From SHAP Scores to Feature Importance Scores

A central goal of eXplainable Artificial Intelligence (XAI) is to assign relative importance to the features of a Machine Learning (ML) model given some prediction. The importance of this task of explainability by feature attribution is illustrated by the ubiquitous recent use of tools such as SHAP and LIME. Unfortunately, the exact computation of feature attributions, using the game-theoretical foundation underlying SHAP and LIME, can yield manifestly unsatisfactory results, that tantamount to reporting misleading relative feature importance. Recent work targeted rigorous feature attribution, by studying axiomatic aggregations of features based on logic-based definitions of explanations by feature selection. This paper shows that there is an essential relationship between feature attribution and a priori voting power, and that those recently proposed axiomatic aggregations represent a few instantiations of the range of power indices studied in the past. Furthermore, it remains unclear how some of the most widely used power indices might be exploited as feature importance scores (FISs), i.e. the use of power indices in XAI, and which of these indices would be the best suited for the purposes of XAI by feature attribution, namely in terms of not producing results that could be deemed as unsatisfactory. This paper proposes novel desirable properties that FISs should exhibit. In addition, the paper also proposes novel FISs exhibiting the proposed properties. Finally, the paper conducts a rigorous analysis of the best-known power indices in terms of the proposed properties.

On Correcting SHAP Scores

Recent work uncovered examples of classifiers for which SHAP scores yield misleading feature attributions. While such examples might be perceived as suggesting the inadequacy of Shapley values for explainability, this paper shows that the source of the identified shortcomings of SHAP scores resides elsewhere. Concretely, the paper makes the case that the failings of SHAP scores result from the characteristic functions used in earlier works. Furthermore, the paper identifies a number of properties that characteristic functions ought to respect, and proposes several novel characteristic functions, each exhibiting one or more of the desired properties. More importantly, some of the characteristic functions proposed in this paper are guaranteed not to exhibit any of the shortcomings uncovered by earlier work. The paper also investigates the impact of the new characteristic functions on the complexity of computing SHAP scores. Finally, the paper proposes modifications to the tool SHAP to use instead one of our novel characteristic functions, thereby eliminating some of the limitations reported for SHAP scores.