K. Tanaka, M. Studeny, A. Takemura, T. Sei:
A linearalgebraic tool for conditional independence inference.
Journal of Algebraic Statistics
6 (2015), n. 2, pp. 150167.
 Abstract

In this note, we propose a new linearalgebraic 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 linearalgebraic 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
 Keywords
 conditional independence inference
 automated theorem proving
 semielementary imset
 A
pdf version of the published paper (424kB) is available.
The paper builds on results from the following publications:
 R. Bouckaert, R. Hemmecke, S. Lindner, M. Studeny:
Efficient algorithms for conditional independence inference.
Journal of Machine Learning Research
11 (2010), pp. 34533479.
 M. Studeny (2005). Probabilistic Conditional Independence
Structures. London: SpringerVerlag.
 M. Baioletti, G. Busanello, B. Vantaggi:
Conditional independence structure and its closure: Inferential rules and algorithms.
International Journal of Approximate Reasoning
50 (2009), pp. 10971114.
 T. Kashimura, T. Sei, A. Takemura , K. Tanaka (2012)
Cones of elementary imsets and supermodular functions: a review and some new results.
In Proceedings of the Second CRESTSBM International Conference ``Harmony of Groebner Bases
and the Modern Industrial Society, pages 117152.