Learning Belief Networks in Pseudo-independent Domains Learning Belief Networks in Pseudo-independent Domains

A pseudo-independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. It has been shown that several commonly used algorithms for learning belief networks will fail when the data generating model is a PI model. A better understanding of these models will facilitate the design of better learning algorithms to copy with them. We propose formal deenitions of the whole spectrum of discrete PI models. We present a parameterization of PI models which leads to a better understanding of the mechanism that forms PI models. We then show that the well-known parity problems in machine learning is a degeneration of PI models. Therefore, PI models form a more general class of challenging problems for learning from data. Using an abstraction of a class of algorithms for learning belief networks , we show that PI models form the dividing line between success and failure of an algorithm using some form of conditional independence test and a single link search. We proposed several strategies to manage the computational complexity when a single link search is extended into a multi-link search. The eeectiveness of these strategies are demonstrated with experimental results.