  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.
