaussian processes, leveraging closed-form decompositions and recursive algorithms.

Findings

Exact Shapley values computed in quadratic time for FANOVA GPs.

Method captures both expected contributions and uncertainty.

Empirical results demonstrate improved scalability and explanation quality.

Abstract

Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely limiting the practical application of this powerful approach. The challenge is further compounded when the predictive model is probabilistic - as in Gaussian processes (GPs) - where the outputs are random variables rather than point estimates, necessitating additional computational effort in modeling higher-order moments. In this work, we demonstrate that for an important class of GPs known as FANOVA GP, which explicitly models all main effects and interactions, *exact* Shapley attributions for both local and global explanations can be computed in *quadratic time*. For local, instance-wise explanations, we define a stochastic cooperative game over function components and compute the exact stochastic Shapley value in quadratic time only, capturing both the expected contribution and uncertainty. For global explanations, we introduce a deterministic, variance-based value function and compute exact Shapley values that quantify each feature's contribution to the model's overall sensitivity. Our methods leverage a closed-form (stochastic) M\"{o}bius representation of the FANOVA decomposition and introduce recursive algorithms, inspired by Newton's identities, to efficiently compute the mean and variance of Shapley values. Our work enhances the utility of explainable AI, as demonstrated by empirical studies, by providing more scalable, axiomatically sound, and uncertainty-aware explanations for predictions generated by structured probabilistic models.