Gradient and Newton Boosting for Classification and Regression

Abstract

Boosting algorithms are frequently used in applied data science and in research. To date, the distinction between boosting with either gradient descent or second-order Newton updates is often not made in both applied and methodological research, and it is thus implicitly assumed that the difference is irrelevant. The goal of this article is to clarify this situation. In particular, we present gradient and Newton boosting, as well as a hybrid variant of the two, in a unified framework. We compare these boosting algorithms with trees as base learners using various datasets and loss functions. Our experiments show that Newton boosting outperforms gradient and hybrid gradient-Newton boosting in terms of predictive accuracy on the majority of datasets. We also present evidence that the reason for this is not faster convergence of Newton boosting. In addition, we introduce a novel tuning parameter for tree-based Newton boosting which is interpretable and important for predictive accuracy.