M. Studeny: Bayesian networks from the point of view of chain graphs. In Uncertainty in Artificial Intelligence. Proceedings of the 14th Conference (G. F. Cooper, S. Moral eds.), Morgan Kaufmann, San Francisco 1998, pp. 496-503.

The paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with respect to a chain graph which is Markov equivalent to the Bayesian network. A graphical characterization of such graphs is given. The class of equivalent graphs can be represented by a distinguished graph which is called the largest chain graph. The factorization formula with respect to the largest chain graph is a basis of a proposal of how to represent the corresponding (discrete) probability distribution in a computer (i.e. 'parametrize' it). This way does not depend on the choice of a particular Bayesian network from the class of equivalent networks and seems to be the most efficient way from the point of view of memory demands. A separation criterion for reading independency statements from a chain graph is formulated in a simpler way. It resembles the well-known d-separation criterion for Bayesian networks and can be implemented 'locally'.

AMS classification 68T30, 62H05

Bayesian network
chain graph
Markov equivalence
factorization formula
superactive route

A pdf copy (343kB) is available.

The paper builds on the following works: