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Graphical Models: Queries, Complexity, Algorithms (Tutorial)

Authors Martin C. Cooper , Simon de Givry , Thomas Schiex

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Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Graph algorithms
Keywords
  • Computational complexity
  • tree decomposition
  • graphical models
  • submodularity
  • message passing
  • local consistency
  • artificial intelligence
  • valued constraints
  • optimization

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Abstract

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.

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Martin C. Cooper, Simon de Givry, and Thomas Schiex. Graphical Models: Queries, Complexity, Algorithms (Tutorial). In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.4

Author Details

Martin C. Cooper
  • Université Fédérale de Toulouse, ANITI, IRIT, Toulouse, France
Simon de Givry
  • Université Fédérale de Toulouse, ANITI, INRAE, UR 875, Toulouse, France
Thomas Schiex
  • Université Fédérale de Toulouse, ANITI, INRAE, UR 875, Toulouse, France

Funding

The authors have received funding from the French "Investing for the Future – PIA3" program under the Grant agreement ANR-19-PI3A-000, in the context of the ANITI project.
  • Cooper, Martin C.: Funded by ANR-18-CE40-0011
  • de Givry, Simon: Funded by ANR-16-CE40-0028.
  • Schiex, Thomas: Funded by ANR-16-CE40-0028.

Supplementary Materials

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