Chernoff bounds


The Chernoff bounds are a way of bounding the probability that a sum of independent random variables takes on extreme values. Compared with Chebyshev's inequality, it requires a stronger assumption (independence), but is a far tighter bound. They are commonly used to analyze randomized algorithms and PAC-learning methods.


This concept has the prerequisites:


  • Give the general statement of Chernoff bounds in terms of moment generating functions
  • Derive the bound using Markov's inequality
  • Be able to use it to bound probabilities of extreme values
  • When would you use the Chernoff bound vs. the Chebyshev bound?

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Supplemental resources (the following are optional, but you may find them useful)


See also