Efficient Contrastive Explanations on Demand

Recent work revealed a tight connection between adversarial robustness and restricted forms of symbolic explanations, namely distance-based (formal) explanations. This connection is significant because it represents a first step towards making the computation of symbolic explanations as efficient as deciding the existence of adversarial examples, especially for highly complex machine learning (ML) models. However, a major performance bottleneck remains, because of the very large number of features that ML models may possess, in particular for deep neural networks. This paper proposes novel algorithms to compute the so-called contrastive explanations for ML models with a large number of features, by leveraging on adversarial robustness. Furthermore, the paper also proposes novel algorithms for listing explanations and finding smallest contrastive explanations. The experimental results demonstrate the performance gains achieved by the novel algorithms proposed in this paper.

SHAP scores fail pervasively even when Lipschitz succeeds

The ubiquitous use of Shapley values in eXplainable AI (XAI) has been triggered by the tool SHAP, and as a result are commonly referred to as SHAP scores. Recent work devised examples of machine learning (ML) classifiers for which the computed SHAP scores are thoroughly unsatisfactory, by allowing human decision-makers to be misled. Nevertheless, such examples could be perceived as somewhat artificial, since the selected classes must be interpreted as numeric. Furthermore, it was unclear how general were the issues identified with SHAP scores. This paper answers these criticisms. First, the paper shows that for Boolean classifiers there are arbitrarily many examples for which the SHAP scores must be deemed unsatisfactory. Second, the paper shows that the issues with SHAP scores are also observed in the case of regression models. In addition, the paper studies the class of regression models that respect Lipschitz continuity, a measure of a function's rate of change that finds important recent uses in ML, including model robustness. Concretely, the paper shows that the issues with SHAP scores occur even for regression models that respect Lipschitz continuity. Finally, the paper shows that the same issues are guaranteed to exist for arbitrarily differentiable regression models.

The Sets of Power

Measures of voting power have been the subject of extensive research since the mid 1940s. More recently, similar measures of relative importance have been studied in other domains that include inconsistent knowledge bases, intensity of attacks in argumentation, different problems in the analysis of database management, and explainability. This paper demonstrates that all these examples are instantiations of computing measures of importance for a rather more general problem domain. The paper then shows that the best-known measures of importance can be computed for any reference set whenever one is given a monotonically increasing predicate that partitions the subsets of that reference set. As a consequence, the paper also proves that measures of importance can be devised in several domains, for some of which such measures have not yet been studied nor proposed. Furthermore, the paper highlights several research directions related with computing measures of importance.

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.

Distance-Restricted Explanations: Theoretical Underpinnings & Efficient Implementation

The uses of machine learning (ML) have snowballed in recent years. In many cases, ML models are highly complex, and their operation is beyond the understanding of human decision-makers. Nevertheless, some uses of ML models involve high-stakes and safety-critical applications. Explainable artificial intelligence (XAI) aims to help human decision-makers in understanding the operation of such complex ML models, thus eliciting trust in their operation. Unfortunately, the majority of past XAI work is based on informal approaches, that offer no guarantees of rigor. Unsurprisingly, there exists comprehensive experimental and theoretical evidence confirming that informal methods of XAI can provide human-decision makers with erroneous information. Logic-based XAI represents a rigorous approach to explainability; it is model-based and offers the strongest guarantees of rigor of computed explanations. However, a well-known drawback of logic-based XAI is the complexity of logic reasoning, especially for highly complex ML models. Recent work proposed distance-restricted explanations, i.e. explanations that are rigorous provided the distance to a given input is small enough. Distance-restricted explainability is tightly related with adversarial robustness, and it has been shown to scale for moderately complex ML models, but the number of inputs still represents a key limiting factor. This paper investigates novel algorithms for scaling up the performance of logic-based explainers when computing and enumerating ML model explanations with a large number of inputs.

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.

Locally-Minimal Probabilistic Explanations

Formal abductive explanations offer crucial guarantees of rigor and so are of interest in high-stakes uses of machine learning (ML). One drawback of abductive explanations is explanation size, justified by the cognitive limits of human decision-makers. Probabilistic abductive explanations (PAXps) address this limitation, but their theoretical and practical complexity makes their exact computation most often unrealistic. This paper proposes novel efficient algorithms for the computation of locally-minimal PXAps, which offer high-quality approximations of PXAps in practice. The experimental results demonstrate the practical efficiency of the proposed algorithms.

The Pros and Cons of Adversarial Robustness

Robustness is widely regarded as a fundamental problem in the analysis of machine learning (ML) models. Most often robustness equates with deciding the non-existence of adversarial examples, where adversarial examples denote situations where small changes on some inputs cause a change in the prediction. The perceived importance of ML model robustness explains the continued progress observed for most of the last decade. Whereas robustness is often assessed locally, i.e. given some target point in feature space, robustness can also be defined globally, i.e. where any point in feature space can be considered. The importance of ML model robustness is illustrated for example by the existence of competitions evaluating the progress of robustness tools, namely in the case of neural networks (NNs) but also by efforts towards robustness certification. More recently, robustness tools have also been used for computing rigorous explanations of ML models. In contrast with the observed successes of robustness, this paper uncovers some limitations with existing definitions of robustness, both global and local, but also with efforts towards robustness certification. The paper also investigates uses of adversarial examples besides those related with robustness.

Refutation of Shapley Values for XAI -- Additional Evidence

Recent work demonstrated the inadequacy of Shapley values for explainable artificial intelligence (XAI). Although to disprove a theory a single counterexample suffices, a possible criticism of earlier work is that the focus was solely on Boolean classifiers. To address such possible criticism, this paper demonstrates the inadequacy of Shapley values for families of classifiers where features are not boolean, but also for families of classifiers for which multiple classes can be picked. Furthermore, the paper shows that the features changed in any minimal $l_0$ distance adversarial examples do not include irrelevant features, thus offering further arguments regarding the inadequacy of Shapley values for XAI.

A Refutation of Shapley Values for Explainability

Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized into a number of possible issues. Each of those issues relates with features being relevant or irrelevant for a prediction, and all are significant regarding the inadequacy of Shapley values for rule-based explainability. This earlier work devised a brute-force approach to identify Boolean functions, defined on small numbers of features, and also associated instances, which displayed such inadequacy-revealing issues, and so served as evidence to the inadequacy of Shapley values for rule-based explainability. However, an outstanding question is how frequently such inadequacy-revealing issues can occur for Boolean functions with arbitrary large numbers of features. It is plain that a brute-force approach would be unlikely to provide insights on how to tackle this question. This paper answers the above question by proving that, for any number of features, there exist Boolean functions that exhibit one or more inadequacy-revealing issues, thereby contributing decisive arguments against the use of Shapley values as the theoretical underpinning of feature-attribution methods in explainability.