Formula for entropy conditional on >1 variables?

by Inquirer
Tags: conditional entropy, entropy, multiple variables
Inquirer is offline
Oct6-11, 06:34 PM
P: 4

I want to compute the conditional entropy H(A | B,C), given probability distributions for each of the variables.

It would be nice to have a right-hand side not involving conditionals. H(A|B) = H(A,B) - H(B) but how does it work out if there are more than one conditional variable?

I tried, as a dumb guess, H(A,B,C) - H(B,C), but from using it further down the line, I doubt that's correct.

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Inquirer is offline
Oct7-11, 11:25 AM
P: 4
I worked through it again and discovered an error or two in my calculations. In the end it looks like

H(A|B,C) = H(A,B,C) - H(B,C)

is correct after all.

This is quite clear when illustrated with a Venn diagram similar to the one here.

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