如果蓝线部分为YiYi, 可以算出它的期望和区间 (右侧蓝色部分), 随机变量YiYi满足 Hoeffding's lemma 的条件, 所以可以使用这个定理得出第三行, 公式整理后得到第四行. 这里的tt只要满足大于 0 取任何值不等式都成立, 所以令tt等于右下角黑色字体的公式, 整理后即为Hoeffding's inequality 的形式. ...
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?
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?
"本科生能看懂的学习理论(六)严紧版的霍夫丁引理 Hoeffding Lemma (tight) 与 霍夫丁不等式 Hoeffding Inequality"[EB/OL]. 知乎, 2023-09-30[2023-10-06]. [4] Smith, John, and Peter Johnson. "Bayesian Statistics and Modelling." Journal of Statistical Methods 35, no. 2 (2021): 123-145. ...
Lemma 5 (Hoeffding’s Inequality With Dependent Summands =-=[21]-=-): Consider random variables bounded as almost surely. Assume also they can be partitioned into collectively exhaustive and mutually exclusive subsets with respective cardinalities such that the varia......
We have already stated that if all you are given is the variance of a r.v., then Chebyshev’s Inequality is essentially the best you can do. Thus, more information is needed to acheive substantially tighter bounds. We begin with the case in which the r.v. is the sum of a sequence ...
“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 ...