On Tackling Explanation Redundancy in Decision Trees

Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of recent proposals for applying interpretable ML models in high-risk applications. The belief in DT interpretability is justified by the fact that explanations for DT predictions are generally expected to be succinct. Indeed, in the case of DTs, explanations correspond to DT paths. Since decision trees are ideally shallow, and so paths contain far fewer features than the total number of features, explanations in DTs are expected to be succinct, and hence interpretable. This paper offers both theoretical and experimental arguments demonstrating that, as long as interpretability of decision trees equates with succinctness of explanations, then decision trees ought not be deemed interpretable. The paper introduces logically rigorous path explanations and path explanation redundancy, and proves that there exist functions for which decision trees must exhibit paths with arbitrarily large explanation redundancy. The paper also proves that only a very restricted class of functions can be represented with DTs that exhibit no explanation redundancy. In addition, the paper includes experimental results substantiating that path explanation redundancy is observed ubiquitously in decision trees, including those obtained using different tree learning algorithms, but also in a wide range of publicly available decision trees. The paper also proposes polynomial-time algorithms for eliminating path explanation redundancy, which in practice require negligible time to compute. Thus, these algorithms serve to indirectly attain irreducible, and so succinct, explanations for decision trees

Delivering Inflated Explanations

In the quest for Explainable Artificial Intelligence (XAI) one of the questions that frequently arises given a decision made by an AI system is, ``why was the decision made in this way?'' Formal approaches to explainability build a formal model of the AI system and use this to reason about the properties of the system. Given a set of feature values for an instance to be explained, and a resulting decision, a formal abductive explanation is a set of features, such that if they take the given value will always lead to the same decision. This explanation is useful, it shows that only some features were used in making the final decision. But it is narrow, it only shows that if the selected features take their given values the decision is unchanged. It's possible that some features may change values and still lead to the same decision. In this paper we formally define inflated explanations which is a set of features, and for each feature of set of values (always including the value of the instance being explained), such that the decision will remain unchanged. Inflated explanations are more informative than abductive explanations since e.g they allow us to see if the exact value of a feature is important, or it could be any nearby value. Overall they allow us to better understand the role of each feature in the decision. We show that we can compute inflated explanations for not that much greater cost than abductive explanations, and that we can extend duality results for abductive explanations also to inflated explanations

On Computing Probabilistic Abductive Explanations

The most widely studied explainable AI (XAI) approaches are unsound. This is the case with well-known model-agnostic explanation approaches, and it is also the case with approaches based on saliency maps. One solution is to consider intrinsic interpretability, which does not exhibit the drawback of unsoundness. Unfortunately, intrinsic interpretability can display unwieldy explanation redundancy. Formal explainability represents the alternative to these non-rigorous approaches, with one example being PI-explanations. Unfortunately, PI-explanations also exhibit important drawbacks, the most visible of which is arguably their size. Recently, it has been observed that the (absolute) rigor of PI-explanations can be traded off for a smaller explanation size, by computing the so-called relevant sets. Given some positive {\delta}, a set S of features is {\delta}-relevant if, when the features in S are fixed, the probability of getting the target class exceeds {\delta}. However, even for very simple classifiers, the complexity of computing relevant sets of features is prohibitive, with the decision problem being NPPP-complete for circuit-based classifiers. In contrast with earlier negative results, this paper investigates practical approaches for computing relevant sets for a number of widely used classifiers that include Decision Trees (DTs), Naive Bayes Classifiers (NBCs), and several families of classifiers obtained from propositional languages. Moreover, the paper shows that, in practice, and for these families of classifiers, relevant sets are easy to compute. Furthermore, the experiments confirm that succinct sets of relevant features can be obtained for the families of classifiers considered.Comment: arXiv admin note: text overlap with arXiv:2207.04748, arXiv:2205.0956

