Hoeffding's inequality example
NettetSorted by: 3 A trivial example would be if $X_i$ is deterministic (say always equal to 0). The right hand side would then be the dirac mass at 0 (as seen in the proof of Hoeffding's inequality ). There can't be any other example as that would contradict the hypothesis that $\bar {X}$ is bounded, since Nettet26. jul. 2024 · Proof for Hoeffding's inequality for sum of rvs uses the above lemma (in Wikipedia link for Hoeffdings inequality and in text books like Concentration Inequalities). Hoeffdings inequality for rvs $(Y_i)$ does not assume that the rvs are zero mean.
Hoeffding's inequality example
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http://cs229.stanford.edu/extra-notes/hoeffding.pdf NettetThis is indeed the case. Such inequalities are typically known as Bernstein inequalities. As a concrete example, suppose we had X 1;:::;X n which were i.i.d from a distribution with mean , bounded support [a;b], with variance E[(X )2] = ˙2. Then, P(j b j t) 2exp nt2 2(˙2 + (b a)t) : This inequality implies that, with probability at least 1 ...
http://cau.ac.kr/~mhhgtx/courses/AdaptiveFilters/References/Hoeffding.pdf http://chihaozhang.com/teaching/SP2024spring/notes/lec8.pdf
NettetThe Hoeffding's inequality (1) assumes that the hypothesis h is fixed before you generate the data set, and the probability is with respect to random data sets D. The learning algorithm picks a final hypothesis g based on D. i.e., after generating the data set. Thus we cannot plug in g for h in the Hoeffding's inequality. Nettet15. mar. 2016 · 1 A famous use of Hoeffding inequality is to proove regret bounds in bandit problems. The famous UCB algorithm has a bound that can be prooved using this inequality (see e.g. http://www.stat.berkeley.edu/~bartlett/courses/2014fall-cs294stat260/lectures/bandit-ucb-notes.pdf for the proof) Share Cite Improve this …
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NettetStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … paraphrasing and citingNettetMcDiarmid’s Inequality. One of the reasons that the Azuma-Hoeffding inequality is useful is that it leads to concentration bounds fornonlinearfunctions of bounded random variables. A striking example is the following inequality of McDiarmid. Theorem 1.6. paraphrasing and grammar checkerNettetExample: Hoeffding’s Inequality Proof Define A(λ) = log EeλX = log Z eλxdP(x) , where X∼ P. Then Ais the log normalization of the exponential family random variable Xλwith … times coffee shop kaneoheNettet28. sep. 2024 · The Hoeffding Inequality is as follows: 𝕡 [ v-u >eps]2e-2 (eps)2N What the Hoeffding Inequality gives us is a probabilistic guarantee that v doesn’t stray too … paraphrasing and citation activitiesNettetTheorem 1 Hoeffding’s Inequality Let Z 1,Z 2,...,Zn be independent bounded random variables such that Z i ∈ [a i,b i] with probability 1. Let S n = P n i=1 Z i. Then for any t > … paraphrasing and in text citation apaNettet24. jan. 2024 · 4. After looking at the problem again, I figured out what was wrong in my "conditional Hoeffding inequality" proof attempt : In the paper's setting, is not equal to but rather (by definition of conditional probability). Therefore, the "true" conditional Hoeffding inequality I want to prove is in fact (with the same notations) : If I proceed ... timesco healthcare limitedNettet20. sep. 2024 · The Hoeffding Inequality is as follows: 𝕡[ v-u >eps]2e-2 (eps)2N What the Hoeffding Inequality gives us is a probabilistic guarantee that v doesn’t stray too far … times coffee shop koolau