Scaling Bayesian network discovery through incremental recovery

Bayesian networks are a type of graphical models that, e.g., allow one to analyze the interaction among the variables in a database. A well-known problem with the discovery of such models from a database is the ``problem of high-dimensionality''. That is, the discovery of a network from a database with a moderate to large number of variables quickly becomes intractable. Most solutions towards this problem have relied on prior knowledge on the structure of the network, e.g., through the definition of an order on the variables. With a growing number of variables, however, this becomes a considerable burden on the data miner. Moreover, mistakes in such prior knowledge have large effects on the final network. Another approach is rather than asking the expert insight in the structure of the final network, asking the database. Our work fits in this approach. More in particular, before we start recovering the network, we first cluster the variables based on a chi-squared measure of association. Then we use an incremental algorithm to discover the network. This algorithm uses the small networks discovered for the individual clusters of variables as its starting point. We illustrate the feasibility of our approach with some experiments. More in particular, we show that in the case where one knows the network, and thus the order, our algorithm yields almost the same network which is, moreover, still an I-map.