Marginal problem in different calculi of AI.
In Advances in Intelligent Computing - IPMU'94
(B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh eds.),
Lecture Notes in Computer Science 945, Springer-Verlag,
Berlin - Heidelberg 1995, pp. 348-359.
- By the marginal problem is understood the problem
of the existence of a global (full-dimensional) knowledge representation
which has prescribed less-dimensional representations as marginals.
It arises in several calculi of artificial intelligence: probabilistic
reasoning, theory of relational databases, possibility theory,
Dempster-Shafer's theory of belief functions, Spohn's theory of ordinal
conditional functions. The following result, already known in
probabilistic framework and in the framework of relational databases,
is shown also for the other calculi: the running intersection
property is a necessary and sufficient condition for pairwise
compatibility of prescribed less-dimensional knowledge representations
being equivalent to the existence of a global representation having
them as marginals. Moreover, a simple method of solving the marginal
problem in the possibilistic framework and its subframeworks is
- AMS classification 68T30, 94D05, 68P15
- marginal problem
- database relation
- natural conditional function
- possibility theory
- Dempster-Shafer's theory
- running intersection property
pdf copy (converted postscript version) (219kB) is available.
The paper builds on the following works:
- P.P. Shenoy: Conditional independence in valuation-based
systems. International Journal of Approximate Reasoning
10 (1994), n. 3, pp. 203-234.
- M. Studeny:
Conditional independence and natural conditional functions.
International Journal of Approximate Reasoning
12 (1995), n. 1, pp. 43-68.
- H.G. Kellerer: Verteilungsfunktionen mit gegebenem
Marginalverteilungen. (in German)
Z. Wahrsch. Verw. Gebiete 3 (1964), pp. 247-270.