Randomized gradient boosting machine
Name
18m1223277.pdf
Description
Published version
Size
1.45 MB
Format
Adobe PDF
Checksum (MD5)
63688a6a1d6bac90cdc3494aa395a00c
Author(s)
Mazumder, Rahul
Date Issued
October 2020
Journal
SIAM Journal on Optimization
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Lu, Haihao and Rahul Mazumder. “Randomized gradient boosting machine.” SIAM Journal on Optimization, 30, 4 (October 2020): 780--2808 © 2020 The Author(s)
Version
Final published version
Abstract
The Gradient Boosting Machine (GBM) introduced by Friedman [J. H. Friedman, Ann. Statist., 29 (2001), pp. 1189-1232] 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 the 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 the 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.
MIT Department
Sloan School of Management
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/18M1223277
