The chernoff bound

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August undefined, 2024

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 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 ...

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網頁For the function Q ( x) := P ( Z > x) where Z ∼ N ( 0, 1) Q ( x) = ∫ x ∞ 1 2 π exp ( − u 2 2) d u, for x ≥ 0 the following bound is given in many communication systems textbooks: Q ( x) ≤ 1 2 exp ( − x 2 2). The bound without the 1 2 in front of the exponential can be proven directly by Chernoff bound on the Gaussian distribution. 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 ... ruth\u0027s brownies

Chernoff-Hoeffding Bound_qqiseeu的博客-CSDN博客

網頁2024年4月12日 · The results indicated that CA4G and FA4G bound to the AKT PH domain and inhibited its translocation to the cell ... J. Chernoff, S.P. Kunapuli Gq-mediated Akt translocation to the membrane: A novel PIP3-independent mechanism in … 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3月6日 · 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 … is chi japanese or chinese

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網頁本文使用 Zhihu On VSCode 创作并发布今天介绍一个在算法分析以及机器学习中比较常用的技术，Chernoff界。这个技术主要是用来衡量尾概率，即如果样本值偏离期望，那么偏 … 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 is chi number same as nhs number網頁2024年5月13日 · The Chernoff bound is an important inequality relation in probability theory. The original version of the Chernoff bound is to give an exponential decreasing … ruth\u0027s brother in ozark

"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 ... " - The chernoff bound

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Chernoff-Hoeffding Bound_qqiseeu的博客-CSDN博客

The chernoff bound

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