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2

Responding to your comments, and bringing it back to my original comment: Line 4 of Friedman's algorithm can be viewed as "finding the best function $g \in \mathcal{G}$ that fits the pseudo-residuals via minimizing $\sum_i [\tilde{y}_i - g(x_i)]^2$," with $\mathcal{G}$ containing all functions of the form $g(\cdot) := \beta h(\cdot; a)$. Once you ...

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It depends, actually. There are two possible behaviors, described in section 3 of "Experiments with a New Boosting Algorithm" by Freund and Schapire: We first mention briefly a small implementation issue: Many learning algorithms can be modified to handle examples that are weighted by a distribution such as the one created by the boosting ...

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You understanding is completely correct. Starting at step 1, you initialise uniform weights $w_i = 1 / N$. Beginning at step 2, in say iteration $m = 1$, you sample a bootstrap dataset $\mathcal{B}_1$, which consists of $N$ data points. This bootstrap dataset $\mathcal{B}_1$ is the result of sampling each point $(x_i, y_i)$ in the original training dataset ...

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