All Questions
Tagged with it.information-theory reference-request
15 questions with no upvoted or accepted answers
15
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0
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476
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Any references on zeta-function like sums of inverse determinants over lattices of matrices?
I'm sorry for the title, it was little difficult to phrase..
Let us consider a matrix lattice $L\subset M_n(\mathbb{C})$. By this I mean a discrete additive group in $M_n(\mathbb{C})$. Let us ...
- 201
6
votes
0
answers
120
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Functional Equation of Zeta Function on Statistical Model
I've been studying [1] because I was interested in his ideas on the zeta function. I'll define it here (c.f. p. 31):
The Kullback-Leibler distance is defined as
$$
K(w)=\int q(x)f(x, w)dx\quad
f(x,w)...
- 429
4
votes
0
answers
214
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Maximum entropy methods for probabilistic number theory
Might there be a good survey paper on the application of maximum entropy inference for non-trivial problems in probabilistic number theory?
So far I am aware of the work of Ioannis Kontoyiannis, an ...
- 3,871
4
votes
0
answers
174
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Determine binary function $f(x)$ by partial observation of $x$
Let $\boldsymbol{x} = (\boldsymbol{x}_1, \dots, \boldsymbol{x}_n)$ be a $n$-dimensional random vector on $\mathbb{R}$ (i.e. $\boldsymbol{x}$ is a random variable). Suppose we have a binary function
$f:...
- 1,551
3
votes
0
answers
140
views
Applications of list decoding
This is citation from http://en.wikipedia.org/wiki/List_decoding:
Algorithms developed for list decoding of several interesting code families have found interesting applications in computational ...
- 2,576
2
votes
0
answers
45
views
Moduli spaces of 'generalized mutually unbiased bases'
Mutually unbiased bases in $\mathbb{C}^n$ with a chosen inner product are collections of orthonormal bases such that for each pair of orthonormal bases $e_i,f_i$, $i=1,\ldots,n$ we have $|\langle e_i, ...
- 1,071
2
votes
0
answers
159
views
1-bit binary secret sharing
As we know, a $(t,r,n)$-ramp scheme is described by means of two thresholds $t$ and $r$. Every set with at most $t$ participants is forbidden, while every set with at least $r$ participants is ...
- 1,551
2
votes
0
answers
156
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Looking for Camion - Abelian codes
I am looking for a copy of the old report "Paul Camion - Abelian codes", Technical Report 1059, University of Wisconsin 1971. I have asked Paul himself, but he could not help me. Anyone out there has ...
- 21
1
vote
0
answers
95
views
Reference request: Time and proofs of shared pasts
Is there research about structures for notions of time with distributed systems of information, as with blockchains?
I am thinking of tuples $(I, T, P, A, \prec, s, \eta, u)$ where
$I$, $T$ and $P$ ...
- 3,249
1
vote
0
answers
135
views
Error correcting codes via random matrices: How close to the Shannon bound?
I have a vague and probably rather naive question on error correcting codes.
Suppose we want to encode binary vectors of length $k$ as binary vectors of length $n$ in such a way that differences of ...
- 623
1
vote
0
answers
115
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Minimal entropy with constraint on $2$-norm: Finding reference
Suppose $p_1,p_2,\dots,p_n \in [0,1]$ and they satisfies
$$ \sum_{j=1}^n p_j = 1 $$
and
$$ \sum_{j=1}^n p_j^2 = C $$
with a given constant $C \in [1/n,1]$. The problem is to find the minimum of
$$ -\...
- 1,551
1
vote
0
answers
438
views
Chain rule for maximal correlation
Let a pair of random variables $(X,Y)$ be defined over finite alphabet $\mathcal{X}\times \mathcal{Y}$ with joint distribution $P_{XY}$. The maximal correlation $\rho(X;Y)$ between $X$ and $Y$ is ...
- 1,109
0
votes
0
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85
views
When is a family of distributions "closed" with respect to minimal sufficient statistics?
As in the title, I am interested in understanding how to express the idea that a parametric family of distribution is "closed" with respect to minimal sufficient statistics. Before giving ...
0
votes
0
answers
52
views
Classifier-specific lower bounds on the misclassification rate in binary classification
Consider a binary classification problem for $(X,Y)$, and let $\hat{f}$ be a proposed classifier. We wish to bound the misclassification rate $P(\hat{f}(X)\ne Y)$. There are many known lower bounds on ...
- 13
0
votes
0
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171
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A basic property of maximal correlation
Let $𝑋$ and $𝑌$ be random variables. Then the maximal correlation $\rho_{m}(X;Y)$ is defined as:
$$\rho_{m}(X;Y):=\max_{f,g}\mathbb{E}[f(X)g(Y)],$$
where the maximization is taken over real-valued ...
- 11