We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an end-to-end manner. By penalizing both gating parameters and redundant layers, NNMR yields sparse and interpretable architectures while capturing complex nonlinear relationships driven by high-order synergistic effects. We further develop a post-selection inference procedure based on split-sample, permutation-based hypothesis testing, enabling valid inference without restrictive parametric assumptions. Compared with existing methods, including Bayesian kernel machine regression and widely used post hoc attribution techniques, NNMR scales efficiently to high-dimensional feature spaces while rigorously controlling type I error. Simulation studies demonstrate its superior selection accuracy and inference reliability. Finally, an empirical application reveals sparse, biologically meaningful food group predictors associated with somatic growth among adolescents living in Mexico City.

翻译：我们提出了一种新的神经网络框架，称为神经网络机器回归（NNMR），该框架集成了可训练的输入门控机制和自适应深度正则化，以端到端的方式联合执行特征选择与函数估计。通过对门控参数和冗余层同时施加惩罚，NNMR能够在捕捉由高阶协同效应驱动的复杂非线性关系的同时，产生稀疏且可解释的网络架构。我们进一步开发了一种基于样本分割和置换假设检验的后选择推断程序，使得在无需严格参数假设的条件下仍能进行有效推断。与现有方法（包括贝叶斯核机器回归和广泛使用的后验归因技术）相比，NNMR能够高效扩展到高维特征空间，同时严格控制第一类错误。模拟研究证明了其优越的选择准确性和推断可靠性。最后，一项实证应用揭示了与墨西哥城青少年体格生长相关的、稀疏且具有生物学意义的食物组预测因子。