Ubiquitous computing : techniques for filtering inconsistent information

Cette thèse étudie une approche possible de l'intelligence artificielle pour la détection et le curage d'informations perverties dans les bases de connaissances des objets et composants intelligents en informatique ubiquitaire. Cette approche est traitée d'un point de vue pratique dans le cadre du formalisme SAT; il s'agit donc de mettre en œuvre des techniques de filtrage d'incohérences dans des bases contradictoires. Plusieurs contributions sont apportées dans cette thèse. Premièrement, nous avons travaillé sur l'extraction d'un ensemble maximal d'informations qui soit cohérent avec une série de contextes hypothétiques. Nous avons proposé une approche incrémentale pour le calcul d'un tel ensemble (AC-MSS). Deuxièmement, nous nous sommes intéressés à la tâche d'énumération des ensembles maximaux satisfaisables (MSS) ou leurs complémentaires les ensembles minimaux rectificatifs (MCS) d'une instance CNF insatisfaisable. Dans cette contribution, nous avons introduit une technique qui améliore les performances des meilleures approches pour l'énumération des MSS/MCS. Cette méthode implémente le paradigme de rotation de modèle qui permet de calculer des ensembles de MCS de manière heuristique et efficace. Finalement, nous avons étudié une notion de consensus permettant réconcilier des sources d'informations. Cette forme de consensus peut être caractérisée par différents critères de préférence, comme le critère de maximalité. Une approche incrémentale de calcul d'un consensus maximal par rapport à l'inclusion ensembliste a été proposée. Nous avons également introduit et étudié la concept de consensus admissible qui raffine la définition initialement proposée du concept de consensus.This thesis studies a possible approach of artificial intelligence for detecting and filtering inconsistent information in knowledge bases of intelligent objects and components in ubiquitous computing. This approach is addressed from a practical point of view in the SAT framework;it is about implementing a techniques of filtering inconsistencies in contradictory bases. Several contributions are made in this thesis. Firstly, we have worked on the extraction of one maximal information set that must be satisfiable with multiple assumptive contexts. We have proposed an incremental approach for computing such a set (AC-MSS). Secondly, we were interested about the enumeration of maximal satisfiable sets (MSS) or their complementary minimal correction sets (MCS) of an unsatisfiable CNF instance. In this contribution, a technique is introduced that boosts the currently most efficient practical approaches to enumerate MCS. It implements a model rotation paradigm that allows the set of MCS to be computed in an heuristically efficient way. Finally, we have studied a notion of consensus to reconcile several sources of information. This form of consensus can obey various preference criteria, including maximality one. We have then developed an incremental algorithm for computing one maximal consensus with respect to set-theoretical inclusion. We have also introduced and studied the concept of admissible consensus that refines the initial concept of consensus

On Explaining Random Forests with SAT

8 pages, 1 figure, 1 table, IJCAI 2021International audienceRandom Forest (RFs) are among the most widely used Machine Learning (ML) classifiers. Even though RFs are not interpretable, there are no dedicated non-heuristic approaches for computing explanations of RFs. Moreover, there is recent work on polynomial algorithms for explaining ML models, including naive Bayes classifiers. Hence, one question is whether finding explanations of RFs can be solved in polynomial time. This paper answers this question negatively, by proving that computing one PI-explanation of an RF is D^P-complete. Furthermore, the paper proposes a propositional encoding for computing explanations of RFs, thus enabling finding PI-explanations with a SAT solver. This contrasts with earlier work on explaining boosted trees (BTs) and neural networks (NNs), which requires encodings based on SMT/MILP. Experimental results, obtained on a wide range of publicly available datasets, demontrate that the proposed SAT-based approach scales to RFs of sizes common in practical applications. Perhaps more importantly, the experimental results demonstrate that, for the vast majority of examples considered, the SAT-based approach proposed in this paper significantly outperforms existing heuristic approaches

On Admissible Consensuses

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On Explaining Decision Trees

Decision trees (DTs) epitomize what have become to be known as interpretable machine learning (ML) models. This is informally motivated by paths in DTs being often much smaller than the total number of features. This paper shows that in some settings DTs can hardly be deemed interpretable, with paths in a DT being arbitrarily larger than a PI-explanation, i.e. a subset-minimal set of feature values that entails the prediction. As a result, the paper proposes a novel model for computing PI-explanations of DTs, which enables computing one PI-explanation in polynomial time. Moreover, it is shown that enumeration of PI-explanations can be reduced to the enumeration of minimal hitting sets. Experimental results were obtained on a wide range of publicly available datasets with well-known DT-learning tools, and confirm that in most cases DTs have paths that are proper supersets of PI-explanations

On Computing One Max_Subset Inclusion Consensus

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Solving Explainability Queries with Quantification: The Case of Feature Relevancy

Trustable explanations of machine learning (ML) models are vital in high-risk uses of artificial intelligence (AI). Apart from the computation of trustable explanations, a number of explainability queries have been identified and studied in recent work. Some of these queries involve solving quantification problems, either in propositional or in more expressive logics. This paper investigates one of these quantification problems, namely the feature relevancy problem (FRP), i.e.\ to decide whether a (possibly sensitive) feature can occur in some explanation of a prediction. In contrast with earlier work, that studied FRP for specific classifiers, this paper proposes a novel algorithm for the \fprob quantification problem which is applicable to any ML classifier that meets minor requirements. Furthermore, the paper shows that the novel algorithm is efficient in practice. The experimental results, obtained using random forests (RFs) induced from well-known publicly available datasets, demonstrate that the proposed solution outperforms existing state-of-the-art solvers for Quantified Boolean Formulas (QBF) by orders of magnitude. Finally, the paper also identifies a novel family of formulas that are challenging for currently state-of-the-art QBF solvers