M. Studeny:
Structural semigraphoids.
International Journal of General Systems 22
(1994), n. 2, pp. 207-217.
The paper is an overview of the theory developed in the
series of three papers
- M. Studeny:
Description of structures of stochastic conditional independence
by means of faces and imsets.
International Journal of General Systems 23
(1994/5), n. 2-4, p. 123-137, pp. 201-219, pp. 323-341.
- where the proofs of main results are given.
- Abstract
- A new approach to the mathematical description of
structures of stochastic conditional independence by means of imsets
and faces developed in the series of papers mentioned above is related
to the classical approach by means of the notion
of structural semigraphoid. It is shown how to realize the
corresponding deductive mechanism to infer probabilistically valid
consequences of input information about conditional independence
structure, called facial implication. In the case of four attributes
(= random variables), structural semigraphoids are characterized in terms
of inference rules.
- AMS classification 68T30, 62H05
- Keywords
- conditional independence
- dependency model
- semigraphoid
- structural face
- skeletal imset
- structural semigraphoid
- A
scanned pdf copy (698kB) is available. The paper is an overview
of the mentioned theory, the proofs of main results are in the above
mentioned series of papers.
The topic of the paper was motivated by the works:
- J. Pearl: Probabilistic Reasoning in Intelligent Systems:
Networks of Plausible Inference. Morgan Kaufman, San Mateo CA
1988.
- M. Studeny:
Conditional independence relations have no finite complete
characterization. In Information Theory, Statistical Decision
Functions and Random Processes. Transactions of the 11th Prague Conference
vol. B (S. Kubik, J.A. Visek eds.), Kluwer, Dordrecht - Boston - London
(also Academia, Prague) 1992, pp. 377-396.
- D. Geiger and J. Pearl:
Logical and algorithmical properties of conditional independence
and graphical models. Annals of Statistics
21 (1993), n. 4, pp. 2001-2021.