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Margins are Insufficient for Explaining Gradient Boosting
Allan Grønlund · Lior Kamma · Kasper Green Larsen

Tue Dec 08 09:00 AM -- 11:00 AM (PST) @ Poster Session 1 #303
Boosting is one of the most successful ideas in machine learning, achieving great practical performance with little fine-tuning. The success of boosted classifiers is most often attributed to improvements in margins. The focus on margin explanations was pioneered in the seminal work by Schaphire et al. (1998) and has culminated in the $k$'th margin generalization bound by Gao and Zhou (2013), which was recently proved to be near-tight for some data distributions (Gr\o nlund et al. 2019). In this work, we first demonstrate that the $k$'th margin bound is inadequate in explaining the performance of state-of-the-art gradient boosters. We then explain the short comings of the $k$'th margin bound and prove a stronger and more refined margin-based generalization bound that indeed succeeds in explaining the performance of modern gradient boosters. Finally, we improve upon the recent generalization lower bound by Gr\o nlund et al. (2019).

Author Information

Allan Grønlund (Aarhus University, MADALGO)
Lior Kamma (Aarhus University)
Kasper Green Larsen (Aarhus University)

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