# Derive logitboost using the logistic loss function

An additive model constructed using the exponential loss function

$$L(y, f (x)) = \exp(−yf (x))$$

gives Adaboost. How can we derive the corresponding additive model (known as logitboost) using the logistic loss function

$$L(y, f (x)) = \log(1 + \exp(−yf (x)))$$

What steps I should take to do the above proof?

• I suggest modifying this to ask a concrete theoretical question -- e.g. "How does one minimize logistic loss...". – Lev Reyzin Nov 1 '12 at 22:22

Later, Collins, Schapire, and Singer (paper) found an equivalent formulation, with a single-line modification from AdaBoost, setting $$D(i) \propto \frac{1}{1+e^{y_i f_{t-1}(x_i)}}.$$