mlsanityData to 13 Oct 2026

Significance Tests for Neural Networks

arXiv 1902.06021 ↗First posted 16 Feb 2019math.ST cs.LG stat.MLcited by 17

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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.

Key facts. Cited by 17 papers in the map (data through 13 Oct 2026). First posted on arXiv 16 Feb 2019.

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Citing papers per year: 2021: 3; 2022: 6; 2023: 2; 2024: 3; 2025: 3.

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  1. 2021On the Computational Intelligibility of Boolean Classifierscited by 40
  2. 2023Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Meancited by 18
  3. 2022Monotonic Neural Additive Models: Pursuing Regulated Machine Learning Models for Credit Scoringcited by 12
  4. 2024Full Bayesian Significance Testing for Neural Networkscited by 8
  5. 2021Statistical inference for generative adversarial networks and other minimax problemscited by 3
  6. 2025Towards Unified Attribution in Explainable AI, Data-Centric AI, and Mechanistic Interpretabilitycited by 3
  7. 2022Generalized Groves of Neural Additive Models: Pursuing transparent and accurate machine learning models in financecited by 2
  8. 2022Interpretable Selective Learning in Credit Riskcited by 2
  9. 2022Deep Partial Least Squares for Empirical Asset Pricingcited by 1
  10. 2022A Sieve Quasi-likelihood Ratio Test for Neural Networks with Applications to Genetic Association Studiescited by 1
  11. 2023Can I Trust the Explanations? Investigating Explainable Machine Learning Methods for Monotonic Modelscited by 1
  12. 2024Attribution Methods in Asset Pricing: Do They Account for Risk?cited by 1
5 more
  1. 2021An Interpretable Neural Network for Parameter Inferencecited by 0
  2. 2022Consistency of Neural Networks with Regularizationcited by 0
  3. 2024Statistical tuning of artificial neural networkcited by 0
  4. 2025Scale-Insensitive Neural Network Significance Testscited by 0
  5. 2025The Morgan-Pitman Test of Equality of Variances and its Application to Machine Learning Model Evaluation and Selectioncited by 0