Neural Tangent Kernels for Axis-Aligned Tree Ensembles

Ryuichi Kanoh, Mahito Sugiyama
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:23058-23081, 2024.

Abstract

While axis-aligned rules are known to induce an important inductive bias in machine learning models such as typical hard decision tree ensembles, theoretical understanding of the learning behavior is largely unrevealed due to the discrete nature of rules. To address this issue, we impose the axis-aligned constraint on soft trees, which relax the splitting process of decision trees and are trained using a gradient method, and present their Neural Tangent Kernel (NTK), which enables us to analytically describe the training behavior. We study two cases: imposing the axis-aligned constraint throughout the entire training process, and only at the initial state. Moreover, we extend the NTK framework to handle various tree architectures simultaneously, and prove that any axis-aligned non-oblivious tree ensemble can be transformed into axis-aligned oblivious tree ensembles with the same NTK. One can search for suitable tree architecture via Multiple Kernel Learning (MKL), and our numerical experiments show a variety of suitable features depending on the type of constraints. Our NTK analysis highlights both the theoretical and practical impacts of the axis-aligned constraint in tree ensemble learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-kanoh24a, title = {Neural Tangent Kernels for Axis-Aligned Tree Ensembles}, author = {Kanoh, Ryuichi and Sugiyama, Mahito}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {23058--23081}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/kanoh24a/kanoh24a.pdf}, url = {https://proceedings.mlr.press/v235/kanoh24a.html}, abstract = {While axis-aligned rules are known to induce an important inductive bias in machine learning models such as typical hard decision tree ensembles, theoretical understanding of the learning behavior is largely unrevealed due to the discrete nature of rules. To address this issue, we impose the axis-aligned constraint on soft trees, which relax the splitting process of decision trees and are trained using a gradient method, and present their Neural Tangent Kernel (NTK), which enables us to analytically describe the training behavior. We study two cases: imposing the axis-aligned constraint throughout the entire training process, and only at the initial state. Moreover, we extend the NTK framework to handle various tree architectures simultaneously, and prove that any axis-aligned non-oblivious tree ensemble can be transformed into axis-aligned oblivious tree ensembles with the same NTK. One can search for suitable tree architecture via Multiple Kernel Learning (MKL), and our numerical experiments show a variety of suitable features depending on the type of constraints. Our NTK analysis highlights both the theoretical and practical impacts of the axis-aligned constraint in tree ensemble learning.} }
Endnote
%0 Conference Paper %T Neural Tangent Kernels for Axis-Aligned Tree Ensembles %A Ryuichi Kanoh %A Mahito Sugiyama %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-kanoh24a %I PMLR %P 23058--23081 %U https://proceedings.mlr.press/v235/kanoh24a.html %V 235 %X While axis-aligned rules are known to induce an important inductive bias in machine learning models such as typical hard decision tree ensembles, theoretical understanding of the learning behavior is largely unrevealed due to the discrete nature of rules. To address this issue, we impose the axis-aligned constraint on soft trees, which relax the splitting process of decision trees and are trained using a gradient method, and present their Neural Tangent Kernel (NTK), which enables us to analytically describe the training behavior. We study two cases: imposing the axis-aligned constraint throughout the entire training process, and only at the initial state. Moreover, we extend the NTK framework to handle various tree architectures simultaneously, and prove that any axis-aligned non-oblivious tree ensemble can be transformed into axis-aligned oblivious tree ensembles with the same NTK. One can search for suitable tree architecture via Multiple Kernel Learning (MKL), and our numerical experiments show a variety of suitable features depending on the type of constraints. Our NTK analysis highlights both the theoretical and practical impacts of the axis-aligned constraint in tree ensemble learning.
APA
Kanoh, R. & Sugiyama, M.. (2024). Neural Tangent Kernels for Axis-Aligned Tree Ensembles. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:23058-23081 Available from https://proceedings.mlr.press/v235/kanoh24a.html.

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