[Paper Review] Axiomatic Aggregations of Abductive Explanations

Gagan Biradar, Yacine Izza+3 more|arXiv (Cornell University)|Sep 29, 2023

Explainable Artificial Intelligence (XAI)Computer Science3 citations

TL;DR

This paper proposes three axiomatic aggregation methods—Responsibility Index, Deegan-Packel Index, and Holler-Packel Index—that convert multiple abductive explanations into robust feature importance scores. By leveraging cooperative game theory and causal strength metrics, the methods uniquely satisfy desirable properties and outperform LIME and SHAP in identifying model biases under adversarial attacks.

ABSTRACT

The recent criticisms of the robustness of post hoc model approximation explanation methods (like LIME and SHAP) have led to the rise of model-precise abductive explanations. For each data point, abductive explanations provide a minimal subset of features that are sufficient to generate the outcome. While theoretically sound and rigorous, abductive explanations suffer from a major issue -- there can be several valid abductive explanations for the same data point. In such cases, providing a single abductive explanation can be insufficient; on the other hand, providing all valid abductive explanations can be incomprehensible due to their size. In this work, we solve this issue by aggregating the many possible abductive explanations into feature importance scores. We propose three aggregation methods: two based on power indices from cooperative game theory and a third based on a well-known measure of causal strength. We characterize these three methods axiomatically, showing that each of them uniquely satisfies a set of desirable properties. We also evaluate them on multiple datasets and show that these explanations are robust to the attacks that fool SHAP and LIME.

Motivation & Objective

• Address the limitation of abductive explanations, which can produce multiple valid but conflicting minimal feature sets for a single prediction.
• Overcome the shortcomings of post-hoc explanation methods like LIME and SHAP, which are prone to manipulation and fail to capture model structure precisely.
• Develop a principled, axiomatic framework to aggregate multiple abductive explanations into unified, interpretable feature importance scores.
• Ensure the aggregation methods are robust to adversarial attacks that manipulate LIME and SHAP explanations, particularly in detecting sensitive feature influence.

Proposed method

• Propose the Responsibility Index based on the degree of responsibility—a causal strength metric from formal causality theory.
• Introduce the Deegan-Packel and Holler-Packel indices, derived from cooperative game theory, to quantify feature importance in abductive explanation sets.
• Formalize each aggregation method through an axiomatic characterization, proving uniqueness under a defined set of desirable properties.
• Apply the methods to real-world datasets (Compas and German Credit), comparing their performance against LIME and SHAP under adversarial attacks.
• Use SAT/SMT or MILP oracles to compute abductive explanations for each data point before aggregating via the proposed indices.
• Rank features by importance scores and evaluate robustness by measuring the frequency with which sensitive attributes (e.g., Race, Gender) are correctly identified as top contributors.

Experimental results

Research questions

• RQ1 Can abductive explanations be systematically aggregated into feature importance scores that preserve theoretical rigor and improve interpretability?
• RQ2 Do the proposed aggregation methods uniquely satisfy a set of desirable axioms, ensuring fairness and consistency in explanation generation?
• RQ3 How do the proposed methods compare to LIME and SHAP in detecting model biases under adversarial attacks?
• RQ4 To what extent do the aggregation methods maintain robustness when sensitive features are manipulated or correlated with outcomes?
• RQ5 Can the axiomatic framework be generalized to other explanation types beyond abductive explanations?

Key findings

• The Responsibility Index, Deegan-Packel Index, and Holler-Packel Index each uniquely satisfy a distinct set of axioms, ensuring theoretical soundness and interpretability.
• In the LIME attack on the Compas dataset, the sensitive feature 'Race' was ranked in the top three positions for over 84% of test instances using the proposed methods, compared to near 0% with LIME when two uncorrelated features were present.
• In the SHAP attack on the same dataset, the sensitive feature 'Race' was ranked as the most important feature in at least 86% of cases using the proposed indices, versus only 41.6% for SHAP.
• On the German Credit dataset, the sensitive feature 'Gender' was correctly identified as the top feature in over 87% of instances using the proposed methods, while SHAP and LIME failed to rank it highly in any instance.
• The proposed methods correctly identified the sensitive feature as most important in cases where the model was biased, even when LIME and SHAP failed due to their susceptibility to adversarial manipulation.
• The methods demonstrated robustness in identifying model biases in both LIME and SHAP attack scenarios, particularly in cases where the model’s decision was influenced by sensitive attributes.