A Nonparametric Statistics Approach to Feature Selection in Deep Neural Networks with Theoretical Guarantees

• URL: http://arxiv.org/abs/2512.13565v1
• Date: Mon, 15 Dec 2025 17:22:49 GMT
• Title: A Nonparametric Statistics Approach to Feature Selection in Deep Neural Networks with Theoretical Guarantees
• Authors: Junye Du, Zhenghao Li, Zhutong Gu, Long Feng,
• Abstract summary: This paper tackles the problem of feature selection in a highly challenging setting: $mathbbE(y | boldsymbolx) = G(boldsymbolx_mathcalS_0)$.<n>Our approach begins with feature selection in deep neural networks, then generalizes the results to Hlder smooth functions by exploiting the strong approximation capabilities of neural networks.
• Score: 4.1091811628922486
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper tackles the problem of feature selection in a highly challenging setting: $\mathbb{E}(y | \boldsymbol{x}) = G(\boldsymbol{x}_{\mathcal{S}_0})$, where $\mathcal{S}_0$ is the set of relevant features and $G$ is an unknown, potentially nonlinear function subject to mild smoothness conditions. Our approach begins with feature selection in deep neural networks, then generalizes the results to H{ö}lder smooth functions by exploiting the strong approximation capabilities of neural networks. Unlike conventional optimization-based deep learning methods, we reformulate neural networks as index models and estimate $\mathcal{S}_0$ using the second-order Stein's formula. This gradient-descent-free strategy guarantees feature selection consistency with a sample size requirement of $n = Ω(p^2)$, where $p$ is the feature dimension. To handle high-dimensional scenarios, we further introduce a screening-and-selection mechanism that achieves nonlinear selection consistency when $n = Ω(s \log p)$, with $s$ representing the sparsity level. Additionally, we refit a neural network on the selected features for prediction and establish performance guarantees under a relaxed sparsity assumption. Extensive simulations and real-data analyses demonstrate the strong performance of our method even in the presence of complex feature interactions.

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