International audience

More than ever, air transport players (i.e., airline and airport companies) in an intensely competitive climate need to benefit from a carefully optimized management of airport resources to improve the quality of service and control the induced costs. In this paper, we investigate the Airport Check-in Desk Assignment Problem. We propose a Constraint Programming (CP) model for this problem, and present some promising experimental results from data coming from ADP (Aéroport de Paris). Our works are deployed in a preprod environment since 1 year.

We present and evaluate empirically an XAI protocol for ruling interactions between a tree-based ML model (the AI system) and its user U, in the context of a prediction task. The pieces of knowledge held by U concerning the prediction task are supposed to be representable by a set of classification rules that is reliable and consistent, but (typically) incomplete. The proposed protocol aims to help U decide what to do with each prediction made by AI (accept it, reject it). It also aims to improve the quality of further predictions made by AI thanks to the expertise of U, and, reciprocally, to complete the pieces of knowledge held by U by leveraging the predictions made by AI. Experiments show that the approach can prove valuable in practice.

A contrastive explanation is a local explanation that is looked for when the prediction achieved by an ML model on an input instance x differs from what was foreseen. A contrastive explanation indicates how to change x to another instance xc from which a prediction that complies with the user’s expectations can be obtained. In this paper, we present a constraint-based approach to the generation of contrastive explanations that are suited to regression functions represented by boosted trees. We show how to compute the smallest interval containing all the regression values that are attainable given a set of characteristics of x that are protected (i.e., not amenable to change). We also show how to generate minimal contrastive explanations for x given a target interval, i.e., instances with regression values within the specified interval and that are as close as possible to x. Closeness is captured using user-dependent mappings reflecting preferences about value change for the attributes (or combinations of attributes) considered in the representation of x.

Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, provably sound explanations for the predictions made are expected. Recent work have shown how subset-minimal abductive explanations can be derived for boosted trees, using automated reasoning techniques. However, the generation of such well-founded explanations is intractable in the general case. To improve the scalability of their generation, we introduce the notion of tree-specific explanation for a boosted tree. We show that tree-specific explanations are provably sound abductive explanations that can be computed in polynomial time. We also explain how to derive a subset-minimal abductive explanation from a tree-specific explanation. Experiments on various datasets show the computational benefits of leveraging tree-specific explanations for deriving subset-minimal abductive explanations.

International audience

We define contrastive explanations that are suited to tree-based classifiers. In our framework, contrastive explanations are based on the set of (possibly non-independent) Boolean characteristics used by the classifier and are at least as general as contrastive explanations based on the set of characteristics of the instances considered at start. We investigate the computational complexity of computing contrastive explanations for Boolean classifiers (including tree-based ones), when the Boolean conditions used are not independent. Finally, we present and evaluate empirically an algorithm for computing minimum-size contrastive explanations for random forests.

We present two algorithms for generating (resp. evaluating) abductive explanations for boosted regression trees. Given an instance x and an interval I containing its value F (x) for the boosted regression tree F at hand, the generation algorithm returns a (most general) term t over the Boolean conditions in F such that every instance x′ satisfying t is such that F (x′ ) ∈ I. The evaluation algorithm tackles the corresponding inverse problem: given F , x and a term t over the Boolean conditions in F such that t covers x, find the least interval I_t such that for every instance x′ covered by t we have F (x′ ) ∈ I_t . Experiments on various datasets show that the two algorithms are practical enough to be used for generating (resp. evaluating) abductive explanations for boosted regression trees based on a large number of Boolean conditions.

Random forests have long been considered as powerful model ensembles in machine learning. By training multiple decision trees, whose diversity is fostered through data and feature subsampling, the resulting random forest can lead to more stable and reliable predictions than a single decision tree. This however comes at the cost of decreased interpretability: while decision trees are often easily interpretable, the predictions made by random forests are much more difficult to understand, as they involve a majority vote over multiple decision trees. In this paper, we examine different types of reasons that explain "why" an input instance is classified as positive or negative by a Boolean random forest. Notably, as an alternative to prime-implicant explanations taking the form of subset-minimal implicants of the random forest, we introduce majoritary reasons which are subset-minimal implicants of a strict majority of decision trees. For these abductive explanations, the tractability of the generation problem (finding one reason) and the optimization problem (finding one minimum-sized reason) are investigated. Unlike prime-implicant explanations, majoritary reasons may contain redundant features. However, in practice, prime-implicant explanations - for which the identification problem is DP-complete - are slightly larger than majoritary reasons that can be generated using a simple linear-time greedy algorithm. They are also significantly larger than minimum-sized majoritary reasons which can be approached using an anytime Partial MaxSAT algorithm.

International audience

Abductive explanations take a central place in eXplainable Artificial Intelligence (XAI) by clarifying with few features the way data instances are classified. However, instances may have exponentially many minimum-size abductive explanations, and this source of complexity holds even for ``intelligible'' classifiers, such as decision trees. When the number of such abductive explanations is huge, computing one of them, only, is often not informative enough. Especially, better explanations than the one that is derived may exist. As a way to circumvent this issue, we propose to leverage a model of the explainee, making precise her / his preferences about explanations, and to compute only preferred explanations. In this paper, several models are pointed out and discussed. For each model, we present and evaluate an algorithm for computing preferred majoritary reasons, where majoritary reasons are specific abductive explanations suited to random forests. We show that in practice the preferred majoritary reasons for an instance can be far less numerous than its majoritary reasons.

