New algorithm for learning decomposable models

There exist a lot of algorithms for the construction of Bayesian Networks (BN). But almost all computations in BN are carried out by transforming them to another special type of probabilistic models decomposable models (DM). This task of transformation is known to be a NP complex problem and todays algorithms for the construction of BN cannot guarantee the existence of reasonably small DM (it is necessary to fit this DM to the memory of computer). So why not to construct directly DMs? Advantages and disadvantages of the construction of BNs and DMs are discussed. A new algorithm for construction of DMs using tests of independence is presented. It is based on the recursive identification of a simplicial vertex (SV) and its boundary (which forms a clique of DM and enables removing of this vertex). This identification of simplicial vertices is based on definition of the SV and a heuristic approach for finding boundary to a given vertex, which is asymptotically correct. This algorithm needs moreover a heuristic approach how to select a vertex to be simplicial if no such vertex is identified from the definition. A comparison of quality (evaluated as Kullback-Leibler I-divergency) of BNs constructed by program BNPC and DMs constructed by the new algorithm for different sizes of learning data is shown.