# Multivariate conditional entropy

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.

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 $$(A,B,C,D)$$.