Structural imsets: an algebraic method for describing
conditional independence structures.
In Proceedings of the 10th International Conference IPMU 2004
(B. Bouchon-Meunier, G. Colleti, R. R. Yager eds.), Editrice Universita La Sapienza,
Perugia, Italy, 2004, vol. 2, pp. 1323-1330.
- The contribution recalls basic ideas of the method of structural imsets which
is a non-graphical method for describing probabilistic conditional
independence structures based on the use of special integral (= integer-valued)
vectors. The attention is devoted to the concept of independence implication
between structural imsets defined as the inclusion of their induced conditional
independence structures. An algebraic characterization of independence
implication is recalled and implementation aspects are analyzed in more details
from a theoretical point of view.
- AMS classification 68T30
- conditional independence structure
- structural imset
- independence implication
pdf copy of a preprint (285kB) is available.
The paper builds on the following publications:
- A. Schrijver: Theory of Linear and Integer Programming.
John Wiley, 1986.
- M. Studeny, R.R. Bouckaert, T. Kocka:
Extreme supermodular set functions over five variables.
Research report n. 1977,
Institute of Information Theory and Automation,
Prague, January 2000 (32 pages).
- M. Studeny:
Probabilistic Conditional Independence Structures. Springer-Verlag, London, 2005.