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[2510.00545] Bayesian Neural Networks for Functional ANOVA model
Summary
This paper introduces Bayesian-TPNN, a Bayesian inference approach for the functional ANOVA model using Tensor Product Neural Networks, improving computational efficiency and enabling higher-order component detection.
Why It Matters
As machine learning increasingly demands interpretability, this research addresses the limitations of existing models by providing a more efficient method for analyzing complex data structures. The Bayesian-TPNN framework enhances the functional ANOVA model, making it a significant contribution to statistical learning and data analysis.
Key Takeaways
- Bayesian-TPNN improves upon the ANOVA-TPNN model by reducing computational costs.
- The proposed method enables the detection of higher-order components without prior specification.
- An efficient MCMC algorithm is developed to support Bayesian inference in this context.
- Theoretical consistency of the Bayesian-TPNN posterior is established.
- The model demonstrates strong performance across multiple benchmark datasets.
Statistics > Machine Learning arXiv:2510.00545 (stat) [Submitted on 1 Oct 2025 (v1), last revised 20 Feb 2026 (this version, v2)] Title:Bayesian Neural Networks for Functional ANOVA model Authors:Seokhun Park, Choeun Kim, Jihu Lee, Yunseop Shin, Insung Kong, Yongdai Kim View a PDF of the paper titled Bayesian Neural Networks for Functional ANOVA model, by Seokhun Park and 5 other authors View PDF HTML (experimental) Abstract:With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal the contributions of different variable groups. Recently, Tensor Product Neural Network (TPNN) has been developed and applied as basis functions in the functional ANOVA model, referred to as ANOVA-TPNN. A disadvantage of ANOVA-TPNN, however, is that the components to be estimated must be specified in advance, which makes it difficult to incorporate higher-order TPNNs into the functional ANOVA model due to computational and memory constraints. In this work, we propose Bayesian-TPNN, a Bayesian inference procedure for the functional ANOVA model with TPNN basis functions, enabling the detection of higher-order components with reduced computational cost compared to ANOVA-TPNN. We develop an efficient MCMC algorithm and demonstrate that Bayesian-TPNN performs well by analyzing multiple benchmark datasets. Theoretically, we ...
