How to calculate threshold level for mutual information scores?

Question

Im quite new to the world of statistics, and only just finished work on my first (successful) attempt to calculate mutual information scores.

Now lets say that for the column pairs AB, BC, CD and DE I have mutual information scores 0.1111, 0,9999, 1.23 and 1.5.

I need to use these values to accertain which of column pairs AB, BC, CD and DE are dependent of each other, and which are not.

To do so, I need to colculate a threshold limit. I assume that if the threshold level is X, the all MI scores larger than X means that the two columns are related, while scores < X means that the two columns are not related.

Can someone point me towards a suitable threhold calculation process?

Answer 1

You could try shuffling your data to make it independent, and use the same procedure to compute the MI score. This would provide a surrogate for the null hypothesis, and if you are okay with p-values, perhaps you can choose a threshold by selecting something like p-value of 0.05.

Answer 2

Computing Normalized Mutual Information will put the values into more meaningful terms (NMI = 0, two variables contain no information about one another, NMI = 1, two variables contain perfect information about one another).

To determine a threshold I think it will really depends on what you plan to do after you state the dependence/independence between two nodes. NMI = 0.2 may seem low, but it means that the two variables still contain some information about one another, so your 'threshold' should depend on your specific goal.