Gradient boosting with vector-valued leafs

David Cortes

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arXiv · 2606.29326

Gradient boosting with vector-valued leafs

David Cortes

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Abstract

Gradient boosting in the form of decision tree ensembles has successfully been applied to a variety of problems using simple objective functions based on log-likelihoods of a single variable. The concept extends naturally to objective functions operating on vectors - for example, multinomial logistic log-likelihood for multi-class classification, where observations have a score for each class - but popular frameworks approach these functions by either updating one value of the input vectors at a time, or by using a diagonal upper bound on the second derivative. This work extends the usual gradient boosting framework to functions of vector inputs and sketches a simple algorithm that can be used efficiently with histogram-based decision trees.

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David Cortes. 2026-06-28. Gradient boosting with vector-valued leafs. https://arxiv.org/abs/2606.29326

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