On Fci Deficiency

Causally insuucient structures (models with latent or hidden variables, or with confounding etc.) of joint probability distributions have been subject of intense study not only in statistics, but also in various AI systems. In AI, belief networks, being representations of joint probability distribution with an underlying directed acyclic graph structure, are paid special attention due to the fact that eecient reasoning (uncertainty propagation) methods have been developed for belief network structures. Algorithms have been therefore developed to acquire the belief network structure from data. As artifacts due to variable hiding negatively innuence the performance of derived belief networks, models with latent variables have been studied and several algorithms for learning belief network structure under causal insuuciency have also been developed. Regrettably, some of them are known already to be erroneous (e.g. IC algorithm of 12]). This paper is devoted to another algorithm, the Fast Causal Inference (FCI) Algorithm of 17]. It is proven by a specially constructed example that this algorithm, as it stands in 17], is also erroneous. Fundamental reason for failure of this algorithm is the temporary introduction of non-real links between nodes of the network with the intention of later removal. While for trivial dependency structures these non-real links may be actually removed, this may not be the case for complex ones, e.g. for the case described in this paper. A remedy of this failure is proposed.