Graph Deep Factors for Probabilistic Time-series Forecasting

Deep probabilistic forecasting techniques can model large collections of time-series. However, recent 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 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, a relational global model 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, a relational local model 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. Furthermore, we target addressing the common nature of many time-series forecasting applications where time-series are provided in a streaming version, however, most methods fail to leverage the newly incoming time-series values and result in worse performance over time. In this paper, we propose an online incremental learning framework for probabilistic forecasting. The framework is theoretically proven to have lower time and space complexity. The framework can be universally applied to many other machine learning-based methods.