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,
- 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
- AMS classification 68T30
- standard imset
- learning Bayesian networks
- quality criterion
pdf version (227kB) is available.
The paper builds on the ideas delevoped in Chapter 8 of
- M. Studeny:
Probabilistic Conditional Independence Structures. Springer-Verlag, London, 2005.