#perfect-map

2 questions from Probabilistic & Graphical Models

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hardAI-checkedProbabilistic & Graphical Models

Graph 0 below is a perfect map for a set of independencies $\mathcal{U}$ . Which statement about graphs 1–3 is correct?

Four DAGs over x1 to x7 with the same skeleton. All have x1 to x3, x2 to x4, x3 to x6, x4 to x7 and x7 to x6. Graph 0 adds x2 to x5, x5 to x7, x3 to x7. Graph 1 adds x2 to x5, x7 to x5, x3 to x7. Graph 2 adds x2 to x5, x5 to x7, x7 to x3. Graph 3 adds x5 to x2, x5 to x7, x3 to x7.

Graph 3 is a perfect map; graphs 1 and 2 are not I-maps1
All three are I-maps because they share graph 0's skeleton2
Graph 1 is a perfect map; graphs 2 and 3 are I-maps only3
Graphs 2 and 3 are perfect maps; graph 1 is not an I-map4

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