This tag is for [Entropy](http://en.wikipedia.org/wiki/Entropy_(information_theory)) in Mathematics.

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3
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Can I map entropy values to a common range so that they are comparable?

I am using the standard Shannon entropy formula for calculating the entropy of a system at different states. The system has a different number of possible outcomes at each state, in other words the ...
4
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2answers
861 views

Can I normalize KL-divergence to be $\leq 1$?

The Kullback-Leibler divergence has a strong relationship with mutual information, and mutual information has a number of normalized variants. Is there some similar, entropy-like value that I can use ...
1
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1answer
223 views

How do I go about calculating the entropy level of this algorithm?

I have a set of items. These items are (pseudo)randomly placed into buckets. The buckets are ordered and items placed in them are ordered. After all of the items are placed in buckets, the items ...
3
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1answer
255 views

Entropy of $X =\{1,2,\ldots,\infty\}$ with the probability of $\{1/2^1,1/2^2,\ldots,1/2^\infty\}$?

I'm studing for an information theory exam, maybe some of you can help me here with an exercise. What's the entropy of $X$ as $\{1,2,\ldots,n\}$ ($n$=infinity) where the probabilities are $P \{1/2^1, ...
22
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2answers
1k views

An information theory inequality which relates to Shannon Entropy

For $a_1,...,a_n,b_1,...,b_n>0,\quad$ define $a:=\sum a_i,\ b:=\sum b_i,\ s:=\sum \sqrt{a_ib_i}$. Is the following inequality true?: $${\frac{\Bigl(\prod a_i^{a_i}\Bigr)^\frac1a}a \cdot ...
0
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1answer
232 views

Relative Entropy given two non-equivalent sets

I am trying to calculate the relative entropy given two collections and have a question regarding some issues. Supposed we have two sets, $Real$ and $Calculated$, and their respective probability ...
4
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2answers
1k views

Derivation of the maximum entropy distribution

I am reading a book and having trouble following something. The problem is to try to maximize the differential entropy $-\int_{0}^{\infty}p(r)\log p(r)$ under the constraints that ...