  Time series prediction is a widespread and well studied problem with
applications in many domains (medical, geoscience, network analysis, finance,
econometry etc.). In the case of multivariate time series, the key to good
performances is to properly capture the dependencies between the variates.
Often, these variates are structured, i.e. they are localised in an abstract
space, usually representing an aspect of the physical world, and prediction
amounts to a form of diffusion of the information across that space over time.
Several neural network models of diffusion have been proposed in the
literature. However, most of the existing proposals rely on some a priori
knowledge on the structure of the space, usually in the form of a graph
weighing the pairwise diffusion capacity of its points. We argue that this
piece of information can often be dispensed with, since data already contains
the diffusion capacity information, and in a more reliable form than that
obtained from the usually largely hand-crafted graphs. We propose instead a
fully data-driven model which does not rely on such a graph, nor any other
prior structural information. We conduct a first set of experiments to measure
the impact on performance of a structural prior, as used in baseline models,
and show that, except at very low data levels, it remains negligible, and
beyond a threshold, it may even become detrimental. We then investigate,
through a second set of experiments, the capacity of our model in two respects:
treatment of missing data and domain adaptation.
