A linear-algebraic tool for conditional independence inference

  • Kentaro Tanaka aculty of Economics, Seikei University, Tokyo
  • Milan Studeny Institute of Information Theory and Automation of the CAS, Prague
  • Akimichi Takemura Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo
  • Tomonari Sei Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama
Keywords: Conditional independence inference, Automated theorem proving


In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables.