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The chernoff bound

網頁Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, in particular when the variance of the random variables is small. [2] It is similar to, but incomparable with, one of Bernstein's inequalities . 網頁2.6.1 The Union Bound The Robin to Chernoff-Hoeffding’s Batman is the union bound. It shows how to apply this single bound to many problems at once. It may appear crude, but can usually only be significantly improved if special structure is available in the 1 t.

for Positive Tail Probabilities

網頁2024年4月11日 · Metastatic prostate cancer (mPCa) has limited therapeutic options and a high mortality rate. The p21-activated kinase (PAK) family of proteins is important in cell survival, proliferation, and motility in physiology, and pathologies such as infectious, inflammatory, vascular, and neurological diseases as well as cancers. Group-I PAKs … 網頁2024年1月6日 · The proof proceeds by applying the Hoeffding lemma to obtain a bound on the moment generating functions: E ( e t X i) ≤ e O ( t 2 σ i 2). This leads to the inequality P ( S n ≥ λ σ) ≤ exp ( ( O ( t 2 σ 2) − t λ σ)). At this point, the author chooses to optimize this with respect to t ∈ [ 0, 1]. However, the Hoeffding lemma ... dewalt create account https://patriaselectric.com

Chernoff-Hoeffding Bound_qqiseeu的博客-CSDN博客

網頁我们看到， Chernoff bound关注的对象是对于 n 个数的和或均值分布尾部的部分，其刻画了样本均值的尾数概率随着样本数量增加而指数衰减的现象。 当然，我们可以再进一步， … 網頁1990) that Chernoff's bound is asymptotically (in t) tight, that is, P[X > t] = exp{inf[O - log.Mx(O) - o(l)]t} The remainder of this article is organized as follows. In Section 2 we prove that the moment bound is not greater than Chernoff's bound for all distributions provided 網頁2024年4月15日 · The query complexity lower bound is then lifted to a query-space lower bound for a non-uniform (preprocessing) adversary solving the same problem [11, 12, 37]. Building on ideas developed in these lines of work, we present a new technique for translating sampling lower bounds to space lower bounds for problems in the context of … church messages on wisdom

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The chernoff bound

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網頁for a Poisson distributed random variable Z with expectation E ( Z) = λ, P ( Z ≥ λ + t) ≤ exp ( − t 2 2 ( λ + t / 3)). This is true if Z is binomial ( λ, 1). In fact, the author cited a reference for binomial distributions. But I do not see how this could transfer to Poisson distribution. As far as I remember, it seems all these ... 網頁Stat 928: Statistical Learning Theory Lecture: 6 Hoeffding, Chernoff, Bennet, and Bernstein Bounds Instructor: Sham Kakade 1 Hoeffding’s Bound We say Xis a sub-Gaussian random variable if it has quadratically bounded logarithmic moment generating func-tion,e.g. ...

The chernoff bound

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網頁Chernoff bound P(X-EX \geq t) \leq \inf_{\lambda \geq 0} E[e^{\lambda(X-EX)}]e^{-\lambda t} 我们发现, 这个上界随着 t 增长衰减的速率取决于矩母函数的上界, 这启发我们, 如果一个 … 網頁CS174 Lecture 10 John Canny Chernoff Bounds Chernoff bounds are another kind of tail bound. Like Markoff and Chebyshev, they bound the total amount of probability of some …

網頁2024年5月2日 · 在介绍Chernoff边界之前，首先回顾一下两个重要不等式，Markov不等式和Chebyshev不等式。定理1 Markov不等式： 令X为非负随机变量，那么对于任意的a>0， … 網頁In the case of commuting density operators it coincides with the classical Chernoff bound. Moreover, the bound turns out to be tight in some non-commutative special cases, too. The general ...

網頁2006年7月30日 · DOI: 10.1214/08-AOS593 Corpus ID: 15418499 THE CHERNOFF LOWER BOUND FOR SYMMETRIC QUANTUM HYPOTHESIS TESTING @article{Nussbaum2006THECL, title={THE CHERNOFF LOWER BOUND FOR SYMMETRIC QUANTUM HYPOTHESIS TESTING}, author={Michael Nussbaum and … 網頁2015年5月31日 · Chernoff Bound. Chernoff bounding technique指的是用moment-generating function来处理多个随机变量之和的期望的技巧。. 所谓moment-generating function被定义为随机变量 的指数函数的期望 。. 先来看一个简单的例子：考虑 独立同分布 的Bernoulli随机变量 及它们的和 ，易见 。. 现在要 ...

In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function or exponential moments. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster … 查看更多內容 The generic Chernoff bound for a random variable $${\displaystyle X}$$ is attained by applying Markov's inequality to $${\displaystyle e^{tX}}$$ (which is why it sometimes called the exponential Markov or exponential … 查看更多內容 The bounds in the following sections for Bernoulli random variables are derived by using that, for a Bernoulli random variable $${\displaystyle X_{i}}$$ with probability p of being equal to 1, 查看更多內容 Chernoff bounds have very useful applications in set balancing and packet routing in sparse networks. The set balancing problem arises while designing statistical experiments. Typically while designing a statistical experiment, given the … 查看更多內容 When X is the sum of n independent random variables X1, ..., Xn, the moment generating function of X is the product of the individual moment generating functions, giving … 查看更多內容 Chernoff bounds may also be applied to general sums of independent, bounded random variables, regardless of their distribution; this is known as Hoeffding's inequality. … 查看更多內容 Rudolf Ahlswede and Andreas Winter introduced a Chernoff bound for matrix-valued random variables. The following version of the inequality can be found in the work of Tropp. 查看更多內容 The following variant of Chernoff's bound can be used to bound the probability that a majority in a population will become a minority in a sample, or vice versa. Suppose there is a general population A and a sub-population B ⊆ A. Mark the relative size of … 查看更多內容

網頁18.310 lecture notes February 21, 2015 Cherno bounds, and some applications Lecturer: Michel Goemans 1 Preliminaries Before we venture into Cherno bound, let us recall … church messages for signs網頁APPLICATIONS OF CHERNOFF BOUNDS 5 Hence, the ideal choice of tfor our bound is ln(1 + ). Substituting this value into our expression, we nd that Pr(X (1 + ) ) (e (1+ )(1+ )) This bound is quite cumbersome to use, so it is useful to provide a slightly less unwieldy church messenger devoured lamb joint first網頁Chernoff Bound On this page Chernoff Bound on the Right Tail Application to the Normal Distribution Chernoff Bound on the Left Tail Sums of Independent Random Variables Interact If the form of a distribution is intractable in that it … church metalhttp://prob140.org/fa18/textbook/chapters/Chapter_19/04_Chernoff_Bound church messianic網頁The Wikipedia page for the Binomial Distribution states the following lower bound, which I suppose can also be generalized as a general Chernoff lower bound. Pr ( X ≤ k) ≥ 1 ( n + 1) 2 exp ( − n D ( k n p)) if p < k n < 1. Clearly this is tight up to the ( n + 1) − 2 factor. However computationally it seems that ( n + 1) − 1 would ... church messenger of truth網頁2015年5月10日 · 13. I have to prove that, when bounding tail probabilities of a nonnegative random variable, the moments method is always better than the classical Chernoff … church metal building costs網頁2024年4月11日 · We study the shotgun assembly problem for the lattice labeling model, where i.i.d. uniform labels are assigned to each vertex in a d-dimensional box of side length n. We wish to recover the labeling configuration on the whole box given empirical profile of labeling configurations on all boxes of side length r. We determine the threshold around … dewalt crate tough system 2.0 4in1