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:

$\sum _{i}\log \left(1+e^{-y_{i}f(x_{i})}\right)$

See also

• Logistic model tree