LogitBoost

LogitBoost is a boosting algorithm formulated by Jerome Friedman, Trevor Hastie, and Robert Tibshirani. The original paper casts the AdaBoost algorithm into a statistical 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:

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