We propose a neural network model for contextual regression in which the regression model depends on contextual features that determine the active submodel and an algorithm to fit the model. The proposed simple contextual neural network (SCtxtNN) separates context identification from context-specific regression, resulting in a structured and interpretable architecture with fewer parameters than a fully connected feed-forward network. We show mathematically that the proposed architecture is sufficient to represent contextual linear regression models using only standard neural network components. Numerical experiments are provided to support the theoretical result, showing that the proposed model achieves lower excess mean squared error and more stable performance than feed-forward neural networks with comparable numbers of parameters, while larger networks improve accuracy only at the cost of increased complexity. The results suggest that incorporating contextual structure can improve model efficiency while preserving interpretability.

翻译：我们提出了一种用于上下文回归的神经网络模型，其中回归模型依赖于决定活跃子模型的上下文特征，并设计了一种拟合该模型的算法。所提出的简单上下文神经网络通过将上下文识别与特定上下文回归分离，形成了一种结构化且可解释的架构，其参数量少于全连接前馈网络。我们从数学上证明，该架构仅需使用标准神经网络组件即可充分表示上下文线性回归模型。通过数值实验验证了理论结果，表明与具有可比参数量的前馈神经网络相比，所提模型实现了更低的超额均方误差和更稳定的性能，而更大的网络虽能提升精度，但代价是复杂度增加。结果表明，融合上下文结构可以在保持可解释性的同时提升模型效率。