Exercise 1.9

Answers

We have μ = 0.9, N = 10, and want ν ≤ 0.1, i.e. |μ − ν| = μ − ν ≥ 0.9 − 0.1 = 0.8. Let’s pick 𝜖 = 0.7, then according to Hoeffding Inequity, we have

P(ν ≤ 0.1) = P(μ − ν ≥ 0.8) = P(|μ − ν|≥ 0.8) ≤ P(|μ − ν|0.7) = P(|μ − ν|𝜖) ≤ 2e−2𝜖2N ≈ 0.0001109032

This is an upper bound of the probability from previous problem and is much larger than the calculated probability.

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2021-12-07 18:16
Comments
  • If the in-sample error and the out-of-sample error are measured as percentages, does that mean the tolerance we pick is also a percentage?
    Peaceful_Guy • 2023-09-27