LogitBoost is a boosting algorithm formulated by Jerome Friedman, Trevor Hastie, and Robert Tibshirani. The original paper [Jerome Friedman, Trevor Hastie and Robert Tibshirani. Additive logistic regression: a statistical view of boosting. Annals of Statistics 28(2), 2000. 337-407] 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.

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 = sum_t alpha_t h_t

the LogitBoost algorithm minimizes the logistic loss:

:sum_i logleft( 1 + e^{-y_i f(x_i)} ight)


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