Semiparametric Regression for Spatial Data via Deep Learning
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Abstract (arXiv)
In this work, we propose a deep learning-based method to perform semiparametric regression analysis for spatially dependent data. To be specific, we use a sparsely connected deep neural network with rectified linear unit (ReLU) activation function to estimate the unknown regression function that describes the relationship between response and covariates in the presence of spatial dependence. Under some mild conditions, the estimator is proven to be consistent, and the rate of convergence is determined by three factors: (1) the architecture of neural network class, (2) the smoothness and (intrinsic) dimension of true mean function, and (3) the magnitude of spatial dependence. Our method can handle well large data set owing to the stochastic gradient descent optimization algorithm. Simulation studies on synthetic data are conducted to assess the finite sample performance, the results of which indicate that the proposed method is capable of picking up the intricate relationship between response and covariates. Finally, a real data analysis is provided to demonstrate the validity and effectiveness of the proposed method.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 20 of its 50 references that are in the map. First posted on arXiv 10 Jan 2023.
Builds on
20 of 50 references.
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Citing papers per year: 2023: 1; 2024: 0; 2025: 0; 2026: 1.
2 papers.