Q-intersection Algorithms for Constraint-Based Robust Parameter Estimation

Clément Carbonnel (1) , Gilles Trombettoni (2) , Philippe Vismara (2) , Gilles Chabert (3)

1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
2 COCONUT - Agents, Apprentissage, Contraintes
3 TASC - Theory, Algorithms and Systems for Constraints

Given a set of axis-parallel n-dimensional boxes, the q-intersection is defined as the smallest box encompassing all the points that belong to at least q boxes. Computing the q-intersection is a combinatorial problem that allows us to han-dle robust parameter estimation with a numerical constraint programming approach. The q-intersection can be viewed as a filtering operator for soft constraints that model measure-ments subject to outliers. This paper highlights the equiva-lence of this operator with the search of q-cliques in a graph whose boxicity is bounded by the number of variables in the constraint network. We present a computational study of the q-intersection. We also propose a fast heuristic and a sophisti-cated exact q-intersection algorithm. First experiments show that our exact algorithm outperforms the existing one while our heuristic performs an efficient filtering on hard problems.

Mots clés: q-intersection; soft numerical constraints; parameter estimation; intersection graph

Domaines: Intelligence artificielle [cs.AI]; Mathématique discrète [cs.DM]

Clément Carbonnel, Gilles Trombettoni, Philippe Vismara, Gilles Chabert. Q-intersection Algorithms for Constraint-Based Robust Parameter Estimation. 28th AAAI Conference on Artificial Intelligence, Jul 2014, Québec City, Canada. pp.2630-2636, ⟨10.1609/aaai.v28i1.9117⟩. ⟨hal-01084606⟩