Chernoff bound dependent variable
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 … 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.
Chernoff bound dependent variable
Did you know?
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 … 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
WebChernoff Bounds for settings with limited dependence. Asked 9 years, 10 months ago. Modified 9 years, 10 months ago. Viewed 1k times. 1. Could someone point me to a way … WebThe Chernoff bound is like a genericized trademark: it refers not to a particular inequality, but rather a technique for obtaining exponentially decreasing bounds on tail probabilities. …
WebI am looking for tail bounds (preferably exponential) for a linear combination of dependent and bounded random variables. consider K i j = ∑ r = 1 N ∑ c = 1 N W i r C r c W j c where i ≠ j, W ∈ { + 1, − 1 } and W follows Bernoulli ( 0.5), and C = Toeplitz ( … 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 is in the “tails” of the distribution (e.g., not near the middle). Usually statements in the form of …
WebIn 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
In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function or exponential moments. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay … See more The generic Chernoff bound for a random variable $${\displaystyle X}$$ is attained by applying Markov's inequality to $${\displaystyle e^{tX}}$$ (which is why it sometimes called the exponential Markov or exponential … See more The bounds in the following sections for Bernoulli random variables are derived by using that, for a Bernoulli random variable $${\displaystyle X_{i}}$$ with probability p of being equal to 1, One can encounter … See more Rudolf Ahlswede and Andreas Winter introduced a Chernoff bound for matrix-valued random variables. The following version of the … See more The following variant of Chernoff's bound can be used to bound the probability that a majority in a population will become a minority in a sample, or vice versa. Suppose there is a general population A and a sub-population B ⊆ A. Mark the relative size of the … See more When X is the sum of n independent random variables X1, ..., Xn, the moment generating function of X is the product of the individual moment generating functions, giving that: See more Chernoff bounds may also be applied to general sums of independent, bounded random variables, regardless of their distribution; this is known as Hoeffding's inequality. The proof follows a similar approach to the other Chernoff bounds, but applying See more Chernoff bounds have very useful applications in set balancing and packet routing in sparse networks. The set balancing problem arises while designing statistical … See more hippo insurance login agentWebThus, special cases of the Bernstein inequalities are also known as the Chernoff bound, Hoeffding's inequality and Azuma's inequality . Some of the inequalities [ edit] 1. Let be independent zero-mean random variables. Suppose that almost surely, for all Then, for all positive , 2. Let be independent zero-mean random variables. homes for sale in amberwood humble texasWebWe seek to derive a probabilistic tool known as the Cherno Bound, a useful bound on deviation from the expected value of the sum of independent random variables. First, we … hippo insurance mortgagee changeWebrandom variables with ... R𝜖 Q2exp(−𝑘𝜖2/4) Two Extensions: 1.Dependent Random Variables 2.Sums of random matrices. Expander Chernoff Bound [AKS’87, G’94] … hippo insurance financial informationWebDec 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. homes for sale in amber meadows charlotte ncWebHoeffding, Chernoff, Bennet, and Bernstein Bounds Instructor: Sham Kakade 1 Hoeffding’s Bound We say Xis a sub-Gaussian random variable if it has quadratically bounded logarithmic moment generating func-tion,e.g. lnEe (X ) 2 2 b: For a sub-Gaussian random variable, we have P(X n + ) e n 2=2b: Similarly, P(X n ) e n 2=2b: 2 Chernoff Bound hippo insurance mortgagee clause updateWebNov 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 ... hippo insurance mortgagee update