Brief Description of MB Fan Search Inputs and Output.
The MB Fan Search algorithm uses the principle of the PC algorithm to search for Markov blanket DAGs for a given target T with respect to conditional independence information I for a list of variables <v1, ..., vn, T>. Assuming the independence information provided by I is accurate, it returns a pattern containing:
(a) The target T, the true parents and children of T, and the true parents of the children of T.
(b) All edges among T, true parents of T, true children of T, and true parents of children of T. Some of these edges may not be oriented as -->.
(c) Possibly some extra nodes and edges to account for the possibility that if some edges T---v were actually oriented as T-->v, these nodes and adjacencies would be required in the MB DAG of T.
(d) No nodes or adjacencies or --> edges that do no belong in some MB DAG consistent with independence facts supplied by (2).
There may also be some bidirected <-> edges in G_out if the independence information from (2), above, is inconsistent. These <-> edges may either be left in the final graph or oriented as if they were directed edges.