= AdaBoost training error bound
{c}
{title2=$\widehat R_{01}\le\prod_m2\sqrt{\epsilon_m(1-\epsilon_m)}\le e^{-2\sum_m\gamma_m^2}$}
For <AdaBoost> with initial uniform weights, labels and base predictions in $\{-1,1\}$, and edges $\gamma_m=1/2-\epsilon_m>0$, the training <exponential classification risk> equals the product of stage normalizers. A wrongly classified point has exponential loss at least one, so empirical classification error is bounded by this product. The final inequality uses $\sqrt{1-4\gamma_m^2}\le e^{-2\gamma_m^2}$. The result concerns training error, not a guarantee against overfitting or mislabeled observations.
// Target: probability-and-statistics.bigb
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