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Time series prediction is a widespread and well studied problem withapplications in many domains (medical, geoscience, network analysis, finance,econometry etc.). In the case of multivariate time series, the key to goodperformances is to properly capture the dependencies between the variates.Often, these variates are structured, i.e. they are localised in an abstractspace, usually representing an aspect of the physical world, and predictionamounts to a form of diffusion of the information across that space over time.Several neural network models of diffusion have been proposed in theliterature. However, most of the existing proposals rely on some a prioriknowledge on the structure of the space, usually in the form of a graphweighing the pairwise diffusion capacity of its points. We argue that thispiece of information can often be dispensed with, since data already containsthe diffusion capacity information, and in a more reliable form than thatobtained from the usually largely hand-crafted graphs. We propose instead afully data-driven model which does not rely on such a graph, nor any otherprior structural information. We conduct a first set of experiments to measurethe impact on performance of a structural prior, as used in baseline models,and show that, except at very low data levels, it remains negligible, andbeyond 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.

Structured Time Series Prediction without Structural Prior