参考文章 百度百科:切尔诺夫限 视频:Proof of the Chernoff Bound @ CMU oneday:Inequalities: Chernoff bound oneday:Inequalities: Hoeffding's inequality 编辑于 2024-10-18 14:57・IP 属地上海 马尔可夫 大数定律 中心极限定理 赞同5添加评论 分享喜欢收藏申请转载 ...
The Chernoff Bound, due to Herman Rubin, states that if \\\(\\\overline{X}\\\) is the average of n independent observations on a random variable X with mean μ a) \\\leq [E({e}^{t(X-a)})]^{n}.$$ The proof which follows shortly is a simple application of the Markov inequ...
Proof: 我们对要证明的部分稍加变换,就可以采用上面类似的过程, {\rm P}[X<(1-\delta)\mu]={\rm P}[-X>-(1-\delta)\mu]={\rm P}[\exp(-tX)>\exp(-t(1-\delta)\mu)] 即相当于t=-t,\delta=-\delta带入Theorem 1中,有\mathbb{P}[X<(1-\delta)\mu]<[\frac{e^{-\delta}}{(1...
bound of Eqn 4 4 is stronger than Eqn 4 5 but the latter is generally easier to use and sufficient in most applications Proof Using Markov s inequality for any t 0 we have Pr X 1 8 tL Pr e 1 t E elxl etl l iJ l1 For 0 8 I we set t ln l 8 0 to get 4 4 Pr X 1 ...
Proof We first present the proof of upper bound. Deriving from the definition of upper bound of throughput in (4), and the departure process in (1), it follows that P(DSU(t)≥λU,tSUt)=P(inf0≤s≤t{ASU(s)+SSU(t−s)}≥λU,tSUt).Since the arrival process of SU is assumed ...
The Chernoff Bound, due to Herman Rubin, states that if \\\(\\\overline{X}\\\) is the average of n independent observations on a random variable X with mean μ a) \\\leq [E({e}^{t(X-a)})]^{n}.$$ The proof which follows shortly is a simple application of the Markov inequ...
The Chernoff Bound, due to Herman Rubin, states that ifX¯is the average ofnindependent observations on a random variableXwith meanμ<athen, for allt, The proof which follows shortly is a simple application of the Markov inequality that states that for a positive random variableY,P(Y≥b) ...
can provide a very accurate and small representation of the large data set. The key tool in showing how many of these simple estimates are needed for a fixed accuracy trade-off is the Chernoff-Hoeffding inequality [2, 6]. This document provides a simple form of this bound, and two example...
can provide a very accurate and small representation of the large data set. The key tool in showing how many of these simple estimates are needed for a fixed accuracy trade-off is the Chernoff-Hoeffding inequality [2, 6]. This document provides a simple form of this bound, and two example...
Proof: We first prove the upper bound and then, the lower bound. The upper bound in (3): This follows from the Chernoff bound if we show that the value of the supremum in (1) does not change if we relax the condition θ≥ 0 and allow θ to take negative values. Since eθx...