Description of conditional independence structures by means of
imsets: a connection with product formula validity.
In Uncertainty in Intelligent Systems (B. Bouchon-Meunier,
L. Valverde, R.R. Yager eds.), North-Holland,
Amsterdam - London - New York - Tokyo 1993, pp. 179-194.
The paper is a contribution to (an extension of) the theory
developed in the series of 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.
- Main features of a new approach to the mathematical description
of structures of stochastic conditional independence, namely by means of
so-called imsets, are recalled. It is shown that a probability
measure has conditional independence structure given by an imset if and
only if it satisfies the corresponding product formula. This result
is proved under a formal assumption that the corresponding imset is
regular in a certain sense. It is shown that every imset over
at most four attributes (= variables) is regular in this sense.
- AMS classification 68T30 , 62H05
- stochastic conditional independence
- regular imset
- product formula
pdf copy (converted postscript version) (229kB) is available.
Except the above mentioned series the paper builds also on the work: