A conditional independence algorithm for learning undirected graphical models

When it comes to learning graphical models from data, approaches based on conditional independence tests are among the most popular methods. Since Bayesian networks dominate research in this field, these methods usually refer to directed graphs, and thus have to determine not only the set of edges, but also their direction. At least for a certain kind of possibilistic graphical models, however, undirected graphs are a much more natural basis. Hence, in this area, algorithms for learning undirected graphs are desirable, especially, since first learning a directed graph and then transforming it into an undirected one wastes resources and computation time. In this paper I present a general algorithm for learning undirected graphical models, which is strongly inspired by the well-known Cheng–Bell–Liu algorithm for learning Bayesian networks from data. Its main advantage is that it needs fewer conditional independence tests, while it achieves results of comparable quality.