Graphical Models: Queries, Complexity, Algorithms

Martin Cooper (1, 2, 3) , Simon de Givry (4, 2) , Thomas Schiex (4, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 UT - Université de Toulouse
3 UT3 - Université Toulouse III - Paul Sabatier
4 MIAT INRAE - Unité de Mathématiques et Informatique Appliquées de Toulouse

Graphical models (GMs) define a family of mathematical models aimed at the concise description of multivariate functions using decomposability. We restrict ourselves to functions of discrete variables but try to cover a variety of models that are not always considered as "Graphical Models", ranging from functions with Boolean variables and Boolean co-domain (used in automated reasoning) to functions over finite domain variables and integer or real co-domains (usual in machine learning and statistics). We use a simple algebraic semi-ring based framework for generality, define associated queries, relationships between graphical models, complexity results, and families of algorithms, with their associated guarantees.

Mots clés: artificial intelligence; valued constraints; optimization; tree decomposition; graphical models; submodu- larity; message passing; local consistency

Domaines: Modélisation et simulation; Analyse numérique [cs.NA]

Martin Cooper, Simon de Givry, Thomas Schiex. Graphical Models: Queries, Complexity, Algorithms. Leibniz International Proceedings in Informatics , 2020, 154, pp.4:1--4:22. ⟨10.4230/LIPIcs.STACS.2020.4⟩. ⟨hal-02547692⟩