Cs229 Supplemental Lecture Notes Hoeffding's Inequality
نویسنده
چکیده
A basic question in probability, statistics, and machine learning is the following: given a random variable Z with expectation E[Z], how likely is Z to be close to its expectation? And more precisely, how close is it likely to be? With that in mind, these notes give a few tools for computing bounds of the form P(Z ≥ E[Z] + t) and P(Z ≤ E[Z]− t) (1) for t ≥ 0. Our first bound is perhaps the most basic of all probability inequalities, and it is known as Markov’s inequality. Given its basic-ness, it is perhaps unsurprising that its proof is essentially only one line.
منابع مشابه
Hoeffding's Inequality
Notice that nR̂n(h) ∼ binom(n,R(h)) and so E [ R̂n(h) ] = R(h). We would like to understand how accurate R̂n(h) is as an estimate of R(h). Thankfully there are many well known concentration inequalities that provide us with quantitative answers to this question. The goal of this lecture is to establish one such bound: Hoeffding’s inequality [2]. This inequality was originally proved in the 1960’s ...
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