Hi,
Is it possible to have topologically different Markov Random Fields (few different edges) and yet yielding the same inference results ?
Thanks!
Hi, Is it possible to have topologically different Markov Random Fields (few different edges) and yet yielding the same inference results ? Thanks! 


If two distributions have graphs that are Markov equivalent then that means that they are both a factorization of the same probability distribution. Example: if $p_{X_1, X_2, X_2} = p_{X_1}p_{X_2\mid X_1}p_{X_3\mid X_2}$ then there also exists other factorizations. To evaluate these factorizations would be equivalent to evaluating the joint distribution. Another example: $\arg\max_x P(A\in x,B) = \arg\max_x P(A\in x \mid B)P(B) = \arg\max_x P(B\mid A\in x)P(A\in x)$. The answer is therefore yes, it is possible to have differing edges and still obtain the same result. 

