This paper addresses learning stochastic rules especially on an inter-attribute relation based on a Minimum Description Length (MDL) principle with a finite number of examples, assuming an application to the design of intelligent relational database systems. The stochastic rule in this paper consists of a model giving the structure like the dependencies of a Bayesian Belief Network (BBN) and some stochastic parameters each indicating a conditional probability of an attribute value given the state determined by the other attributes' values in the same record. Especially, we propose the extended version of the algorithm of Chow and Liu in that our learning algorithm selects the model in the range where the dependencies among the attributes are represented by some general plural number of trees.
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