Infinitesimal gradient boosting

Clément Dombry and Jean-Jil Duchamps

Stochastic Processes and their Applications, 2024, vol. 170, issue C

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.

Keywords: Gradient boosting; Softmax regression tree; Vanishing-learning-rate asymptotic; Convergence of Markov processes (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414924000164
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:170:y:2024:i:c:s0304414924000164

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2024.104310

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().