  Spatiotemporal graph neural networks have shown to be effective in time
series forecasting applications, achieving better performance than standard
univariate predictors in several settings. These architectures take advantage
of a graph structure and relational inductive biases to learn a single (global)
inductive model to predict any number of the input time series, each associated
with a graph node. Despite the gain achieved in computational and data
efficiency w.r.t. fitting a set of local models, relying on a single global
model can be a limitation whenever some of the time series are generated by a
different spatiotemporal stochastic process. The main objective of this paper
is to understand the interplay between globality and locality in graph-based
spatiotemporal forecasting, while contextually proposing a methodological
framework to rationalize the practice of including trainable node embeddings in
such architectures. We ascribe to trainable node embeddings the role of
amortizing the learning of specialized components. Moreover, embeddings allow
for 1) effectively combining the advantages of shared message-passing layers
with node-specific parameters and 2) efficiently transferring the learned model
to new node sets. Supported by strong empirical evidence, we provide insights
and guidelines for specializing graph-based models to the dynamics of each time
series and show how this aspect plays a crucial role in obtaining accurate
predictions.
