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 Webbgocphim.net
Cherno bounds, and some applications 1 Preliminaries
WebbCOMPARISON OF G D P C W I T H STATE-OF-THE-ART from (8) of Chernoff bound, will be used as the calculation ALGORITHMS window of the Brier score. Using the optimal parameters defined for high accuracy, To study how the concept drift affects the Brier score, the labeled A., 5, e, , and N (Table XI) and data stream no. 3 data streams used … Webb14 mars 2016 · I'm trying to derive the Chernoff bound erfc(x) ≤ exp( − x2), by first showing: erfc(x) = 2 π∫π 20exp( − x2 cos2θ)dθ This equality should be derived by considering 2 independent, standard gaussian random variables x1, x2 and the region in the x1x2 -plane where x1 ≤ x. What I have so far, is come up with a diagram like this: newmarket challenge whip
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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. WebbProof of the Chernoff bound First write the inequality as an inequality in exponents, multiplied by t>0: Pr[X<(1−δ)µ] = Pr[exp(−tX) > exp(−t(1−δ)µ)] Its not clear yet why we … WebbHere, we revisit several of these results, showing that a standard probabilistic tool—the Chernoff bound—is applicable, and illustrating how its use simplifies the analysis. A … newmarket charitable foundation