用密集ReLU网络建模时空依赖，提升预测精度与理论可靠性。
Dense ReLU Neural Networks for Temporal-spatial Model
- 基于ReLU的全连接网络，显式处理时间与空间依赖性。
- 在高维数据上通过流形建模降低维度，克服维数灾难。
- 适用于具有短程依赖的数据，适合复杂函数类的时空建模。
本文研究使用修正线性单元（ReLU）激活函数的全连接深度神经网络，用于非参数估计。我们推导出非渐近界，得到收敛速率，同时考虑观测数据中时间与空间的依赖性。通过建模跨时间和空间的依赖关系，所提模型更真实反映现实数据的复杂结构，提升预测性能与理论稳健性。为应对维数灾难，我们基于流形对数据建模，探索高维数据的内在维度。本工作拓展了现有时空分析的理论框架，将其推广至更一般情形下的神经网络，并证明所用证明技术对具有短程依赖的模型有效。通过多种合成响应函数的实验仿真，验证了该方法优于现有文献中的经典方法。结果表明，密集神经网络在广泛函数类上的时空建模中具备强大能力。
原文摘要 · Abstract (English)
In this paper, we focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both temporal and spatial dependence in the observed measurements. By accounting for dependencies across time and space, our models better reflect the complexities of real-world data, enhancing both predictive performance and theoretical robustness. We also tackle the curse of dimensionality by modeling the data on a manifold, exploring the intrinsic dimensionality of high-dimensional data. We broaden existing theoretical findings of temporal-spatial analysis by applying them to neural networks in more general contexts and demonstrate that our proof techniques are effective for models with short-range dependence. Our empirical simulations across various synthetic response functions underscore the superior performance of our method, outperforming established approaches in the existing literature. These findings provide valuable insights into the strong capabilities of dense neural networks (Dense NN) for temporal-spatial modeling across a broad range of function classes.
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