Randomized Gradient Boosting Machine
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Gradient Boosting Machine (GBM) introduced by Friedman is an extremely powerful supervised learning algorithm that is 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, there is a big gap between its theoretical understanding and its success in practice. In this work, we propose Randomized Gradient Boosting Machine (RGBM) which leads to significant computational gains compared to GBM, by using a randomization scheme to reduce the search in the space of weak learners. Our analysis provides a formal justification of commonly used ad hoc heuristics employed by GBM implementations such as XGBoost, and suggests alternatives. In particular, we also provide a principled guideline towards better step-size selection in RGBM that does not require a line search. The analysis of RGBM 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. We demonstrate the effectiveness of RGBM over GBM in terms of obtaining a model with good training/test data fidelity with a fraction of the computational cost, via numerical experiments on several real datasets.
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