M. Studeny: An algebraic approach to structural learning Bayesian networks. In Proceedings of the 11th International Conference IPMU 2006 (B. Bouchon-Meunier, R. R. Yager eds.), Editions EDK, Paris, France 2006, pp. 2284-2291.

The basic idea of the paper is that every Bayesian network (BN) model is uniquely described by a certain integral vector, named a standard imset. Every score equivalent decomposable criterion Q for learning BN models appears to be an affine function of the standard imset. The algebraic view can naturally be extended to databases: if a criterion Q of the above mentioned kind is fixed then every database can be represented in the form of a data vector (relative to Q), which is a vector of the same dimension as the standard imset.

AMS classification 68T30

standard imset
learning Bayesian networks
quality criterion

A pdf version (227kB) is available.

The paper builds on the ideas delevoped in Chapter 8 of