How are the "Link Strength true", "Link Strength blind" and "Mutual Information" calculated in this report on Bayesian networks? I'm trying to understand how to calculate the strength of every arc in a Bayesian Network.
I came across this report Measuring Connection Strengths and Link Strengths in Discrete Bayesian Networks, but I got lost in the calculation.
In particular, how are the values of Link Strength true, Link Strength blind, and Mutual Information computed in Table 1?
The $MI$ is easy enough.
For $MI(X \to Z)$, we get $U([0.5, 0.5]) - 0.5 U([0.9, 0.1]) - 0.5 U([0.1, 0.9])$. The $[0.5, 0.5]$ comes from $0.5 [0.9, 0.1] + 0.5[0.1, 0.9]$ -- this is how to calculate $P(Z)$ from $P(Z|X)$ and $P(X)$.
For $MI(X \to Y)$, we need to marginalize out $Z$. This takes a bit of work, but is not too hard. I manually verified all of the reported values in the figure, and they are all correct.
The $\mathrm{LS}{\mathrm{true}}$ values are a bit trickier, but still feasible. I managed to get the same values. It is important when calculating $\mathrm{LS}{\mathrm{true}}(X \to Z)$ that $Y$ is not a parent, so it does not come into it -- which is why the MI gives exactly the same value.
The &quot;blind&quot; version took me a bit more effort to implement, but again, I am getting the same values as reported in the table.
I used the &quot;simple formula&quot; at the top of page 5.