WebOct 21, 2024 · The Chernoff-Cramèr bound is a widely used technique to analyze the upper tail bound of random variable based on its moment generating function. By elementary proofs, we develop a user-friendly reverse Chernoff-Cramèr bound that yields non-asymptotic lower tail bounds for generic random variables. The new reverse Chernoff … Web5.3 The Cramér-Chernoff Method and Subgaussian Random Variables 62 5.4 Notes 64 5.5 Bibliographical Remarks 66 5.6 Exercises 66 Part II Stochastic Bandits with Finitely Many Arms 73 6 The Explore-Then-Commit Algorithm 75 6.1 Algorithm and Regret Analysis 75 6.2 Notes 78 6.3 Bibliographical Remarks 78 6.4 Exercises 79 7 The Upper Confidence ...
Probabilistic robustness estimates for feed-forward neural networks
WebOct 24, 2024 · The so-called Cramér-Chernoff bounding method determines the best possible bound for a tail probability that one can possibly obtain by using Markov’s … WebChernoff-Cramer bound´ Under a finite variance, squaring within Markov’s in-equality (THM 7.1) produces Chebyshev’s inequality (THM 7.2). This “boosting” can be pushed … garmin gps in canada
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Web(2+6+6 pts) Using Cramer-Chernoff bounds, solve the following: (a) Consider a random variable X~ N(0,02), obtain an upper bound for P[X>t). (b) Consider X is a geometric random variable with probability of success p. WebAug 1, 1985 · An inequality due to Chernoff is generalized and a related Cramer-Rao type of inequality is studied. Discover the world's research. 20+ million members; 135+ million publications; 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 $${\displaystyle X_{i}}$$ with probability p of being equal to 1, One can encounter … 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. Let M1, ..., Mt be independent matrix valued random … 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 known as Hoeffding's inequality. The proof follows a similar approach to the other Chernoff bounds, but applying See more Chernoff bounds have very useful applications in set balancing and packet routing in sparse networks. The set balancing problem arises while designing statistical experiments. Typically while designing a statistical experiment, given the features … 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 general population A and a sub-population B ⊆ A. Mark the relative size of the … See more black reunion band