Bayesian Additive Regression Trees for functional ANOVA model

• URL: http://arxiv.org/abs/2509.03317v2
• Date: Thu, 04 Sep 2025 12:40:40 GMT
• Title: Bayesian Additive Regression Trees for functional ANOVA model
• Authors: Seokhun Park, Insung Kong, Yongdai Kim,
• Abstract summary: ANOVA Bayesian Additive Regression Trees (ANOVA-BART) is a novel extension of Bayesian Additive Regression Trees (BART)<n>Our proposed ANOVA-BART enhances interpretability, preserves and extends the theoretical guarantees of BART, and achieves superior predictive performance.<n>These results suggest that ANOVA-BART offers a compelling alternative to BART by balancing predictive accuracy, interpretability, and theoretical consistency.
• Score: 13.402140652721618
• License: http://creativecommons.org/licenses/by/4.0/
• 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 superior predictive 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 surpasses 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.

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