Question on Mutual Information MI()

[jonnyschaefer]

Hello,

I have problems understanding the way the use of MI(x, y, xy, unit = "log2") is intended.

The documentation states:

x: a numeric probability vector P(X).
y: a numeric probability vector P(Y).
xy: a numeric joint-probability vector P(X,Y).

How can xy be a vector?
If I understand mutual information correctly it should be a 2D matrix, so that xy[i,j] gives the joint probability, right?

https://en.wikipedia.org/wiki/Mutual_information#In_terms_of_PMFs_for_discrete_distributions

[HajkD]

Hi @jonnyschaefer

Yes, there are two ways the MI() function could have been implemented.

• Version one, MI() takes the the joint probability P(X,Y) as 2D matrix and then internally converts it to a joint probability vector xy[i,j] through indexing.

• Version two (which is what I implemented), MI() takes the the joint probability P(X,Y) directly as probability vector AFTER the user converts their 2D matrix to a joint probability vector { xy[i,j] }.

I chose version two to give users maximum flexibility on how to define their joint probabilities.

I hope this clarifies the usability?

Any concrete suggestions for improvement are always welcome.

With many thanks and very best wishes,
Hajk