Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input features, statistical inference and hypothesis testing of feature associations remain largely unexplored. We propose a permutation-based approach to testing that uses the partial derivatives of the network output with respect to specific inputs to assess both the significance of input features and whether significant features are linearly associated with the network output. These tests, which can be flexibly applied to a variety of network architectures, enhance the explanatory power of neural networks, and combined with powerful predictive capability, extend the applicability of these models.

翻译：神经网络是强大的预测模型，但它们在揭示预测变量与结果之间关系的本质方面提供的洞察有限。尽管已提出多种方法量化输入特征的相对贡献，但特征关联的统计推断与假设检验仍鲜有研究。我们提出了一种基于排列的检验方法，利用网络输出对特定输入的偏导数来评估输入特征的显著性，并检验显著特征是否与网络输出呈线性关联。这些检验可灵活应用于多种网络架构，增强了神经网络的解释能力，并结合其强大的预测性能，拓展了这些模型的适用性。