WebbChernoff Bound on the Left Tail. By an analogous argument we can derive a Chernoff bound on the left tail of a distribution. For a fixed $t > 0$, the function $g(x) = e^{-tx}$ is … 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 faster than … Visa mer 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 … Visa mer Chernoff bounds may also be applied to general sums of independent, bounded random variables, regardless of their distribution; this is … Visa mer Chernoff bounds have very useful applications in set balancing and packet routing in sparse networks. The set balancing problem arises while designing statistical … Visa mer 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 … Visa mer 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: and: Visa mer 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 … Visa mer Rudolf Ahlswede and Andreas Winter introduced a Chernoff bound for matrix-valued random variables. The following version of the inequality can be found in the work of Tropp. Visa mer

Five Proofs of Cherno ’s Bound with Applications - fu-berlin.de

WebbFor sufficiently large values of λ, (say λ >1000), the normal distribution with mean λ and variance λ (standard deviation ) is an excellent approximation to the Poisson … WebbHere is an explicit proof that a standard Chernoff bound is tight up to constant factors in the exponent for a particular range of the parameters. (In particular, whenever the … the hundred dresses audiobook length

Singletons for simpletons revisiting windowed backoff with …

Webb4 mars 2024 · Proof of bound. A proof of Theorem 1, and other theorems in a similar spirit, are currently available here, and hopefully will be available in some citable publication … Webb13 maj 2024 · The Chernoff bound is an important inequality relation in probability theory. The original version of the Chernoff bound is to give an exponential decreasing bound on … Webb3 juli 2024 · We propose a Chernoff-bound approach and examine standard deviation value to enhance the accuracy of the existing fast incremental model tree with the drift detection (FIMT-DD) algorithm. It is a data stream mining algorithm that can observe and form a model tree from a large dataset. the hundred dresses audiobook