We present and evaluate d4Max, an exact approach for solving the Weighted Max#SAT problem. The Max#SAT problem extends the model counting problem (#SAT) by considering a tripartition of the variables {X, Y, Z}, and consists in maximizing over X the number of assignments to Y that can be extended to a solution with some assignment to Z. The Weighted Max#SAT problem is an extension of the Max#SAT problem with weights associated on each interpretation. We test and compare our approach with other state-of-the-art solvers on the challenging task in probabilistic inference of finding the marginal maximum a posteriori probability (MMAP) of a given subset of the variables in a Bayesian network and on exist-random quantified SSAT benchmarks. The results clearly show the overall superiority of d4Max in term of speed and number of instances solved. Moreover, we experimentally show that, in general, d4Max is able to quickly spot a solution that is close to optimal, thereby opening the door to an efficient anytime approach.

In the domain of partial classification, recent studies about multiobjective local search (MOLS) have led to new algorithms offering high performance, particularly when the data are imbalanced. In the presence of such data, the class distribution is highly skewed and the user is often interested in the least frequent class. Making further improvements certainly requires exploiting complementary solving techniques (notably, for the rule mining problem). As Constraint Programming (CP) has been shown to be effective on various combinatorial problems, it is one such promising complementary approach. In this paper, we propose a new hybrid combination, based on MOLS and CP that are quite orthogonal. Indeed, CP is a complete approach based on powerful filtering techniques whereas MOLS is an incomplete approach based on Pareto dominance. Experimental results on real imbalanced datasets show that our hybrid approach is statistically more efficient than a simple MOLS algorithm on both training and tests instances, in particular, on partial classification problems containing many attributes.

In this paper, we investigate the computational intelligibility of Boolean classifiers, characterized by their ability to answer XAI queries in polynomial time. The classifiers under consideration are decision trees, DNF formulae, decision lists, decision rules, tree ensembles, and Boolean neural nets. Using 9 XAI queries, including both explanation queries and verification queries, we show the existence of large intelligibility gap between the families of classifiers. On the one hand, all the 9 XAI queries are tractable for decision trees. On the other hand, none of them is tractable for DNF formulae, decision lists, random forests, boosted decision trees, Boolean multilayer perceptrons, and binarized neural networks.

One of the key purposes of eXplainable AI (XAI) is to develop techniques for understanding predictions made by Machine Learning (ML) models and for assessing how much reliable they are. Several encoding schemas have recently been pointed out, showing how ML classifiers of various types can be mapped to Boolean circuits exhibiting the same input-output behaviours. Thanks to such mappings, XAI queries about classifiers can be delegated to the corresponding circuits. In this paper, we define new explanation and/or verification queries about classifiers. We show how they can be addressed by combining queries and transformations about the associated Boolean circuits. Taking advantage of previous results from the knowledge compilation map, this allows us to identify a number of XAI queries that are tractable provided that the circuit has been first turned into a compiled representation.

Most of state-of-the-art parallel SAT solvers are portfolio-based ones. They aim at running several times the same solver with different parameters. In this paper, we propose a solver called Dolius, based on the divide and conquer paradigm. In contrast to most current parallel efficient engines, Dolius does not need shared memory, can be distributed, and scales well when a large number of computing units is available.

Modern complete SAT solvers almost uniformly implement variations of the clause learning framework introduced by Grasp and Chaff. The success of these solvers has been theoretically explained by showing that the clause learning framework is an implementation of a proof system which is as poweful as resolution. However, exponential lower bounds are known for resolution, which suggests that significant advances in SAT solving must come from implementations of more powerful proof systems. We present a clause learning SAT solver that uses extended resolution. It is based on a restriction of the application of the extension rule. This solver outperforms existing solvers on application instances from recent SAT competitions as well as on instances that are provably hard for resolution.

In this paper a learning based local search approach for propositional satisfiability is presented. It is based on an original adaptation of the conflict driven clause learning (CDCL) scheme to local search. First an extended implication graph for complete assignments of the set of variables is proposed. Secondly, a unit propagation based technique for building and using such implication graph is designed. Finally, we show how this new learning scheme can be integrated to the state-of-the-art local search solver WSAT. Interestingly enough, the obtained local search approach is able to prove unsatisfiability. Experimental results show very good performances on many classes of SAT instances from the last SAT competitions.

Solving quantified Boolean formulas (QBF) has become an attractive research area in artificial intelligence. Many important artificial intelligence problems (planning, nonmonotonic reasoning, formal verification, etc.) can be reduced to QBFs. A new DLL-based method is proposed that integrates binary decision diagram (BDD) to set free the variable ordering heuristics that are traditionally constrained by the static order of the QBF quantifiers. BDD is used to represent in a compact form the set of models of the Boolean formula. Interesting reduction operators are proposed in order to dynamically reduce the BDD size and to answer the validity of the QBF. Experimental results on instances from the QBF'03 evaluation show that our approach can efficiently solve instances that are very hard for current QBF solvers.