Optional stopping theorem

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:

$\sum _i\log (1+e^{-y_{i}f(x_i)})$

See also

• Logistic model tree