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Discovering temporal lagged and inter-dependencies in multivariate time series data is an important task. However, in many realworld applications, such as commercial cloud management, manufacturing predictive maintenance, and portfolios performance analysis, such dependencies can be non-linear and time-variant, which makes it more challenging to extract such dependencies through traditional methods such as Granger causality or clustering. In this work, we present a novel deep learning model that uses multiple layers of customized gated recurrent units (GRUs) for discovering both time lagged behaviors as well as inter-timeseries dependencies in the form of directed weighted graphs. We introduce a key component of Dual-purpose recurrent neural network that decodes information in the temporal domain to discover lagged dependencies within each time series, and encodes them into a set of vectors which, collected from all component time series, form the informative inputs to discover inter-dependencies. Though the discovery of two types of dependencies are separated at different hierarchical levels, they are tightly connected and jointly trained in an end-to-end manner. With this joint training, learning of one type of dependency immediately impacts the learning of the other one, leading to overall accurate dependencies discovery. We empirically test our model on synthetic time series data in which the exact form of (non-linear) dependencies is known. We also evaluate its performance on two real-world applications, (i) performance monitoring data from a commercial cloud provider, which exhibit highly dynamic, non-linear, and volatile behavior and, (ii) sensor data from a manufacturing plant. We further show how our approach is able to capture these dependency behaviors via intuitive and interpretable dependency graphs and use them to generate highly accurate forecasts.

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In many real-world applications, data is represented in the form of networks with structures and attributes changing over time. The dynamic changes not only happen at nodes/edges, forming local subnetwork processes, but also eventually influence global states of networks. The need to understand what these local network processes are, how they evolve and consequently govern the progression of global network states has become increasingly important. In this paper, we explore these questions and develop a novel algorithm for mining a succinct set of subnetworks that are predictive and evolve along with the progression of global network states. Our algorithm is designed in the framework of logistic regression that fits a model for multi-states of network samples. Its objective function considers both the spatial network topology and temporal smooth transition between adjacent global network states, and we show that its global optimum solution can be achieved via steepest descent. Extensive experimental analysis on both synthetic and real world datasets demonstrates the effectiveness of our algorithm against competing methods, not only in the prediction accuracy but also in terms of domain relevance of the discovered subnetworks.