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) and moments so don't have enough knowledge to understand what it means. As I know so far, the moments generating functions find moments mathematical presentation for a random variable (Please correct me if I am wrong). 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?