Suchergebnisse
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In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events.
Learn how to use the union bound and its extension, the Bonferroni inequalities, to bound the probability of union of events. See examples of applications in random graphs and expected value of events.
Learn how to use the union bound to bound the probability of multiple events occurring, and how to apply Jensen's inequality and Hoe ding's inequality to convex functions. See examples, proofs, and slides from CSE312 course at UW.
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Boole's inequality (or the union bound ) states that for any at most countable collection of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the events in the collection.
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Dieses letzte Gesetz nennt man auch die Union Bound (weil es die Wahrscheinlichkeit der Vereinigung, also der Union beschränkt). Andere Namen sind Bonferroni-Ungleichung oder auch Boolesche Ungleichung.
Learn how to use Hoeffding's inequality and union bounds to derive upper bounds for the deviation of the empirical mean from the true mean in stochastic online learning and multi-armed bandit problems. See the proof, corollary and implications of the theorem.
Proposition 1.1. Let X be a Gaussian random variable with mean μ and variance σ2 then for any t > 0, it holds. IP(X. t2. e −. 2σ2. − μ > t) ≤ √ . 2π t. By symmetry we also have. IP(X. −. t2. e 2σ2. − μ < −t) ≤ √ . 2π t. 14. Figure 1.1.
