Abstract: This paper presents an extension to the Conservative PC algorithm which is able to detect violations of adjacency faithfulness under causal sufficiency and triangle faithfulness. Violations can be characterized by pseudo-independent relations and equivalent edges, both generating a pattern of conditional independencies that cannot be modeled faithfully. Both cases lead to uncertainty about specific parts of the skeleton of the causal graph. These ambiguities are modeled by an f-pattern. We prove that our Adjacency Conservative PC algorithm is able to correctly learn the f-pattern. We argue that the solution also applies for the finite sample case if we accept that only strong edges can be identified. Experiments based on simulations and the ALARM benchmark model show that the rate of false edge removals is significantly reduced, at the expense of uncertainty on the skeleton and a higher sensitivity for accidental correlations. [Copyright &y& Elsevier]
International Journal of Approximate Reasoning. Sep2009, Vol. 50 Issue 8, p1306-1313. 8p.
GRAPH theory, EQUIVALENCE relations (Set theory), DISTRIBUTION (Probability theory), MARKOV processes, and FACTORIZATION (Mathematics)
Abstract: This paper deals with chain graphs under the classic Lauritzen–Wermuth–Frydenberg interpretation. We prove that the strictly positive discrete probability distributions with the prescribed sample space that factorize according to a chain graph G with dimension d have positive Lebesgue measure wrt , whereas those that factorize according to G but are not faithful to it have zero Lebesgue measure wrt . This means that, in the measure-theoretic sense described, almost all the strictly positive discrete probability distributions with the prescribed sample space that factorize according to G are faithful to it. [Copyright &y& Elsevier]