In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its ... Hoeffding's lemma · Azuma's inequality · McDiarmid's inequality · Chernoff bound |
| Неравенство Хёфдинга |  |
Неравенство Хёфдинга даёт верхнюю границу вероятности того, что сумма случайных величин отклоняется от своего математического ожидания.
Неравенство Хёфдинга было доказано Василием Хёфдингом в 1963 году. Википедия
The simplest way to remember this inequality is to think of f(t) = t2, and note that if E[Z] = 0 then f(E[Z]) = 0, while we generally have E[Z2] > 0. In any ... |
19 окт. 2023 г. · Hoeffding's Inequality is an important concentration inequality in Mathematical Statistics and Machine Learning (ML), leveraged extensively ... |
We will use this to prove Hoeffding's inequality. Corollary 2. Let Z be a random variable on R. Then for all t > 0. Pr (Z ≥ t) ≤ inf. |
Another commonly useful exponential concentration inequality applies to bounded random variables. This is called Hoeffding's inequality. |
Hoeffding quantifies “usually” and “close” for us. (Note that the general form of Hoeffding's inequality is for random variables in some range a ≤ Zi ≤ b. As we ... |
Hoeffding's inequality requires {Xj} to be bounded, while Chebychev doesn't, but the bounds don't have to be zero and one. If, say, a ≤ Yi ≤ b with ... |
With Hoeffding's Inequalities the tails of the error probability are starting to look more Gaussian, i.e. they decay exponentially with t2, and they correspond ... |
Now, we can apply this upper bound to derive Hoeffding's inequality. i=1(bi−ai)2 . This completes the proof of the Hoeffding's theorem. |
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