  Modeling multivariate time series as temporal signals over a (possibly
dynamic) graph is an effective representational framework that allows for
developing models for time series analysis. In fact, discrete sequences of
graphs can be processed by autoregressive graph neural networks to recursively
learn representations at each discrete point in time and space. Spatiotemporal
graphs are often highly sparse, with time series characterized by multiple,
concurrent, and long sequences of missing data, e.g., due to the unreliable
underlying sensor network. In this context, autoregressive models can be
brittle and exhibit unstable learning dynamics. The objective of this paper is,
then, to tackle the problem of learning effective models to reconstruct, i.e.,
impute, missing data points by conditioning the reconstruction only on the
available observations. In particular, we propose a novel class of
attention-based architectures that, given a set of highly sparse discrete
observations, learn a representation for points in time and space by exploiting
a spatiotemporal propagation architecture aligned with the imputation task.
Representations are trained end-to-end to reconstruct observations w.r.t. the
corresponding sensor and its neighboring nodes. Compared to the state of the
art, our model handles sparse data without propagating prediction errors or
requiring a bidirectional model to encode forward and backward time
dependencies. Empirical results on representative benchmarks show the
effectiveness of the proposed method.
