AdaBoost
Thus, after selecting an optimal classifier h t {\displaystyle h_{t}\,} for the distribution D t {\displaystyle D_{t}\,} , the examples x i {\displaystyle x_{i}\,} that the classifier h t {\displaystyle h_{t}\,} identified correctly are weighted less and those that it identified incorrectly are weighted more. Therefore, when the algorithm is testing the classifiers on the distribution D t + 1 {\displaystyle D_{t+1}\,} , it will select a classifier that better identifies those examples that the previous classifer missed.
where Z t {\displaystyle Z_{t}} is a normalization factor (chosen so that D t + 1 {\displaystyle D_{t+1}} will be a probability distribution, i.e. sum one over all x).
Output the final classifier:
H ( x ) = sign ( ∑ t = 1 T α t h t ( x ) ) {\displaystyle H(x)={\textrm {sign}}\left(\sum _{t=1}^{T}\alpha _{t}h_{t}(x)\right)}
The equation to update the distribution D t {\displaystyle D_{t}} is constructed so that:
− α t y i h t ( x i ) { < 0 , y ( i ) = h t ( x i ) > 0 , y ( i ) ≠ h t ( x i ) {\displaystyle -\alpha _{t}y_{i}h_{t}(x_{i}){\begin{cases}<0,&y(i)=h_{t}(x_{i})\\>0,&y(i)\neq h_{t}(x_{i})\end{cases}}}