WebIn 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 … WebFeb 20, 2024 · In probability theory, a Chernoff boundis an exponentially decreasing upper bound on the tail of a random variable based on its moment generating functionor exponential moments. The minimum of all such exponential bounds forms theChernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian).

CS229 Supplemental Lecture notes Hoeffding’s inequality

WebChernoff bound [ edit] The probability that a Poisson binomial distribution gets large, can be bounded using its moment generating function as follows (valid when and for any ): where we took . This is similar to the tail bounds of a binomial distribution . … WebHere 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 variables are 0 or 1, and 1 with probability 1/2 or less, and ϵ ∈ (0, 1 / 2), and the Chernoff upper bound is less than a constant.) breastfeeding snacks healthy

Minimize Chernoff Bound Exponential Distribution

WebThe Chernoff bound gives a much tighter control on the proba-bility that a sum of independent random variables deviates from its expectation. Although here we study it … WebChernoff's distribution In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable where W is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying W (0) = 0. If then V (0, c) has density where gc has Fourier transform given by WebTo simplify the derivation, let us use the minimization of the Chernoff bound of (10.26) as a design criterion. Moreover, let us assume for simplicity that n e = n t. Hence, we may … breastfeeding snacks at night