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Results tagged with it.information-theory
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user 101100
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
1
answer
173
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Mutual information inequality
I am trying to prove three inequalities that would help me solve the proof of a larger theorem.
Let $P(X,Y)$ be a discrete bivariate distribution and
$$
I(X;Y) = \sum_{i,j} p(x_i, y_j) \log \frac{p(x …
- 189
2
votes
1
answer
104
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Mutual information and bivariate function of independent variables
Let $X, Y, Z$ be discrete random variables with $X$ and $Y$ independent of $Z$, while $X$ and $Y$ can be dependent. For the mutual information, we have $I(X; Y,Z) = I(X;Y)$. Now consider $I(X; f(Y,Z)) …
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1
vote
2
answers
123
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Maximization of information over set of non-injective functions (Equality)
Let $X$, $Y$, $Z$ be discrete random variables, with $Y$ and $Z$ independent. Does the following equality hold if $Z$ is independent also of $X$?
$$
\max_{f_{Y,Z}} \big\{ \ I(X; f_{Y,Z}(Y,Z)) \ \big\} …
- 189
0
votes
Maximization of information over set of non-injective functions (Equality)
I think I might be able to provide a proof for a slightly modified version of the hypotheses, which would still be enough for the theorem that I am trying to prove.
Let $F_1:=\{(y,z) \to f_1(y,z)\}$ a …
- 189
2
votes
1
answer
92
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Maximization of information over set of non-injective functions
Let $X$, $Y$, $Z$ be discrete random variables, with $Y$ and $Z$ independent. Does the following equality hold?
$$
\max_{f_{Y,Z}} \big\{ \ I(X; f_{Y,Z}(Y,Z)) \ \big\} \le \max_{f_X, f_Y} \big \{ \ I(X …
- 189
0
votes
1
answer
131
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Adding an independent variable does not increase conditional information
Given $P(X, Y, \hat{Y})$ discrete with $\hat{Y}$ independent of both $X$ and $Y$, one would thus expect that the following relationship holds
$$
\max_{f}I(X;Y,\hat{Y} \mid f(Y,\hat{Y})) = \max_{f_1, f …
- 189
2
votes
1
answer
124
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Entropy of distribution with block matrix support
Let $P(X_1,X_2)$ be a discrete bivariate distribution that has the form shown in the figure below, i.e. its support can be split into blocks that do not overlap on either dimensions.
Let's build $P …
- 189