# Full Bayesian Significance Testing for Neural Networks

arXiv: https://arxiv.org/abs/2401.13335 · HTML: https://mlsanity.com/paper/2401.13335/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 90 references that are in the map.
- First posted on arXiv 24 Jan 2024.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Learning Traffic as Images: A Deep Convolutional Neural Network for Large-Scale Transportation Network Speed Prediction](https://mlsanity.com/paper/1701.04245/) (2017)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semantics](https://mlsanity.com/paper/2211.09510/) (2022)
- [Investigating the influence of noise and distractors on the interpretation of neural networks](https://mlsanity.com/paper/1611.07270/) (2016)
- [Coupled Layer-wise Graph Convolution for Transportation Demand Prediction](https://mlsanity.com/paper/2012.08080/) (2020)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)

## Built on by (most cited first, 8 of 8)

- [BIGCity: A Universal Spatiotemporal Model for Unified Trajectory and Traffic State Data Analysis](https://mlsanity.com/paper/2412.00953/) (2024)
- [Learning Universal Multi-level Market Irrationality Factors to Improve Stock Return Forecasting](https://mlsanity.com/paper/2502.04737/) (2025)
- [Learnable Sparse Customization in Heterogeneous Edge Computing](https://mlsanity.com/paper/2412.07216/) (2024)
- [Simple and Efficient Heterogeneous Temporal Graph Neural Network](https://mlsanity.com/paper/2510.18467/) (2025)
- [ICAD-LLM: One-for-All Anomaly Detection via In-Context Learning with Large Language Models](https://mlsanity.com/paper/2512.01672/) (2025)
- [HieraMix: A Hierarchical MLP-Mixer for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2512.07854/) (2025)
- [ProDiff: Prototype-Guided Diffusion for Minimal Information Trajectory Imputation](https://mlsanity.com/paper/2505.23048/) (2025)
- [RoSA: Enhancing Parameter-Efficient Fine-Tuning via RoPE-aware Selective Adaptation in Large Language Models](https://mlsanity.com/paper/2511.21733/) (2025)

## Abstract (arXiv)

Significance testing aims to determine whether a proposition about the population distribution is the truth or not given observations. However, traditional significance testing often needs to derive the distribution of the testing statistic, failing to deal with complex nonlinear relationships. In this paper, we propose to conduct Full Bayesian Significance Testing for neural networks, called textitnFBST, to overcome the limitation in relationship characterization of traditional approaches. A Bayesian neural network is utilized to fit the nonlinear and multi-dimensional relationships with small errors and avoid hard theoretical derivation by computing the evidence value. Besides, textitnFBST can test not only global significance but also local and instance-wise significance, which previous testing methods don't focus on. Moreover, textitnFBST is a general framework that can be extended based on the measures selected, such as Grad-textitnFBST, LRP-textitnFBST, DeepLIFT-textitnFBST, LIME-textitnFBST. A range of experiments on both simulated and real data are conducted to show the advantages of our method.