Learning Bayesian belief networks based on the minimum description length principle: Basic properties

This paper addresses the problem of learning Bayesian belief networks (BBN) based on the minimum description length (MDL) principle. First, we give a formula of description length based on which the MDL-based procedure learns a BBN. Secondly, we point out that the difference between the MDL-based and Cooper and Herskovits procedures is essentially in the priors rather than in the approaches (MDL and Bayesian), and recommend a class of priors from which the formula is obtained. Finally, we show as a merit of using the formula that a modified version of the Chow and Liu algorithm is obtained. The modified algorithm finds a set of trees rather than a spanning tree based on the MDL principle.