# Graph Neural Processes for Spatio-Temporal Extrapolation

arXiv: https://arxiv.org/abs/2305.18719 · HTML: https://mlsanity.com/paper/2305.18719/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [Sequential Neural Processes](https://mlsanity.com/paper/1906.10264/) (2019)
- [Bike Flow Prediction with Multi-Graph Convolutional Networks](https://mlsanity.com/paper/1807.10934/) (2018)
- [UrbanFM: Inferring Fine-Grained Urban Flows](https://mlsanity.com/paper/1902.05377/) (2019)
- [Conditional Local Convolution for Spatio-temporal Meteorological Forecasting](https://mlsanity.com/paper/2101.01000/) (2021)
- [STCN: Stochastic Temporal Convolutional Networks](https://mlsanity.com/paper/1902.06568/) (2019)
- [Neural Processes with Stochastic Attention: Paying more attention to the context dataset](https://mlsanity.com/paper/2204.05449/) (2022)
- [Recurrent Attentive Neural Process for Sequential Data](https://mlsanity.com/paper/1910.09323/) (2019)
- [Robustifying Sequential Neural Processes](https://mlsanity.com/paper/2006.15987/) (2020)
- [Decoupling Long- and Short-Term Patterns in Spatiotemporal Inference](https://mlsanity.com/paper/2109.09506/) (2021)
- [Predicting Urban Water Quality with Ubiquitous Data](https://mlsanity.com/paper/1610.09462/) (2016)

## Built on by (most cited first, 19 of 19)

- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [Spatio-Temporal Field Neural Networks for Air Quality Inference](https://mlsanity.com/paper/2403.02354/) (2024)
- [Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations](https://mlsanity.com/paper/2402.12598/) (2024)
- [Geometry-aware Active Learning of Spatiotemporal Dynamic Systems](https://mlsanity.com/paper/2504.19012/) (2025)
- [AirRadar: Inferring Nationwide Air Quality in China with Deep Neural Networks](https://mlsanity.com/paper/2501.13141/) (2025)
- [Robust Traffic Forecasting against Spatial Shift over Years](https://mlsanity.com/paper/2410.00373/) (2024)
- [Space to Policy: Scalable Brick Kiln Detection and Automatic Compliance Monitoring with Geospatial Data](https://mlsanity.com/paper/2412.04065/) (2024)
- [Scalable Spatiotemporal Inference with Biased Scan Attention Transformer Neural Processes](https://mlsanity.com/paper/2506.09163/) (2025)
- [Generalising Traffic Forecasting to Regions without Traffic Observations](https://mlsanity.com/paper/2508.08947/) (2025)
- [AnchorGK: Anchor-based Incremental and Stratified Graph Learning Framework for Inductive Spatio-Temporal Kriging](https://mlsanity.com/paper/2512.21569/) (2025)
- [ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion](https://mlsanity.com/paper/2609.37078/) (2026)
- [Spatio-Temporal Partial Sensing Forecast for Long-term Traffic](https://mlsanity.com/paper/2408.02689/) (2024)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [Inductive Spatio-Temporal Kriging with Physics-Guided Increment Training Strategy for Air Quality Inference](https://mlsanity.com/paper/2503.09646/) (2025)
- [DIFFUMA: High-Fidelity Spatio-Temporal Video Prediction via Dual-Path Mamba and Diffusion Enhancement](https://mlsanity.com/paper/2507.06738/) (2025)
- [Neural Bridge Processes](https://mlsanity.com/paper/2508.07220/) (2025)
- [Spatio-temporal Multivariate Time Series Forecast with Chosen Variables](https://mlsanity.com/paper/2510.24027/) (2025)
- [Amortized Counterfactual Prediction with Graph Neural Networks](https://mlsanity.com/paper/2610.13724/) (2026)

## Abstract (arXiv)

We study the task of spatio-temporal extrapolation that generates data at target locations from surrounding contexts in a graph. This task is crucial as sensors that collect data are sparsely deployed, resulting in a lack of fine-grained information due to high deployment and maintenance costs. Existing methods either use learning-based models like Neural Networks or statistical approaches like Gaussian Processes for this task. However, the former lacks uncertainty estimates and the latter fails to capture complex spatial and temporal correlations effectively. To address these issues, we propose Spatio-Temporal Graph Neural Processes (STGNP), a neural latent variable model which commands these capabilities simultaneously. Specifically, we first learn deterministic spatio-temporal representations by stacking layers of causal convolutions and cross-set graph neural networks. Then, we learn latent variables for target locations through vertical latent state transitions along layers and obtain extrapolations. Importantly during the transitions, we propose Graph Bayesian Aggregation (GBA), a Bayesian graph aggregator that aggregates contexts considering uncertainties in context data and graph structure. Extensive experiments show that STGNP has desirable properties such as uncertainty estimates and strong learning capabilities, and achieves state-of-the-art results by a clear margin.