A new approach for learning belief networks using independence criteria

In the paper we describe a new independence-based approach for learning Belief Networks. The proposed algorithm avoids some of the drawbacks of this approach by making an intensive use of low order conditional independence tests. Particularly, the set of zero- and first-order independence statements are used in order to obtain a prior skeleton of the network, and also to fix and remove arrows from this skeleton. Then, a refinement procedure, based on minimum cardinality d-separating sets, which uses a small number of conditional independence tests of higher order, is carried out to produce the final graph. Our algorithm needs an ordering of the variables in the model as the input. An algorithm that partially overcomes this problem is also presented.