Adaptive boosting: AdaBoost, Basic Algorithm

The algorithm here is rather straightforward. Assume that our weak classifier is a decision tree and we consider a binary set of outputs with $y_i \in \{-1,1\}$ and $i=0,1,2,\dots,n-1$ as our set of observations. Our design matrix is given in terms of the feature/predictor vectors $\boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}]$. Finally, we define also a classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\boldsymbol{y}$.

We have already defined the misclassification error $\mathrm{err}$ as

$$\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)),$$

where the function $I()$ is one if we misclassify and zero if we classify correctly.

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