Bayesian Additive Regression Trees for functional ANOVA model
arXiv:2509.03317v4 Announce Type: replace Abstract: Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and interactions among predictors. However, the accuracy of BART often comes at the cost of interpretability. To address this limitation, we propose ANOVA Bayesian Additive Regression Trees (ANOVA-BART), a novel extension of BART based on the functional ANOVA decomposition, which is used to decompose the variability of a function into different interactions, each representing the contribution of a different set of covariates or factors. Our proposed ANOVA-BART enhances interpretability, preserves and extends th
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Abstract:Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and interactions among predictors. However, the accuracy of BART often comes at the cost of interpretability. To address this limitation, we propose ANOVA Bayesian Additive Regression Trees (ANOVA-BART), a novel extension of BART based on the functional ANOVA decomposition, which is used to decompose the variability of a function into different interactions, each representing the contribution of a different set of covariates or factors. Our proposed ANOVA-BART enhances interpretability, preserves and extends the theoretical guarantees of BART, and achieves comparable prediction performance. Specifically, we establish that the posterior concentration rate of ANOVA-BART is nearly minimax optimal, and further provides the same convergence rates for each interaction that are not available for BART. Moreover, comprehensive experiments confirm that ANOVA-BART is comparable to BART in both accuracy and uncertainty quantification, while also demonstrating its effectiveness in component selection. These results suggest that ANOVA-BART offers a compelling alternative to BART by balancing predictive accuracy, interpretability, and theoretical consistency.
Subjects:
Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:2509.03317 [stat.ML]
(or arXiv:2509.03317v4 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2509.03317
arXiv-issued DOI via DataCite
Submission history
From: Seokhun Park [view email] [v1] Wed, 3 Sep 2025 13:50:45 UTC (466 KB) [v2] Thu, 4 Sep 2025 12:40:40 UTC (462 KB) [v3] Wed, 4 Feb 2026 06:28:53 UTC (540 KB) [v4] Tue, 31 Mar 2026 06:49:05 UTC (540 KB)
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