The final form of Tao's inequality relating conditional expectation and conditional mutual information

Ahlswede R (2007)
ADVANCES IN MATHEMATICS OF COMMUNICATIONS 1(2): 239-242.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
Recently Terence Tao approached Szemeredi's Regularity Lemma from the perspectives of Probability Theory and Information Theory instead of Graph Theory and found a stronger variant of this lemma, which involves a new parameter. To pass from an entropy formulation to an expectation formulation he found the following: Let Y, and X, X' be discrete random variables taking values in Y and X, respectively, where Y subset of [-1, 1], and with X' = f(X) for a (deterministic) function f. Then we have E(vertical bar E(Y vertical bar X') - E(Y vertical bar X)vertical bar) <= 2I(X Lambda Y vertical bar X')1/2. We show that the constant 2 can be improved to (2ln2)1/2 and that this is the best possible constant.
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Zeitschriftentitel
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
Band
1
Ausgabe
2
Seite(n)
239-242
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Ahlswede R. The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 2007;1(2):239-242.
Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 1(2), 239-242. doi:10.3934/amc.2007.1.239
Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS 1, 239-242.
Ahlswede, R., 2007. The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 1(2), p 239-242.
R. Ahlswede, “The final form of Tao's inequality relating conditional expectation and conditional mutual information”, ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 1, 2007, pp. 239-242.
Ahlswede, R.: The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 1, 239-242 (2007).
Ahlswede, Rudolf. “The final form of Tao's inequality relating conditional expectation and conditional mutual information”. ADVANCES IN MATHEMATICS OF COMMUNICATIONS 1.2 (2007): 239-242.