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...

sequence of random matrices. Analogous to the well-known Chernoff bound for sums of scalars, a bound on the following is sought for a given parameter t: Pr...

Azuma–Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, in particular when the variance of the...

in Massachusetts. Chernoff turned 100 on July 1, 2023. Chernoff bound (also known as Chernoff's inequality) Chernoff face Chernoff's distribution Bather...

is bounded above by the entropy of a binomial distribution with the same number parameter and the same mean. Therefore, the entropy is also bounded above...

apply a Chernoff concentration bound for 1 k ∑ i Q i 2 {\textstyle {\frac {1}{k}}\sum _{i}Q_{i}^{2}} around 1. This requires upper-bounding the cumulant...

the Paley-Zygmund inequality provides a lower bound on the deviation probability. The generic Chernoff bound: 63–65  requires the moment generating function...

{\mu }}-{\sqrt {\lambda }})^{2}}} The upper bound is proved using a standard Chernoff bound. The lower bound can be proved by noting that P ( X − Y ≥ 0...

the runs are wrong drops off exponentially as a consequence of the Chernoff bound. Unsolved problem in computer science ⁠ P = ? B P P {\displaystyle {\mathsf...

{\tfrac {\gamma N}{2}}} by linearity of expectation. Now applying Chernoff bound, we have bound error probability of more than γ N {\displaystyle \gamma N}...

2 {\displaystyle \|X+Y\|_{vp}^{2}\leq (\|X\|_{vp}+\|Y\|_{vp})^{2}} (Chernoff bound) If X {\textstyle X} is subgaussian, then P r ( X ≥ t ) ≤ e − t 2 2...

with k < n), but Hoeffding's bound evaluates to a positive constant. A sharper bound can be obtained from the Chernoff bound: F ( k ; n , p ) ≤ exp ⁡ (...

{\displaystyle K^{*}(q)={\frac {1}{2}}(q-k+k\ln {\frac {k}{q}})} , the standard Chernoff bound yields ln ⁡ P r ( X ≥ ( 1 + ϵ ) k ) ≤ − k 2 ( ϵ − ln ⁡ ( 1 + ϵ ) ) ln...

{Full} (k)].} But by the multiplicative form of the Chernoff bound, when the load factor is bounded away from one, the probability that a block of length...

achieve any desired probability of correctness less than 1, using the Chernoff bound. This number of repeats increases if c becomes closer to 1/2, but it...

{\displaystyle \left\lceil \log {\frac {n}{\log(d/\lambda )}}\right\rceil .} The Chernoff bound states that, when sampling many independent samples from a random variable...

Kullback–Leibler divergence Hellinger distance Mahalanobis distance Chernoff bound Rényi entropy F-divergence Fidelity of quantum states Dodge, Yadolah...

M.; Raviv, J. (1970). "Probability of error, equivocation, and the Chernoff bound". IEEE Transactions on Information Theory. 16 (4): 368–372. CiteSeerX 10...

tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma. Although others before him proved theorems...

is also polynomial-time, and has an error probability ≤ 1/en by the Chernoff bound (see BPP). If we can fix R then we obtain an algorithm that is deterministic...

special cases of the Bernstein inequalities are also known as the Chernoff bound, Hoeffding's inequality and Azuma's inequality. The martingale case...

with Markov's inequality to bound the upper tail of a real random variable X. This statement is also called the Chernoff bound. Since x ↦ e x t {\displaystyle...

advantage of the independence of the function arguments to provide a Chernoff-bound-like argument. For better readability, we will introduce a notational...

-(Z_{t}-Z_{t-1})+A_{t}\leq Y_{t}-Y_{t-1}\leq -(Z_{t}-Z_{t-1})+B_{t}} Applying Chernoff bound to Y n − Y 0 {\displaystyle Y_{n}-Y_{0}} , we have for ϵ > 0 {\displaystyle...

achieve any desired probability of correctness less than 1, using the Chernoff bound. The complexity class is unchanged by allowing error as high as 1/2...

{\displaystyle [m]} , the number of keys per bin could be analyzed using the Chernoff bound. A deterministic hash function cannot offer any such guarantee in an...

bound is given by a = 1 / π {\displaystyle a=1/\pi } and b = 2 π {\displaystyle b=2\pi } with maximum absolute relative error of 1.17%. The Chernoff bound...

1-e^{-2\gamma ^{2}k},} where γ = 1/2 - ε - δ. This follows by applying the Chernoff bound. With the advent of quantum computing, there has been a significant...

fair Cheeger bound Chemometrics Chernoff bound – a special case of Chernoff's inequality Chernoff face Chernoff's distribution Chernoff's inequality Chi...

Uniform integrability Markov's inequality Chebyshev's inequality = Chernoff bound Chernoff's inequality Bernstein inequalities (probability theory) Hoeffding's...