Seeing the Forest for the Trees: The Gaussian Process Limit of BART

arXiv:2607.28844 · math.ST, stat.ME, stat.ML, stat.TH · Submitted 2026-07-30 · Read on arXiv

math.ST, stat.ME, stat.ML, stat.TH

Submitted: 2026-07-30

Updated: 2026-08-31

Comments: 20 pages, 5 figures, plus references and appendices

Project page: https://corymccartan.com

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Ablation — 10× in this paper · explained in 1 episode
• Ablation Study — 9× in this paper · explained in 3 episodes
• Bayesian Additive Regression Trees — 9× in this paper
• Generalization — 6× in this paper · explained in 14 episodes
• Trace — 6× in this paper · explained in 2 episodes
• Curse of Dimensionality — 5× in this paper · explained in 6 episodes
• Kernel Ridge Regression — 5× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 4× in this paper · explained in 7 episodes
• XGBoost — 4× in this paper · explained in 3 episodes
• Causal Inference — 3× in this paper · explained in 5 episodes
• Gaussian Process (GP) — 3× in this paper · explained in 2 episodes
• Hyperparameters — 3× in this paper · explained in 2 episodes
• Lasso — 3× in this paper · explained in 2 episodes
• Uncertainty Quantification — 3× in this paper · explained in 9 episodes
• Bayesian Inference — 2× in this paper · explained in 6 episodes
• Papers — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 5 episodes
• Ablation Studies — 1× in this paper · explained in 1 episode
• Absorb — 1× in this paper · explained in 1 episode
• Asymptotic Normality — 1× in this paper · explained in 2 episodes
• Augmentation — 1× in this paper · explained in 2 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Data Augmentation — 1× in this paper · explained in 10 episodes
• Ensemble Learning — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Minimax Optimality — 1× in this paper · explained in 3 episodes
• Monte Carlo Sampling — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• The Mondrian Kernel
• Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences
• Bayesian Additive Distribution Regression
• On the Gaussian process limit of Bayesian Additive Regression Trees
• Highly Adaptive Ridge
• Lassoed Tree Boosting
• Higher Order Spline Highly Adaptive Lasso Estimators of Functional Parameters: Pointwise Asymptotic Normality and Uniform Convergence Rates
• Scalable piecewise smoothing with BART

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