Q4 - Definition of I_{sep}

Q4 - Definition of I_{sep}

Noam P 30 Mar 2017 13:37

Hi,
We've seen this definition:

(1)

\begin{align} I_{sep}(G) = \{X \perp Y | Z : Z \ separates \ X \ and \ Y\} \end{align}

Does this definition rely on some probability? Or is it that given a graph G we construct the set of all X,Y,Z where Z separates X and Y and then, given a probability p we say that:

(2)

\begin{align} I_{sep}(G) \subseteq I(p) \end{align}

If p satisfies all these properties?

Re: Q4 - Definition of I_{sep}

Amir Globerson 30 Mar 2017 17:11

The definition of I_{sep}(G) doesn't rely on any distribution. As you wrote, it's a property of the graph.
And if p is a Markov network on G, then I_{sep}(G)\subset I(p) as you wrote.