# Bayesian Neural Networks for Functional ANOVA model

arXiv: https://arxiv.org/abs/2510.00545 · HTML: https://mlsanity.com/paper/2510.00545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 58 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 27 of 27)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Detecting Statistical Interactions from Neural Network Weights](https://mlsanity.com/paper/1705.04977/) (2017)
- [A Systematic Comparison of Bayesian Deep Learning Robustness in Diabetic Retinopathy Tasks](https://mlsanity.com/paper/1912.10481/) (2019)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Mean](https://mlsanity.com/paper/2301.11862/) (2023)
- [Statistical Aspects of SHAP: Functional ANOVA for Model Interpretation](https://mlsanity.com/paper/2208.09970/) (2022)
- [Neural Decomposition: Functional ANOVA with Variational Autoencoders](https://mlsanity.com/paper/2006.14293/) (2020)
- [Masked Bayesian Neural Networks : Theoretical Guarantee and its Posterior Inference](https://mlsanity.com/paper/2305.14765/) (2023)
- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [Tensor Product Neural Networks for Functional ANOVA Model](https://mlsanity.com/paper/2502.15215/) (2025)
- [META-ANOVA: Screening interactions for interpretable machine learning](https://mlsanity.com/paper/2408.00973/) (2024)

## Abstract (arXiv)

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 prove that the posterior of Bayesian-TPNN is consistent.