Consistency in stochastic networks

Abstract

Stochastic networks are given by graphs, whose vertices (nodes, neurons or spins) can take one out of a finite number of states at any given time. The way each vertex changes its state over time is determined by the edges connecting it with other vertices. The edges represent probabilistic dependencies. Updating is usually performed in a parallel or sequential way. Stochastic networks are used to model expert sytems; in this context confidence numbers are given as dependencies between vertices and the problem is to see, to what extent they are stochastically consistent. Given a graph and a set (or subset) of confidence numbers, we give a procedure that, starting from these confidence numbers, leads to local characteristics which are consistent with the graph.