Clément Carbonnel

IJCAI Conference 2025 Conference Paper

Interpretable DNFs

• Martin C. Cooper
• Imane Bousdira
• Clément Carbonnel

A classifier is considered interpretable if each of its decisions has an explanation which is small enough to be easily understood by a human user. A DNF can be seen as a binary classifier kappa over boolean domains. The size of an explanation of a positive decision taken by a DNF kappa is bounded by the size of the terms in kappa, since we can explain a positive decision by giving a term of kappa that evaluates to true. Since both positive and negative decisions must be explained, we consider that interpretable DNFs are those kappa for which both kappa and its complement can be expressed as DNFs composed of terms of bounded size. In this paper, we investigate the family of k-DNFs whose complements can also be expressed as k-DNFs. We compare two such families, namely depth-k decision trees and nested k-DNFs, a novel family of models. Experimental evidence indicates that nested k-DNFs are an interesting alternative to decision trees in terms of interpretability and accuracy.

ECAI Conference 2025 Conference Paper

Learning Compact Representations of Constraint Networks

• Christian Bessière
• Clément Carbonnel
• Areski Himeur

Passive constraint acquisition aims to learn constraint networks from examples of solutions and non-solutions. There typically exist many constraint networks that are consistent with a given set of examples, so the performance of an acquisition system is critically dependent on its ability to determine which network will generalize the best to unseen data. We introduce a framework for representing constraint networks in compressed form and present a novel method for constraint acquisition. Our method learns a constraint network that achieves a high compression ratio, with the idea that such networks are highly structured and therefore less prone to overfitting. Experiments demonstrate that this approach significantly reduces the number of examples needed for training and achieves a high accuracy on unseen data.

AIJ Journal 2024 Journal Article

Corrigendum to “Learning constraints through partial queries” [Artificial Intelligence 319 (2023) 103896]

• Christian Bessiere
• Clément Carbonnel
• Anton Dries
• Emmanuel Hebrard
• George Katsirelos
• Nadjib Lazaar
• Nina Narodytska
• Claude-Guy Quimper

IJCAI Conference 2023 Conference Paper

Learning Constraint Networks over Unknown Constraint Languages

• Christian Bessiere
• Clément Carbonnel
• Areski Himeur

Constraint acquisition is the task of learning a constraint network from examples of solutions and non-solutions. Existing constraint acquisition systems typically require advance knowledge of the target network's constraint language, which significantly narrows their scope of applicability. In this paper we propose a constraint acquisition method that computes a suitable constraint language as part of the learning process, eliminating the need for any advance knowledge. We report preliminary experiments on various acquisition benchmarks.

AIJ Journal 2023 Journal Article

Learning constraints through partial queries

• Christian Bessiere
• Clément Carbonnel
• Anton Dries
• Emmanuel Hebrard
• George Katsirelos
• Nadjib Lazaar
• Nina Narodytska
• Claude-Guy Quimper

Learning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, we learn constraint networks by asking the user partial queries. That is, we ask the user to classify assignments to subsets of the variables as positive or negative. We provide an algorithm, called QuAcq2, that, given a negative example, elucidates a constraint of the target network in a number of queries logarithmic in the size of the example. The whole constraint network can then be learned with a polynomial number of partial queries. We give information theoretic lower bounds for learning some simple classes of constraint networks and show that our generic algorithm is optimal in some cases. We provide a version of QuAcq2 with a cutoff mechanism that controls the time to generate a query. Our experiments illustrate the good behavior of QuAcq2 in practice, especially in the case where QuAcq2 is executed to learn the missing constraints in a partially filled constraint model. Our experiments also show that QuAcq2 requires significantly fewer queries to learn a network than its predecessor QuAcq1.

KR Conference 2023 Conference Paper

Tractable Explaining of Multivariate Decision Trees

• Clément Carbonnel
• Martin C. Cooper
• Joao Marques-Silva

We study multivariate decision trees (MDTs), in particular, classes of MDTs determined by the language of relations that can be used to split feature space. An abductive explanation (AXp) of the classification of a particular instance, viewed as a set of feature-value assignments, is a minimal subset of the instance which is sufficient to lead to the same decision. We investigate when finding a single AXp is tractable. We identify tractable languages for real, integer and boolean features. Indeed, in the case of boolean languages, we provide a P/NP-hard dichotomy.

FOCS Conference 2018 Conference Paper

The Complexity of General-Valued CSPs Seen from the Other Side

• Clément Carbonnel
• Miguel Romero 0001
• Stanislav Zivný

The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias, Bulatov, and Dalmau [ICALP'07] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithms (unconditionally) as bounded treewidth modulo homomorphic equivalence. The general-valued constraint satisfaction problem (VCSP) is a generalisation of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the k-th level of the Sherali-Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognising the tractable cases; the latter has an application in database theory.

IJCAI Conference 2017 Conference Paper

On the Kernelization of Global Constraints

• Clément Carbonnel
• Emmanuel Hebrard

Kernelization is a powerful concept from parameterized complexity theory that captures (a certain idea of) efficient polynomial-time preprocessing for hard decision problems. However, exploiting this technique in the context of constraint programming is challenging. Building on recent results for the VertexCover constraint, we introduce novel "loss-less" kernelization variants that are tailored for constraint propagation. We showcase the theoretical interest of our ideas on two constraints, VertexCover and EdgeDominatingSet.