Kriging Convolutional Networks

Abstract

Spatial interpolation is a class of estimation problems where locations with known values are used to estimate values at other locations, with an emphasis on harnessing spatial locality and trends. Traditional Kriging methods have strong Gaussian assumptions, and as a result, often fail to capture complexities within the data. Inspired by the recent progress of graph neural networks, we introduce Kriging Convolutional Networks (KCN), a method of combining the advantages of Graph Convolutional Networks (GCN) and Kriging. Compared to standard GCNs, KCNs make direct use of neighboring observations when generating predictions. KCNs also contain the Kriging method as a specific configuration. We further improve the model's performance by adding attention. Empirically, we show that this model outperforms GCNs and Kriging in several applications. The implementation of KCN using PyTorch is publicized at the GitHub repository: https://github.com/tufts-ml/kcn-torch.

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• Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting
• Inductive Representation Learning on Large Graphs
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• Graph Neural Processes for Spatio-Temporal Extrapolation
• MoGERNN: An Inductive Traffic Predictor for Unobserved Locations
• Joint Estimation and Prediction of City-wide Delivery Demand: A Large Language Model Empowered Graph-based Learning Approach
• Inductive Graph Neural Networks for Spatiotemporal Kriging
• Decoupling Long- and Short-Term Patterns in Spatiotemporal Inference
• Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging
• Positional Encoder Graph Neural Networks for Geographic Data
• SSIN: Self-Supervised Learning for Rainfall Spatial Interpolation
• STA-GANN: A Valid and Generalizable Spatio-Temporal Kriging Approach