# Significance Tests for Neural Networks

arXiv: https://arxiv.org/abs/1902.06021 · HTML: https://mlsanity.com/paper/1902.06021/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2019.

## Built on by (most cited first, 17 of 17)

- [On the Computational Intelligibility of Boolean Classifiers](https://mlsanity.com/paper/2104.06172/) (2021)
- [Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Mean](https://mlsanity.com/paper/2301.11862/) (2023)
- [Monotonic Neural Additive Models: Pursuing Regulated Machine Learning Models for Credit Scoring](https://mlsanity.com/paper/2209.10070/) (2022)
- [Full Bayesian Significance Testing for Neural Networks](https://mlsanity.com/paper/2401.13335/) (2024)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Towards Unified Attribution in Explainable AI, Data-Centric AI, and Mechanistic Interpretability](https://mlsanity.com/paper/2501.18887/) (2025)
- [Generalized Groves of Neural Additive Models: Pursuing transparent and accurate machine learning models in finance](https://mlsanity.com/paper/2209.10082/) (2022)
- [Interpretable Selective Learning in Credit Risk](https://mlsanity.com/paper/2209.10127/) (2022)
- [Deep Partial Least Squares for Empirical Asset Pricing](https://mlsanity.com/paper/2206.10014/) (2022)
- [A Sieve Quasi-likelihood Ratio Test for Neural Networks with Applications to Genetic Association Studies](https://mlsanity.com/paper/2212.08255/) (2022)
- [Can I Trust the Explanations? Investigating Explainable Machine Learning Methods for Monotonic Models](https://mlsanity.com/paper/2309.13246/) (2023)
- [Attribution Methods in Asset Pricing: Do They Account for Risk?](https://mlsanity.com/paper/2407.08953/) (2024)
- [An Interpretable Neural Network for Parameter Inference](https://mlsanity.com/paper/2106.05536/) (2021)
- [Consistency of Neural Networks with Regularization](https://mlsanity.com/paper/2207.01538/) (2022)
- [Statistical tuning of artificial neural network](https://mlsanity.com/paper/2409.16426/) (2024)
- [Scale-Insensitive Neural Network Significance Tests](https://mlsanity.com/paper/2501.15753/) (2025)
- [The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selection](https://mlsanity.com/paper/2509.12185/) (2025)

## Abstract (arXiv)

We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using nonparametric techniques. Under technical conditions, the limiting distribution is given by a mixture of chi-square distributions. The tests enable one to discern the impact of individual variables on the prediction of a neural network. The test statistic can be used to rank variables according to their influence. Simulation results illustrate the computational efficiency and the performance of the test. An empirical application to house price valuation highlights the behavior of the test using actual data.