Towards Understanding of Pseudo-independent Domains

A pseudo-independent (PI) domain is a problem domain where a proper subset of a set of collectively dependent variables displays marginal independence. Common algorithms for learning belief networks cannot learn a faithful representation of the domain dependence when the data is obtained from a PI domain. Since we usually have no a priori knowledge whether a domain of interest is PI or not, we may learn an incorrect belief network, suffer from the consequence, and be not aware of it. Design of more reliable learning algorithms depends highly on a better understanding of these domains. This paper reports our progress towards such a goal. We characterize the whole spectrum of discrete PI domains with formal definitions. This forms a basis for studying them. We present our progress on parameterization of PI domains which eventually will lead to a better understanding of the mechanism that forms PI domains. Whether PI domains exist in practice is a common concern. We show that parity and modulus addition problems are special PI domains, which provides positive evidence. Application of our results to learning is discussed.