Infinitesimal gradient boosting

Clément Dombry; Jean-Jil Duchamps

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arXiv · 2104.13208

Infinitesimal gradient boosting

Clément Dombry·Jean-Jil Duchamps

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Abstract

We define infinitesimal gradient boosting as a limit of the popular tree-based gradient boosting algorithm from machine learning. The limit is considered in the vanishing-learning-rate asymptotic, that is when the learning rate tends to zero and the number of gradient trees is rescaled accordingly. For this purpose, we introduce a new class of randomized regression trees bridging totally randomized trees and Extra Trees and using a softmax distribution for binary splitting. Our main result is the convergence of the associated stochastic algorithm and the characterization of the limiting procedure as the unique solution of a nonlinear ordinary differential equation in a infinite dimensional function space. Infinitesimal gradient boosting defines a smooth path in the space of continuous functions along which the training error decreases, the residuals remain centered and the total variation is well controlled.

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BibTeX RIS

Clément Dombry, Jean-Jil Duchamps. 2021-04-26. Infinitesimal gradient boosting. https://arxiv.org/abs/2104.13208

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