Problem
Consider again the Build-PDAG procedure of algorithm but now assume that we apply it in a setting where the independence tests might return incorrect answers owing to limited and noisy data.
a. Provide an example where Build-PDAG can fail to reconstruct the true underlying graph G ∗ even in the presence of a single incorrect answer to an independence question.
b. Now, assume that the algorithm constructs the correct skeleton but can encounter a single incorrect answer when extracting the immoralities.