M. Studeny: 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

A pdf copy (converted postscript version) (229kB) is available.

Except the above mentioned series the paper builds also on the work: