Infinitesimal gradient boosting
| Autor: | Dombry, Clément, Duchamps, Jean-Jil |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 51 pages, 5 figures |
| Databáze: | arXiv |
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