Hoeffding's inequality bounds tail probability for sums of bounded random variables
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Hoeffding's inequality
Hoeffding's inequality bounds tail probability for sums of bounded random variables
Hoeffding's inequality offers an upper limit on the probability that the sum of independent random variables strays significantly from its expected value. This inequality was introduced by Wassily Hoeffding in 1963. It is a foundational result in probability theory, providing a way to quantify the concentration of sums of random variables.
Example
Consider a sequence of 100 independent random variables, each uniformly distributed between 0 and 1. Hoeffding's inequality can be used to bound the probability that their sum deviates from the expected value (which is 50) by more than a certain amount.
Understanding Hoeffding's inequality helps in assessing the reliability of statistical estimates and in designing algorithms with guaranteed performance bounds.
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