# Tagged Questions

**2**

votes

**2**answers

288 views

### What is the maximum entropy distribution on the natural numbers?

On the reals $\mathbb{R}$, the maximum entropy distribution with a given mean and variance is the Gaussian distribution.
Let $\mu, \sigma > 0$. What is the maximum entropy distribution on the ...

**1**

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**1**answer

159 views

### Set of distributions that minimize KL divergence,

Assuming that $p,q$ are probability distributions defined on the same support $\{x_i\}_{0 \leq i \leq n}$, $\epsilon$ a small real number, and $D_{KL}$ the Kullback-Leibler divergence,
is there a ...

**1**

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**1**answer

252 views

### Calculate channel capacity of general channel under constraint

Hi!
Given a conditional distribution $P_{Y|X}$ I'd like to find the prior distribution $P_X$ that maximizes the mutual information $I(X;Y)$ with $P_Y(y)=\int P_{Y|X}(y|x)P_X(x)\text{dx}$ (this ...

**1**

vote

**1**answer

139 views

### The degrees in a random subgraph

Fix some positive integers $N$ and $d_k$, $k=1,2,\dots$ with $N=\sum_{k=1}^\infty d_k$.
Suppose you have a graph $G$ taken randomly uniformly among the set of all (unoriented) graphs with $N$ ...

**7**

votes

**2**answers

312 views

### Entropy conjecture for distributions over $\mathbb{Z}_n$

Suppose we have two independent random variables $X$ (with distribution $p_X$) and $Y$ (with distribution $p_Y$) which take values in the cyclic group $\mathbb{Z}_n$. Let $Z = X +Y$, where the ...