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An additive model constructed using the exponential loss function

$$L(y, f (x)) = \exp(−yf (x))$$

gives Adaboost. How can we derive the corresponding additive model (known as logitboost) using the logistic loss function

$$L(y, f (x)) = \log(1 + \exp(−yf (x)))$$

What steps I should take to do the above proof?

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    $\begingroup$ I suggest modifying this to ask a concrete theoretical question -- e.g. "How does one minimize logistic loss...". $\endgroup$ – Lev Reyzin Nov 1 '12 at 22:22
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Originally, Logitboost was derived by Friedman, Hastie, and Tibshirani (paper) -- their algorithm internally used a numerical procedure, via Newtons method to solve a regression problem.

Later, Collins, Schapire, and Singer (paper) found an equivalent formulation, with a single-line modification from AdaBoost, setting $$D(i) \propto \frac{1}{1+e^{y_i f_{t-1}(x_i)}}.$$

Schapire has a nice summary of boosting here, which also discusses Logitboost.

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  • $\begingroup$ looks like I didn't ask the question clearly, I have cleaned up. I understand the adaboost. $\endgroup$ – add-semi-colons Nov 2 '12 at 0:57
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To get you answer,you may wanna look at this paper http://dept.stat.lsa.umich.edu/~gmichail/ada_final.pdf. Algorithm 2 summarizes the step you have to take to derive a boosting algorithm from any given convex loss including logitboost.

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