Abstract

In learning Bayesian networks one meets the problem of non-unique graphical description of the respective statistical model. One way to avoid this problem is to use special chain graphs, named essential graphs. An alternative algebraic approach uses certain integervalued vectors, named standard imsets, instead. In this paper we present algorithms which make it possible to transform graphical representatives into algebraic ones and conversely. A direct formula is a basis for translation of any chain graph equivalent to a Bayesian network into a standard imset. An inverse algorithm, which gives the essential graph, has two stages. The middle result of this procedure is a certain sequence of sets of variables, which can be turned into a hierarchical junction tree. We present both the mathematical theory and the algorithms, which we implemented in the R language.