Graph-based Forecasting with Missing Data through Spatiotemporal
  Downsampling
Ivan Marisca Cesare Alippi Filippo Maria Bianchi
Given a set of synchronous time series, each associated with a sensor-point
in space and characterized by inter-series relationships, the problem of
spatiotemporal forecasting consists of predicting future observations for each
point. Spatiotemporal graph neural networks achieve striking results by
representing the relationships across time series as a graph. Nonetheless, most
existing methods rely on the often unrealistic assumption that inputs are
always available and fail to capture hidden spatiotemporal dynamics when part
of the data is missing. In this work, we tackle this problem through
hierarchical spatiotemporal downsampling. The input time series are
progressively coarsened over time and space, obtaining a pool of
representations that capture heterogeneous temporal and spatial dynamics.
Conditioned on observations and missing data patterns, such representations are
combined by an interpretable attention mechanism to generate the forecasts. Our
approach outperforms state-of-the-art methods on synthetic and real-world
benchmarks under different missing data distributions, particularly in the
presence of contiguous blocks of missing values.