Chernoff bound examples
WebApr 15, 2013 · We can apply the Chernoff bound in an easy example. Say all X i are fair coin flips, and we’re interested in the probability of getting more than 3/4 of the coins heads. Here μ = n / 2 and λ = 1 / 2, so the probability is bounded from above by ( e ( 3 / … WebHoeffding’s bound is, in general, the most useful. However if p is close to zero then we can derive better bounds from inequalities (2) and (3). For example, suppose that (p − q) = , …
Chernoff bound examples
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WebChernoff-Hoeffding Inequality When dealing with modern big data sets, a very common theme is reducing the set through a random process. These generally work by making … WebLecture 23: Chernoff Bound & Union Bound 1 Slide Credit: Based on Stefano Tessaro’sslides for 312 19au incorporating ideas from Alex Tsun’sand Anna …
WebLet us look at an example to see how we can use Chernoff bounds. Example Let X ∼ B i n o m i a l ( n, p). Using Chernoff bounds, find an upper bound on P ( X ≥ α n), where p < … Webmatrices[1]. For example, the covariance of X 2 Rn⇥d can be written as XTX = Pn i=1 x T i xi where xi denotes i-th row of X. In this section, we state two common bounds on random matrices[1]. 6.2.1 Matrix Chernoff Bound Chernoff’s Inequality has an analogous in matrix setting; the 0,1 random variables translate to positive-
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 faster than exponential (e.g. sub-Gaussian). The Chernoff bound is especially useful for sums of independent random variables, such as sums of Bernoulli random variables.
WebJun 12, 2024 · Jensen's inequality then tells you that this bound is minimized when λ = 1 + ϵ 1 − ϵ 2 2. More generally Jensen's inequality tells you that the Chernoff upper bound is …
WebJun 12, 2024 · Finding the best threshold for bounding error probability in Chernoff (biased coins examples) Asked 2 years, 9 months ago Modified 2 years, 9 months ago Viewed 241 times 1 Suppose we have two biased coins which we want to distinguish: { c 1: P ( H) = 1 / 2 + ϵ c 2: P ( H) = 1 / 2 − ϵ global manufacturing index 2022 ranking listWebLecture 7: Chernoff’s Bound and Hoeffding’s Inequality 2 Note that since the training data {X i,Y i}n i=1 are assumed to be i.i.d. pairs, each term in the sum is an i.i.d random variables. Let L i = ‘(f(X i),Y i) The collection of losses {L global manufacturing definitionWebAPPLICATIONS OF CHERNOFF BOUNDS 3 The proof follows from induction on n. We now construct and prove Markov’s Inequality, a rather primitive tail bound. We examine … boesner edition 15WebChernoff bounds have a particularly simple form in the case of sum of independent variables, since . For example, [5] suppose the variables satisfy , for . Then we have lower tail inequality: If satisfies , we have upper tail inequality: If are i.i.d., and is the variance of , a typical version of Chernoff inequality is: 7. boesner freiburg online shopWebWest Virginia University boesner horairesWebproof of the Chernoff bound comes from using calculus to determine the right constant to use instead of e in the above argument. Example: Fair coin Suppose you toss a fair coin 200 times. How likely is it that you see at least 120 heads? The Chernoff bound says … global manufacturing little rock arkansasWebChernoff Bounds Chernoff bounds are another kind of tail bound. Like Markoff and Chebyshev, they bound the total amount of probability of some random variable Y … global manufacturing index