Chernoff-Hoeffding inequality -- Chernoff bounds, and some applications

https://www.cs.utah.edu/~jeffp/teaching/cs5955/L3-Chern-Hoeff.pdf

【大数据-通过随机过程降维 】

When dealing with modern big data sets, a very common theme is reducing the set through a random process. These generally work by making “many simple estimates” of the full data set, and then judging them as a whole. Perhaps magically, these “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 this bound, and two examples of its use.

【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 a theorem of johnson and lindenstrauss. Random Structures & Algorithms, 22:60–65, 2003. [4] Devdatt P. Dubhashi and Alessandro Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge, 2009. [5] P. Frankl and H. Maehara. The Johnson-Lindenstrauss lemma and the spericity of some graphs. Journal of Combinatorial Theory, Series A, (355–362), 1987. [6] Wassily Hoeffding. Probability inequalities for the sum of bounded random variables. Journal of the American Statisitcal Association, 58:13–30, 1963.

http://math.mit.edu/~goemans/18310S15/chernoff-notes.pdf

Can Markov’s and Chebyshev’s Inequality be improved for this particular kind of random variable?