Errata for ”Sonntag, D. (2013). Chain Graph
Interpretations and their Relations. In
Proceedings of the 12th European Conference on
Symbolic and Quantitative Approaches to
Reasoning under Uncertainty (ECSQARU 2013)
Lecture Notes in Artificial Intelligence 7958,
510-521.”
Dag Sonntag and Jose M. Peña
ADIT, IDA, Linköping University, Sweden
dag.sonntag@liu.se, jose.m.pena@liu.se
Theorem 1, in page 514, is only shown to hold for AMP and MVR CGs.
Hence, it should be changed to:
Theorem 1. A CG in the AMP or MVR interpretation has the minimal set of
non-directed edges for its Markov equivalence class iff no feasible split is possible.
Similarly Theorem 2, in page 515, only holds for AMP and MVR CGs and
should be stated as:
Theorem 2. For any Markov equivalence class of CGs in the AMP or MVR
CG interpretation, there exists a unique minimal (w.r.t. inclusion) set of nondirected edges that is shared by all members of the class.
The proofs for these theorems follows as shown in [1]. To see that the theorems do not hold for the LWF CG interpretation consider the LWF CGs
X→Y →Z−W ←X and X→Y −Z←W ←X. No split is feasible in either CG and
even though they represent the same independence model they do not have the
same set of undirected edges.
Bibliography
References
1. D. Sonntag and J. M. Peña. Chain Graph Interpretations and Their Relations.
International Journal of Approximate Reasoning, 58:39–56, 2014.