Bayesian Networks from the Point of View of Chain Graphs
This work provides a more efficient representation for Bayesian networks, benefiting researchers and practitioners in probabilistic modeling and machine learning, though it appears incremental as it builds on existing graphical models.
The paper argues for using chain graphs to describe probabilistic conditional independence structures, showing that every Bayesian network can be equivalently represented by a factorization formula with respect to a chain graph, and proposes a memory-efficient method for parameterizing discrete probability distributions based on the largest chain graph.
AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with respect to a chain graph which is Markov equivalent to the Bayesian network. A graphical characterization of such graphs is given. The class of equivalent graphs can be represented by a distinguished graph which is called the largest chain graph. The factorization formula with respect to the largest chain graph is a basis of a proposal of how to represent the corresponding (discrete) probability distribution in a computer (i.e. parametrize it). This way does not depend on the choice of a particular Bayesian network from the class of equivalent networks and seems to be the most efficient way from the point of view of memory demands. A separation criterion for reading independency statements from a chain graph is formulated in a simpler way. It resembles the well-known d-separation criterion for Bayesian networks and can be implemented locally.