Bayesian Networks: The Parental Synergy and the Prior Convergence Error

Abstract

In a Bayesian network, for any node its conditional probabilities given all possible combinations of values for its parent nodes are specified. In this paper a new notion, the parental synergy, is introduced which is computed from these conditional probabilities. This paper then conjectures a general expression for what we called the prior convergence error. This error is found in the marginal prior probabilities computed for a node when the parents of this node are assumed to be independent. The prior convergence error, for example, is found in the prior probabilities as computed by the loopy-propagation algorithm; a widely used algorithm for approximate inference. In the expression of the prior convergence error, the parental synergy is an important factor; it determines to what extent the actual dependency between the parent nodes can affect the computed probabilities. This role in the expression of the prior convergence error indicates that the parental synergy is a fundamental feature of a Bayesian network.