# LogitBoost

In machine learning and computational learning theory, 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.[1] Specifically, if one considers AdaBoost as a generalized additive model and then applies the cost function of logistic regression, one can derive the LogitBoost algorithm.

## Minimizing the LogitBoost cost function

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

${\displaystyle f=\sum _{t}\alpha _{t}h_{t}}$

the LogitBoost algorithm minimizes the logistic loss:

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