How can I calculate conditional mutual information of two continuous random variables given a discrete class?

Question

I have 23 continuous random variable and one class variable which is discrete (It's a Naïve Bayes structure). How can I calculate conditional mutual information of these variables conditioned on knowing class information? I have built a structure of Naïve Bayes and also I learned the parameters (mu and covariance).

Answer 1

In the naive Bayes structure, the variables $x_i$ and $x_j$ ($i,j$ are integers from 1 to 23 in your case) are independent given the class variable $C_k$; hence, the conditional mutual information $I(x_i;x_j|C_k)=0$ (for every pair $i,j$).