  Deep probabilistic forecasting techniques have recently been proposed for
modeling large collections of time-series. However, these techniques explicitly
assume either complete independence (local model) or complete dependence
(global model) between time-series in the collection. This corresponds to the
two extreme cases where every time-series is disconnected from every other
time-series in the collection or likewise, that every time-series is related to
every other time-series resulting in a completely connected graph. In this
work, we propose a deep hybrid probabilistic graph-based forecasting framework
called Graph Deep Factors (GraphDF) that goes beyond these two extremes by
allowing nodes and their time-series to be connected to others in an arbitrary
fashion. GraphDF is a hybrid forecasting framework that consists of a
relational global and relational local model. In particular, we propose a
relational global model that learns complex non-linear time-series patterns
globally using the structure of the graph to improve both forecasting accuracy
and computational efficiency. Similarly, instead of modeling every time-series
independently, we learn a relational local model that not only considers its
individual time-series but also the time-series of nodes that are connected in
the graph. The experiments demonstrate the effectiveness of the proposed deep
hybrid graph-based forecasting model compared to the state-of-the-art methods
in terms of its forecasting accuracy, runtime, and scalability. Our case study
reveals that GraphDF can successfully generate cloud usage forecasts and
opportunistically schedule workloads to increase cloud cluster utilization by
47.5% on average.
