This doesn’t quite work. The theorem and examples only work if you maximize the unconditional mutual information, H(X;Y), not H(X;Y|A). And the choice of X is doing a lot of work — it’s not enough to make it “sufficiently rich”.
This doesn’t quite work. The theorem and examples only work if you maximize the unconditional mutual information, H(X;Y), not H(X;Y|A). And the choice of X is doing a lot of work — it’s not enough to make it “sufficiently rich”.