New answers tagged it.information-theory
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votes
Accepted
Reverse Pinsker's inequality for smooth density classes
The answer is no.
E.g., suppose that both $f$ and $g$ are supported on $B=[0,1]$, with $f=1$ on $B$ and
$$g(x)=(1-h+x)\,1(0\le x<h)+1(h\le x<1-h)+(x+h)\,1(1-h\le x\le1)$$
for $h\in(0,1/2)$ and $...
1
vote
Are the derivatives of the differential entropy power alternating?
Michel Ledoux discusses this as the "completely monotone conjecture" in his paper Differentials of entropy and Fisher information along heat flow: a brief review of some conjectures
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