We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these dependencies through a structured latent dynamical component, while a decoder predicts the observations from the latent representations. We consider several variants of this model, corresponding to different prior hypothesis about the spatial relations between the series. The model is evaluated and compared to state-of-the-art baselines, on a variety of forecasting problems representative of different application areas: epidemiology, geo-spatial statistics and car-traffic prediction. Besides these evaluations, we also describe experiments showing the ability of this approach to extract relevant spatial relations.
The classical topic of time series modeling and forecasting has given rise to an extensive literature, both in statistics and machine learning. In statistics, classical linear models are based on auto-regressive and moving average components. Most assume linear and stationary time dependencies with a noise component @cite_25 . In machine learning, non linear extensions of these models based on neural networks were proposed as early as the nineties, opening the way to many other non linear models developed both in statistics and ML, like kernel methods @cite_0 for instance.
@cite_0 @cite_25
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A sheet material having a decorative surface and a working surface, for application to a support surface is disclosed, the working surface of which is provided with a continuous coating of tacky, pressure-sensitive, adhesive, which adhesive is provided with a coating of a discontinuous layer of resilient, non-adhesive particles. The coating of particles have the ability to be deformed under a load and thus, upon application to a support surface, deform, under pressure, to such an extent as to bring the adhesive and the surface into fuller contact. Abstract We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters ( Journal of Forecasting 1982–1985 and International Journal of Forecasting 1985–2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.