Loopy Propagation: the Convergence Error in Markov Networks

Loopy propagation provides for approximate reasoning with Bayesian networks. In previous research, we distinguished between two different types of error in the probabilities yielded by the algorithm; the cycling error and the convergence error. Other researchers analysed an equivalent algorithm for pairwise Markov networks. For such networks with just a simple loop, a relationship between the exact and the approximate probabilities was established. In their research, there appeared to be no equivalent for the convergence error, however. In this paper, we indicate that the convergence error in a Bayesian network is converted to a cycling error in the equivalent Markov network. Furthermore, we show that the prior convergence error in Markov networks is characterised by the fact that the previously mentioned relationship between the exact and the approximate probabilities cannot be derived for the loop node in which this error occurs.