Unifying Attribution-Based Explanations Using Functional Decomposition

TL;DR

This paper introduces a unifying framework for attribution-based explanation methods in machine learning, linking them through functional decomposition and game theory to better understand their properties and guide method selection.

Contribution

It proposes a comprehensive framework that unifies various explanation methods via canonical additive decomposition and game theory, enabling systematic analysis and development of new explanations.

Findings

Most existing attribution methods are special cases of removal-based attribution methods.

Every valid additive decomposition corresponds to a canonical additive decomposition (CAD).

The framework allows for the derivation of new explanation methods and their properties.

Abstract

The black box problem in machine learning has led to the introduction of an ever-increasing set of explanation methods for complex models. These explanations have different properties, which in turn has led to the problem of method selection: which explanation method is most suitable for a given use case? In this work, we propose a unifying framework of attribution-based explanation methods, which provides a step towards a rigorous study of the similarities and differences of explanations. We first introduce removal-based attribution methods (RBAMs), and show that an extensively broad selection of existing methods can be viewed as such RBAMs. We then introduce the canonical additive decomposition (CAD). This is a general construction for additively decomposing any function based on the central idea of removing (groups of) features. We proceed to show that indeed every valid additive decomposition is an instance of the CAD, and that any removal-based attribution method is associated with a specific CAD. Next, we show that any removal-based attribution method can be completely defined as a game-theoretic value or interaction index for a specific (possibly constant-shifted) cooperative game, which is defined using the corresponding CAD of the method. We then use this intrinsic connection to define formal descriptions of specific behaviours of explanation methods, which we also call functional axioms, and identify sufficient conditions on the corresponding CAD and game-theoretic value or interaction index of an attribution method under which the attribution method is guaranteed to adhere to these functional axioms. Finally, we show how this unifying framework can be used to develop new, efficient approximations for existing explanation methods.