K. Tanaka, M. Studeny, A. Takemura, T. Sei: A linear-algebraic tool for conditional independence inference. Journal of Algebraic Statistics 6 (2015), n. 2, pp. 150-167.

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.

AMS classification 90A99, 68T15

conditional independence inference
automated theorem proving
semi-elementary imset

A pdf version of the published paper (424kB) is available.

The paper builds on results from the following publications: