# Learning Global Pairwise Interactions with Bayesian Neural Networks

arXiv: https://arxiv.org/abs/1901.08361 · HTML: https://mlsanity.com/paper/1901.08361/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Toward Explainable AI for Regression Models](https://mlsanity.com/paper/2112.11407/) (2021)
- [Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces](https://mlsanity.com/paper/2212.14855/) (2022)
- [SmoothHess: ReLU Network Feature Interactions via Stein's Lemma](https://mlsanity.com/paper/2311.00858/) (2023)
- [DeepROCK: Error-controlled interaction detection in deep neural networks](https://mlsanity.com/paper/2309.15319/) (2023)
- [Relate and Predict: Structure-Aware Prediction with Jointly Optimized Neural DAG](https://mlsanity.com/paper/2103.02405/) (2021)
- [Error-controlled non-additive interaction discovery in machine learning models](https://mlsanity.com/paper/2408.17016/) (2024)

## Abstract (arXiv)

Estimating global pairwise interaction effects, i.e., the difference between the joint effect and the sum of marginal effects of two input features, with uncertainty properly quantified, is centrally important in science applications. We propose a non-parametric probabilistic method for detecting interaction effects of unknown form. First, the relationship between the features and the output is modelled using a Bayesian neural network, capable of representing complex interactions and principled uncertainty. Second, interaction effects and their uncertainty are estimated from the trained model. For the second step, we propose an intuitive global interaction measure: Bayesian Group Expected Hessian (GEH), which aggregates information of local interactions as captured by the Hessian. GEH provides a natural trade-off between type I and type II error and, moreover, comes with theoretical guarantees ensuring that the estimated interaction effects and their uncertainty can be improved by training a more accurate BNN. The method empirically outperforms available non-probabilistic alternatives on simulated and real-world data. Finally, we demonstrate its ability to detect interpretable interactions between higher-level features (at deeper layers of the neural network).