This was what I expected to see, and I believe it’s equivalent to H(X,Y,Z) = H(X) + H(Y) + H(Z) - I(X;Z) - I(Z;Y) - I(X;Y | Z)
It appears that Z is very artificially constructed—Z is exactly I(X,Y) in the example. Therefore, H(X,Y) = H(X,Y,Z). Since the term I(X,Y | Z) is mutual information about X and Y given Z, that’s just 0. There’s no new mutual information about X and Y that isn’t already in Z. So I believe that we could replace it with +I(X,Y) - I(X,Y,Z), and get inclusion-exclusion.
Hello, world!
I just sent in my application. I’m really curious, and it looks like nothing I’ve ever seen before. I’m still a college student, so I doubt I’ll be accepted (the first few questions make Rationality Boot Camp look as though it’s targeted towards professors and established scientists), but this is something I’m really excited about, and it couldn’t hurt to apply. I’m hoping for the best.
Peace and happiness, wobster109