Labeling evaluation in probabilistic networks

In many pattern recognition problems a probabilistic labeling of a network is given, and it is desired to obtain a unique unambiguous labeling for the network. This labeling should be influenced by the given probabilistic labeling, and by the joint distributions of the labels at subsets of nodes of the network. Relaxation algorithms have frequently been used to find such a labeling, but no method has been available to evaluate the results or to compare two different labelings. A measure is proposed here for evaluating labelings based on the given probabilistic labeling and joint distributions. This measure can also be used to define a termination criterion for relaxation by evaluating the labeling at each iteration. In addition, it could be used to evaluate labelings derived by any other process, and to guide heuristic search.