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Results tagged with it.information-theory
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user 29697
Theoretical and experimental aspects of information theory and coding theory. This tag covers but is not limited to following branches: information theory, information geometry, optimal transportation theory, coding theory.
2
votes
Bounding the difference of mutual information between input-output pairs
The problem is that entropy can differ arbitrarily despite a small total variation distance. Let
$X_1 = 0$ w.prob. $1$.
$X_2 = 0$ w.prob. $1-\delta$ and otherwise, $X_2 \sim \text{Uniform}\{1,\dots,n …
- 4,529
7
votes
Computational complexity theoretic incompleteness: is that a thing?
This might be more of an analogy, but major complexity conjectures like P=NP could be considered related.
Background: a common "complete" problem for a specified time limit is: given a Turing machine, …
- 4,529
22
votes
Accepted
information-theoretic derivation of the prime number theorem
You may be interested in this arxiv paper [1], "Some information-theoretic computations related to the distribution of prime numbers", Ioannis Kontoyiannis, 2007.
It discusses Chebyshev's 1852 result, …
- 4,529
5
votes
What characterizations of relative information are known?
I just want to make a point (and apologies if this seems already clear or obvious) that many such characterizations wil have a simple feature in common: a form of additivity axiom.
This goes right ba …
CommunityBot
- 1
7
votes
Separating Heavier from the Lighter Balls
The answer is indeed asymptotic to $4n/\log(n)$, but I don't know of an elementary or easy construction for this upper bound. I believe simple probabilistic-method type constructions do not work.
Thi …
CommunityBot
- 1
5
votes
concentration inequality for entropy from sample
Here's a step that seems nice enough to point out. It still leaves a parameter to pick, and I'm not sure it's ever better than applying Bernstein, but it does something different.
We can get a probab …
- 4,529