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 … WebSep 23, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
Minimize Chernoff Bound Exponential Distribution
WebThe classical Chernoff bounds concern the sum of independent, nonnegative, and uniformly bounded random variables. In the matrix setting, the analogous theorem concerns a sum of positive-semidefinite random matrices subjected to a uniform eigenvalue bound. Matrix Chernoff I [ edit] 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 dancing fish singapore
Cherno bounds, and some applications 1 Preliminaries
http://cs229.stanford.edu/extra-notes/hoeffding.pdf 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 See more 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. 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 … See more Chernoff bounds have very useful applications in set balancing and packet routing in sparse networks. The set balancing … 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 … See more 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.) dancing flame solar garden torches