Chernoff Inequality - Part II
نویسنده
چکیده
We saw the following in the previous lecture.
منابع مشابه
Chernoff Bounds, and Some Applications
Preliminaries Before we venture into Chernoff bound, let us recall two simple bounds on the probability that a random variable deviates from the mean by a certain amount: Markov's inequality and Chebyshev's inequality. Markov's inequality only applies to non-negative random variables and gives us a bound depending on the expectation of the random variable.
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Before we venture into Chernoff bound, let us recall Chebyshev's inequality which gives a simple bound on the probability that a random variable deviates from its expected value by a certain amount.
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In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key matrix inequality. Concerning the error exponents, the upper bounds lead to noncommutative analogues of the Chernoff bound and the Hoeffding bound, which are identical with the classical counter part if the hypotheses, composed of two density operators, are mutually commutative. Ou...
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In this short note we will present two stability properties of the Chernoff-Ou-Pan inequality, newly obtained in [6], which states that if K is a convex domain in the plane R2 with area a(K) , then one gets a(K) 1 k ∫ π k 0 ωk(θ )wk ( θ + π k ) dθ , where wk(θ ) is defined in [6] (see also §3 below), and the equality holds if and only if K is a circular disc. Mathematics subject classification ...
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Before stating Hoeffding’s Inequality, we recall two intermediate results that we will use in order to prove it. One is Markov’s Inequality and other is Hoeffding’s Lemma. (Note that in class we did not cover Hoeffding’s Lemma, and only gave a brief outline of the Chernoff Bounding Techniques and how they are used to prove Hoeffding’s Inequality. Here we give a full proof of Hoeffding’s Inequal...
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