Multivariate conditional entropy

Question

I would like to take data columns and compute the multivariate conditional entropy. For instance, suppose I have columns $A, B, C D, E$ and I want to compute the conditional entropy $H(E | A,B,C,D)$. Can someone give a little explanation of all this, pointing out the first joint variable $A,B,C,D$ vs the second variable $E$. Then please give the algorithm and math for calculating the conditional entropy.

Answer 1

suppose I have columns A,B,C,D,E

If by "columns" you mean random variables, for which you know the joint (five dimensional) probability function, then to compute $H(E | A,B,C,D)$ you just use the common defition of conditional entropy

$$H(X | Y) = \sum_Y P(Y=y) H(X | Y=y)$$

replacing $X$ by $E$ and $Y$ by your (multivariate) variable $(A,B,C,D)$.