# Semiparametric Regression for Spatial Data via Deep Learning

arXiv: https://arxiv.org/abs/2301.03747 · HTML: https://mlsanity.com/paper/2301.03747/

## 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 (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Deep Network Approximation for Smooth Functions](https://mlsanity.com/paper/2001.03040/) (2020)
- [Drug discovery with explainable artificial intelligence](https://mlsanity.com/paper/2007.00523/) (2020)
- [Group Sparse Regularization for Deep Neural Networks](https://mlsanity.com/paper/1607.00485/) (2016)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Deep Compositional Spatial Models](https://mlsanity.com/paper/1906.02840/) (2019)
- [Deep Integro-Difference Equation Models for Spatio-Temporal Forecasting](https://mlsanity.com/paper/1910.13524/) (2019)
- [On the rate of convergence of fully connected very deep neural network regression estimates](https://mlsanity.com/paper/1908.11133/) (2019)
- [On Deep Instrumental Variables Estimate](https://mlsanity.com/paper/2004.14954/) (2020)
- [Optimal Nonparametric Inference via Deep Neural Network](https://mlsanity.com/paper/1902.01687/) (2019)
- [Calibrating multi-dimensional complex ODE from noisy data via deep neural networks](https://mlsanity.com/paper/2106.03591/) (2021)
- [Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networks](https://mlsanity.com/paper/2204.01682/) (2022)
- [Deep Neural Network Classifier for Multi-dimensional Functional Data](https://mlsanity.com/paper/2205.08592/) (2022)
- [Online Statistical Inference for Parameters Estimation with Linear-Equality Constraints](https://mlsanity.com/paper/2105.10315/) (2021)
- [Variable selection for nonlinear Cox regression model via deep learning](https://mlsanity.com/paper/2211.09287/) (2022)
- [Scalable Semiparametric Spatio-temporal Regression for Large Data Analysis](https://mlsanity.com/paper/2111.15086/) (2021)

## Built on by (most cited first, 2 of 2)

- [Deep Learning for Efficient GWAS Feature Selection](https://mlsanity.com/paper/2312.15055/) (2023)
- [A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment](https://mlsanity.com/paper/2608.14968/) (2026)

## 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.