16. m-Separation Score
16.1. Summary
The m-Separation Score evaluates a candidate graph by comparing its implied m-separation relations to a target set of (in)dependence relations. It is primarily used in oracle or simulation settings where the true m-separations are known.
16.2. When to use
You have a known set of ground-truth independences (for example, from a true graph) and want to score candidate graphs.
You are evaluating or comparing algorithms under a fixed independence oracle.
You want a structural score that does not depend directly on data.
16.3. Model class
Graphical models represented as DAGs, MAGs, or PAGs, evaluated via m- separation.
16.4. Score form (conceptual)
The score typically rewards graphs whose m-separation relations match those of the oracle and penalizes mismatches (false independences or false dependencies).
16.5. Parameters in Tetrad
No parameters.
16.6. Strengths
Clean separation of structural correctness from statistical estimation.
Ideal for simulation studies and theoretical investigations.
16.7. Limitations
Not applicable when oracle m-separations are unknown.
Does not use real data; purely structural.