Kriging Convolutional Networks
This addresses spatial interpolation problems for domains like geostatistics, but it is incremental as it builds on existing GCN and Kriging techniques.
The paper tackles spatial interpolation by introducing Kriging Convolutional Networks (KCN), which combine Graph Convolutional Networks and Kriging to improve performance over traditional methods, showing empirical outperformance in several applications.
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.