Randomized Gradient Boosting Machine

TL;DR

This paper introduces Randomized Gradient Boosting Machine (RGBM), a computationally efficient variant of GBM that uses randomization to reduce search space, backed by theoretical guarantees and demonstrated through experiments.

Contribution

It proposes RGBM with a novel randomization scheme, provides theoretical guarantees, and offers a new step-size selection method without line search.

Findings

RGBM achieves substantial computational gains over GBM.

Theoretical guarantees depend on the Minimal Cosine Angle.

RGBM performs well on real datasets with less computation.

Abstract

Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In spite of the usefulness of GBM in practice, our current theoretical understanding of this method is rather limited. In this work, we propose Randomized Gradient Boosting Machine (RGBM) which leads to substantial computational gains compared to GBM, by using a randomization scheme to reduce search in the space of weak-learners. We derive novel computational guarantees for RGBM. We also provide a principled guideline towards better step-size selection in RGBM that does not require a line search. Our proposed framework is inspired by a special variant of coordinate descent that combines the benefits of randomized coordinate descent and greedy coordinate descent; and may be of independent interest as an optimization algorithm. As a special case, our results for RGBM lead to superior computational guarantees for GBM. Our computational guarantees depend upon a curious geometric quantity that we call Minimal Cosine Angle, which relates to the density of weak-learners in the prediction space. On a series of numerical experiments on real datasets, we demonstrate the effectiveness of RGBM over GBM in terms of obtaining a model with good training and/or testing data fidelity with a fraction of the computational cost.