TaylorBoost: First and second-order boosting algorithms with explicit margin control

A new family of boosting algorithms, denoted Taylor-Boost, is proposed. It supports any combination of loss function and first or second order optimization, and includes classical algorithms such as AdaBoost, Gradient-Boost, or LogitBoost as special cases. Its restriction to the set of canonical losses makes it possible to have boosting algorithms with explicit margin control. A new large family of losses with this property, based on the set of cumulative distributions of zero mean random variables, is then proposed. A novel loss function in this family, the Laplace loss, is finally derived. The combination of this loss and second order TaylorBoost produces a boosting algorithm with explicit margin control.