# Statistical Deep Learning for Spatial and Spatio-Temporal Data

arXiv: https://arxiv.org/abs/2206.02218 · HTML: https://mlsanity.com/paper/2206.02218/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 127 references that are in the map.
- First posted on arXiv 5 Jun 2022.

## Builds on (most cited first, 30 of 64)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [CNN-RNN: A Unified Framework for Multi-label Image Classification](https://mlsanity.com/paper/1604.04573/) (2016)
- [Multiagent Cooperation and Competition with Deep Reinforcement Learning](https://mlsanity.com/paper/1511.08779/) (2015)
- [Action-Conditional Video Prediction using Deep Networks in Atari Games](https://mlsanity.com/paper/1507.08750/) (2015)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Normalizing Flows on Tori and Spheres](https://mlsanity.com/paper/2002.02428/) (2020)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting](https://mlsanity.com/paper/1905.10069/) (2019)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Reinforcement Learning for Autonomous Driving with Latent State Inference and Spatial-Temporal Relationships](https://mlsanity.com/paper/2011.04251/) (2020)
- [Avoiding pathologies in very deep networks](https://mlsanity.com/paper/1402.5836/) (2014)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [A Selective Overview of Deep Learning](https://mlsanity.com/paper/1904.05526/) (2019)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)

## Built on by (most cited first, 15 of 15)

- [Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting](https://mlsanity.com/paper/2306.11472/) (2023)
- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Neural Spatiotemporal Point Processes: Trends and Challenges](https://mlsanity.com/paper/2502.09341/) (2025)
- [Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting](https://mlsanity.com/paper/2507.03855/) (2025)
- [Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields](https://mlsanity.com/paper/2307.08038/) (2023)
- [Modelling wildland fire burn severity in California using a spatial Super Learner approach](https://mlsanity.com/paper/2311.16187/) (2023)
- [Fusing Climate Data Products using a Spatially Varying Autoencoder](https://mlsanity.com/paper/2403.07822/) (2024)
- [Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems](https://mlsanity.com/paper/2306.08445/) (2023)
- [Pedestrian Volume Prediction Using a Diffusion Convolutional Gated Recurrent Unit Model](https://mlsanity.com/paper/2411.03360/) (2024)
- [A Subsampling Based Neural Network for Spatial Data](https://mlsanity.com/paper/2411.03620/) (2024)
- [Spatio-temporal Prediction of Fine-Grained Origin-Destination Matrices with Applications in Ridesharing](https://mlsanity.com/paper/2503.24237/) (2025)
- [Spatial Adapter: Structured Spatial Decomposition and Closed-Form Covariance for Frozen Predictors](https://mlsanity.com/paper/2605.11394/) (2026)
- [TSCoNet: A Two-Stage Copula CNN-LSTM for Uncertainty-Aware Spatio-Temporal Forecasting](https://mlsanity.com/paper/2607.10410/) (2026)

## Abstract (arXiv)

Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.