adaboost summary

1. initialize equal weights for all samples

   $$alpha_{i} = frac{1}{N}$$

2. Repeat t = 1,…,T

   • learn $f_{t}(x)$ with data weights $alpha_{i}$
   • compute weighted error $$weighted_{error_{t}} = sum_{i=1}^{m}alpha_{i}I(y_{i} neq f_{t}(x_{i}))$$
   • compute coefficient $$hat{w_{t}} = frac{1}{2}ln(frac{1 - weighted_{error_{t}} }{weighted_{error_{t}}})$$
     • $hat{w_{t}}$ is higher when weighted_error is larger
   • recomputed weights $alpha_{i}$ $$alpha_{i} = begin{equation} left{ begin{array}{lr} alpha_{i}e^{-hat{w_{t}}} & \ alpha_{i}e^{hat{w{t}}} & end{array} right. end{equation}$$
   • Normalize weights $alpha_{i}$
     • if $x_{i}$ often mistake, weight $alpha_{i}$ gets very large
     • if $x_{i}$ often correct, weight $alpha_{i}$ gets very small $$alpha_{i} = frac{alpha_{i}}{sum_{i}^{m}alpha_{i}}$$

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