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Add textbook reference for proof
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I thought that this proof was helpful for understanding the intuition behind the provided fact. It might be nice to give students a precise reference to easily find this proof (or I can add it into these notes directly)
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jbayrooti authored Mar 20, 2021
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Expand Up @@ -120,7 +120,7 @@ The cascade-type structures (a,b) are clearly symmetric and the directionality o

**Fact:** If $$G,G'$$ have the same skeleton and the same v-structures, then $$I(G) = I(G').$$

Again, it is easy to understand intuitively why this is true. Two graphs are $$I$$-equivalent if the $$d$$-separation between variables is the same. We can flip the directionality of any edge, unless it forms a v-structure, and the $$d$$-connectivity of the graph will be unchanged. We refer the reader to the textbook of Koller and Friedman for a full proof.
Again, it is easy to understand intuitively why this is true. Two graphs are $$I$$-equivalent if the $$d$$-separation between variables is the same. We can flip the directionality of any edge, unless it forms a v-structure, and the $$d$$-connectivity of the graph will be unchanged. We refer the reader to the textbook of Koller and Friedman for a full proof in Theorem 3.7 (page 77).

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