LogitBoost

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LogitBoost is a boosting algorithm formulated by Jerome Friedman, Trevor Hastie, and Robert Tibshirani. The original paper ^[1] casts the AdaBoost algorithm into a statistics framework. Specifically, if one considers AdaBoost as a generalized additive model and then applies the cost functional of logistic regression, one can derive the LogitBoost algorithm.

[edit] Minimizing the LogitBoost Cost Functional

LogitBoost can be seen as a convex optimization. Specifically, given that we seek an additive model of the form

f =	∑	α_th_t
	t

the LogitBoost algorithm minimizes the logistic loss:

$\sum_i \log\left( 1 + e^{-y_i f(x_i)}\right)$

[edit] References

^ Jerome Friedman, Trevor Hastie and Robert Tibshirani. Additive logistic regression: a statistical view of boosting. Annals of Statistics 28(2), 2000. 337-407