TreeCCA: Canonical Correlation Analysis via Gradient-Boosted Trees

arXiv:2607.27027v1 Announce Type: new Abstract: Gradient-boosted trees dominate tabular machine learning, yet canonical correlation analysis has always relied on linear or neural encoders. We propose \textbf{TreeCCA}, the first method to train gradient-boosted tree ensembles end-to-end as CCA encoders, inheriting their plug-and-play reliability: no architecture design, familiar hyperparameters, and strong performance with defaults. The technical enabler is the Eckart-Young (EY) loss, which supplies closed-form per-sample gradients that slot directly into any standard GBT library (XGBoost, LightGBM) as a custom objective. TreeCCA is the first CCA method to combine nonlinear accuracy with native interpretability: every tree split selects one feature, so gain importances reveal which inputs drive cross-view correlation at no extra cost. We demonstrate these properties on synthetic benchmarks, where TreeCCA matches or exceeds Deep CCA (2.61 vs.\ 2.43 on Signed Power; 2.93 vs.\ 2.89 on Hermite), and on a sparse benchmark with zero linear cross-view covariance, where TreeCCA recovers the true support with $\text{Precision@}S = 1.00$ at $p=50$ while PMD finds no signal. On the UCI HAR sensor-fusion benchmark, TreeCCA achieves comparable accuracy to Deep CCA at $5\times$ lower cost, while XGBoost gain importances directly validate a physics-motivated hypothesis about the data --- an interpretation not readily available with neural encoders. Across five popular tabular multi-view datasets, TreeMCCA consistently matches or exceeds linear CCA in both nonlinear correlation extraction and downstream classification accuracy.

Abstract:Gradient-boosted trees dominate tabular machine learning, yet canonical correlation analysis has always relied on linear or neural encoders. We propose \textbf{TreeCCA}, the first method to train gradient-boosted tree ensembles end-to-end as CCA encoders, inheriting their plug-and-play reliability: no architecture design, familiar hyperparameters, and strong performance with defaults. The technical enabler is the Eckart-Young (EY) loss, which supplies closed-form per-sample gradients that slot directly into any standard GBT library (XGBoost, LightGBM) as a custom objective. TreeCCA is the first CCA method to combine nonlinear accuracy with native interpretability: every tree split selects one feature, so gain importances reveal which inputs drive cross-view correlation at no extra cost. We demonstrate these properties on synthetic benchmarks, where TreeCCA matches or exceeds Deep CCA (2.61 vs.\ 2.43 on Signed Power; 2.93 vs.\ 2.89 on Hermite), and on a sparse benchmark with zero linear cross-view covariance, where TreeCCA recovers the true support with $\text{Precision@}S = 1.00$ at $p=50$ while PMD finds no signal. On the UCI HAR sensor-fusion benchmark, TreeCCA achieves comparable accuracy to Deep CCA at $5\times$ lower cost, while XGBoost gain importances directly validate a physics-motivated hypothesis about the data --- an interpretation not readily available with neural encoders. Across five popular tabular multi-view datasets, TreeMCCA consistently matches or exceeds linear CCA in both nonlinear correlation extraction and downstream classification accuracy.

Machine Learning (cs.LG)

arXiv:2607.27027 [cs.LG]

(or arXiv:2607.27027v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.27027 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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TreeCCA: Canonical Correlation Analysis via Gradient-Boosted Trees

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