I went to listen to a workshop and some audience asked the presenter how the moments can improve the mutual information. I am learning the MI (Mutual Information) so didn't have enough knowledge to understand what it means. Then, I have done some research but still have some confusions. I am wondering if anyone has more knowledge about this can clarify for me. Here are my questions.

• Mutual information is usually calculated by bin functions to estimate the probability of two random variable which can be a case of two vectors X and Y. Is the moment generating function another way to estimate probability?

• If moment generating functions can present the probability of X and Y, how do we calculate it?

• Does a MI have a moments generating function?

• If MI has a moments generating function, how can we present a MI of X and Y by its moments functions?