4 3. (20 points) CSPs: Constraining Graph Structure Hired as a consultant, you built a Bayes’ net model of Cheeseboard Pizza customers. Last night, a corporate spy from Zachary’s Pizza deleted the directions from all your arcs. You still have the undirected graph of your model and a list of dependencies. You now have to recover the direction of the arrows to build a graph that allows for these dependencies. Note: X 6⊥⊥ Y means X is not independent of Y . A B C F G E A Distribution properties (dependencies): A 6⊥⊥ G B 6⊥⊥ F B 6⊥⊥ G | C a) (1 pt) Given the ﬁrst constraint only, circle all the topologies that are allowed for the triple ( A,C,G ). A B C F G A G C A G C A G C A G C X 1 X 2 X n E 1 E 2 E n-1 … P C E T N A D r(3, 3, 3, 4) 10 meters exit E A Action: increase elbow position b) (3 pt) Formulate direction-recovery for this graph as a CSP with explicit binary constraints only. The variables and values are provided for you. The variable E A
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