From a6a164fcb795af2fb9c696436c5701aeb3fa9d3b Mon Sep 17 00:00:00 2001 From: jbayrooti <46546745+jbayrooti@users.noreply.github.com> Date: Sat, 20 Mar 2021 00:57:39 -0600 Subject: [PATCH] Add textbook reference for proof 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) --- representation/directed/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/representation/directed/index.md b/representation/directed/index.md index f514c29..ae3adfd 100644 --- a/representation/directed/index.md +++ b/representation/directed/index.md @@ -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).