上述估计称为Chernoff界。 我们来看Chernoff界的应用 例子Chernoff界对高斯随机变量的尾部分析,令X∼N(μ,σ2),为高斯随机变量,那么高斯随机变量的矩生成函数为: E[eλX]=eμλ+σ2λ22,λ∈R 计算Chernoff界: infλ≥0{logE[eλ(X−μ)]−λt}=infλ≥0{λ2σ22−λt}=−t22σ2 ...
We prove the first Chernoff-Hoeffding bounds for general nonreversible finite-state Markov chains based on the standard L_1 (variation distance) mixing-time of the chain. Specifically, consider an ergodic Markov chain M and a weight function f: [n] -> [0,1] on the state space [n] of ...
【对全集多次简单评估,对不同次结果进行聚合二得出对全集的评估】 [2] Herman Chernoff. A measure of asymptotic efficiency for tests of hypothesis based on the sum of observations. Annals of Mathematical Statistics, 23:493–509, 1952. [3] Sanjoy Dasgupta and Anupam Gupta. An elmentary proof of ...
可见Hoeffding不等式是多个随机变量的Chernoff Bound的推广 Hoeffding不等式可以有效估计有界独立随机变量的和偏离期望过远的概率
Chernoff–Hoeffding (CH) bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables (r.v.'s). We present a simple technique that gives slightly better bounds than these and that more importantly requires only limited independence amo...
“many simple estimates” 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 ...
示性函数, Markov 不等式, Chebyshev 不等式, Chernoff 界, Hoeffding 不等式, 泛化误差上界 示性函数 (indicative function) 示性函数的期望恰等于随机事件的概率, 即 E(IA)=P(A). 首先回顾示性函数的定义: IA(x)={1,x∈A,0,x∉A. 容易直接计算其期望, E(IA)=P(A)⋅1+P(A¯)⋅0=P(...
n13 Chernoff&Hoeffding Bounds CS271 Randomness & Computation Lecture 13: October 6 Lecturer: Alistair Sinclair Fall 2011 Based on scribe notes by: James Cook, Fares Hedayati Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. They may be ...
Hence the present gap between the running times of the unweighted and the weighted conditional probability method is a O ( n log mn / ε )-factor.On the other hand we will show, applying such derandomization procedures, which we call the algorithmic Chernoff-Hoeffding inequalities, the first ...
Mitzenmacher, Chernoff-Hoeffding Bounds for Markov Chains: Generalized and Simplified 2012, arXiv preprint arXiv:1201.0559.Kai-Min Chung, Henry Lam, Zhenming Liu, and Michael Mitzenmacher. 2012. Chernoff-Hoeffding bounds for Markov chains: Generalized and simplified. In Proc. STACS, vol. 14. ...