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Results tagged with it.information-theory
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user 1044
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.
6
votes
Accepted
distance in terms of the variance between two absolutely continuous probability measures
The Kullback-Leibler divergence is a special case of Rényi divergence. In your notation, for $\alpha > 0$, the Rényi divergence of order $\alpha$ is defined by
$$
D_\alpha(p_0,p_1)
= \frac{1}{\alpha …
- 1,446
1
vote
Convergence of an empirical distribution w.r.t. the Hellinger distance
Here's a quick argument to get something in the direction of what you want, but rather weaker than you asked for. First of all, using the Cauchy-Schwarz inequality,
$$
\mathbb{E} d_H(P,\hat{P}_n) \le …
- 11.4k
7
votes
Entropy of a general prob. measure
It is not. If a probability measure on $\mathbb{R}$ is absolutely continuous and has density $f$, then "entropy" usually refers to the differential entropy, defined in the Wikipedia page falagar link …
- 11.4k
1
vote
l^p space inequality related to compressed sensing
Regarding the last part of the question, I haven't looked at either of the following books myself, but I've seen them referred to for systematic presentations of the theory of quasinormed spaces (whic …
- 11.4k
5
votes
When are probability distributions completely determined by their moments?
I don't have it on hand, but Billingsley's book "Probability and Measure" has a nice section on this issue, including the classic example of a distribution not uniquely determined by its moments: the …
- 11.4k