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 ...
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(...
(2001). Equitable coloring extends Chernoff-Hoeffding bounds, In Proceedings of RANDOM-APPROX 2001, Berkeley, CA, pp. 285-296.S. V. Pemmaraju, Equitable colorings extend Chernoff-Hoeffding bounds, Proceedings of the 5th International Workshop on Randomization and Approximation Techniques in Computer ...
【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 ...
The key tool in showing how many of these simple estimates are needed for a fixed accuracy trade-off is the Chernoff-Hoeffding inequality[Che52,Hoe63]. This document provides a simple form of this bound, and two examples of its use.
Chernoff Bound与Hoeffding's Ineq 本文主要记录随机变量的Chernoff Bound和其推广Hoeffding不等式。 1.单个随机变量的Chernoff Bound 设X为实随机变量,则有: Pr(X>t)≤infs>0E(esX)estPr(X>t)≤infs>0E(esX)est 证明用Markov不等式即可。 2.多个随机变量的Chernoff Bound...
Chernoff-Hoeffding bounds for applications with limited independence... A Srinivasan,AR Siegel,JP Schmidt 被引量: 0发表: 1993年 Concentration of measure for the analysis of randomized algorithms / Randomized algorithms have become a central part of the algorithms curriculum, based on their ...
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 ...
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 ...
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 ...