Efficient Stepwise Selection in Decomposable Models

In this paper, we present an efficient way of performing stepwise selection in the class of decomposable models. The main contribution of the paper is a simple characterization of the edges that canbe added to a decomposable model while keeping the resulting model decomposable and an efficient algorithm for enumerating all such edges for a given model in essentially O(1) time per edge. We also discuss how backward selection can be performed efficiently using our data structures.We also analyze the complexity of the complete stepwise selection procedure, including the complexity of choosing which of the eligible dges to add to (or delete from) the current model, with the aim ofminimizing the Kullback-Leibler distance of the resulting model from the saturated model for the data.