Chernoff bound dependent variable
WebDec 3, 2015 · Using this representation of X it is straightforward to apply the Central limit theorem to approximate the probability P ( X ≥ 26). As I understand it, in order to apply a Chernoff bound on the probability P ( X ≥ 26) the random variable X needs to be expressed as a sum of binary random variables; the random variables X k are not binary. WebAug 4, 2015 · I am looking for any kind of Chernoff type large deviation bound for the following random variable: $$X = \sum_ {i=1}^NX_i$$ where each $X_i$ is an identically distributed Bernoulli random variable which depends on exactly on $K$ other variables. I want to determine the upper bound on $$Pr [X \ge E [X]+\delta]$$ for some small $\delta …
Chernoff bound dependent variable
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WebRemarkably, the Cherno bound is able to capture both of these phenomena. 4 The Cherno Bound The Cherno bound is used to bound the tails of the distribution for a sum of independent random variables, under a few mild assumptions. Since binomial random variables are sums of independent Bernoulli random variables, it can be used to bound … WebMay 27, 2024 · Chernoff Type Bounds for Uniformly Bounded Conditional Random Variables Ask Question Asked 4 years, 10 months ago Modified 1 year, 11 months ago Viewed 179 times 3 I am considering a set of Bernoulli RVs X 1, X 2, …, X n for which we have a uniform conditional bound P [ X i = 1 X 1, …, X i − 1] ≤ p for fixed p.
WebLecture 23: Chernoff Bound & Union Bound 1 Slide Credit: Based on Stefano Tessaro’sslides for 312 19au ... Putting a limit on the probability that a random variable … Webnare independent (or weakly dependent) random variables, then the random variable f(X 1;:::;X n) is \close" to its mean E[f(X 1;:::;X n)] provided that the function x ... The Cherno ’s bound for a random variable Xis obtained by applying Markov’s inequality to the random variable e X. Proposition 6.2 (Cherno ’s Bound) For any random ...
WebChernoff bound uses logarithmic number of moments, this is possible because you have n i.i.d. random variables, so their sum is very concentrated around their mean. Please note that this just my intuition (it might be very wrong ), sorry I can't provide any hard evidence. Hope that helps :-) Share Cite Follow answered Jun 22, 2012 at 9:08 dtldarek WebMay 27, 2024 · Chernoff Type Bounds for Uniformly Bounded Conditional Random Variables. I am considering a set of Bernoulli RVs X 1, X 2, …, X n for which we have a …
WebSection 2 we prove that the moment bound is not greater than Chernoff's bound for all distributions provided that t > 0. In Section 3 we compute the moment bound for a number of distributions, both discrete and continuous, and show that the moment bound can be substantially tighter than Chernoff's bound. In many cases of interest the order
WebMar 8, 2024 · Chernoff-type bound for sum of Bernoulli random variables, with outcome-dependent success probabilities. Let X = ( X 1, X 2, …, X n) be a sequence of (not … black hills home for saleWebChernoff Bounds: Since Chernoff bounds are valid for all values of s > 0 and s < 0, we can choose s in a way to obtain the best bound, that is we can write P ( X ≥ a) ≤ min s > 0 e − s a M X ( s), P ( X ≤ a) ≤ min s < 0 e − s a M X ( s). Let us look at an example to see how we can use Chernoff bounds. Example Let X ∼ B i n o m i a l ( n, p). gaming chair with catheterWebrandom variables with ... R𝜖 Q2exp(−𝑘𝜖2/4) Two Extensions: 1.Dependent Random Variables 2.Sums of random matrices. Expander Chernoff Bound [AKS’87, G’94] … gaming chair with color changing lightsWebIn order to address this issue we use the Chernoff-Hoeffding bound. Chernoff-Hoeffding Suppose X1,. . ., Xn are independent random variables taking values in between 0 and 1, and let X = X1 + X2 +. . . + Xn be their sum, and E[X] = m. There are many forms of the Chernoff bounds, but here we focus on this one: There are several other kinds of bounds black hills home rentalsWebNov 23, 2024 · In other words,ˆs are weakly dependent binary random variables. In order to obtain a concentration bound for the summation of such variables, one could employ Theorem 1.2 in [42]. Also, s are ... black hills homes and developmentWebJun 7, 2016 · How to apply Chernoff's bound when variables are not independent. Let X = ∑ i = 1 n X i, for Bernoulli random variables X i which are not necessarily independent. … gaming chair with built in joysticks xbox oneWebJun 7, 2016 · How to apply Chernoff's bound when variables are not independent Asked 6 years, 9 months ago Modified 6 years, 9 months ago Viewed 992 times 4 Let X = ∑ i = 1 n X i, for Bernoulli random variables X i which are not necessarily independent. gaming chair with cooling