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When can association graphs admit a causal interpretation? (English) Zbl 0828.05060
Cheeseman, P. (ed.) et al., Selecting models from data: artificial intelligence and statistics IV. Selected papers presented at the fourth international workshop on artificial intelligence and statistics held in January 1993. New York, NY: Springer-Verlag. Lect. Notes Stat., Springer-Verlag. 89, 205-214 (1994).
Summary: We discuss essentially linear structures which are adequately represented by association graphs called covariance graphs and concentration graphs. These do not explicitly indicate a process by which data could be generated in a stepwise fashion. Therefore, on their own, they do not suggest a causal interpretation. By contrast, each directed acyclic graph describes such a process and may offer a causal interpretation whenever this process is in agreement with substantive knowledge about causation among the variables under study. We derive conditions and procedures to decide for any given covariance graph or concentration graph whether all their pairwise independencies can be implied by some directed acyclic graph.
For the entire collection see [Zbl 0793.00022].

05C90 Applications of graph theory
68R10 Graph theory (including graph drawing) in computer science
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)