Abstract:Given an extensive, semi-infinite collection of multivariate coevolving data sequences (e.g., sensor/web activity streams) whose observations influence each other, how can we discover the time-changing cause-and-effect relationships in co-evolving data streams? How efficiently can we reveal dynamical patterns that allow us to forecast future values? In this paper, we present a novel streaming method, ModePlait, which is designed for modeling such causal relationships (i.e., time-evolving causality) in multivariate co-evolving data streams and forecasting their future values. The solution relies on characteristics of the causal relationships that evolve over time in accordance with the dynamic changes of exogenous variables. ModePlait has the following properties: (a) Effective: it discovers the time-evolving causality in multivariate co-evolving data streams by detecting the transitions of distinct dynamical patterns adaptively. (b) Accurate: it enables both the discovery of time-evolving causality and the forecasting of future values in a streaming fashion. (c) Scalable: our algorithm does not depend on data stream length and thus is applicable to very large sequences. Extensive experiments on both synthetic and real-world datasets demonstrate that our proposed model outperforms state-of-the-art methods in terms of discovering the time-evolving causality as well as forecasting.
Abstract:We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms that incorporate long-term temporal dependencies are largely absent from existing studies. In this paper, we introduce a latent state to allow time-dependent modeling and formulate this problem as a dynamics estimation problem in latent states. We face multiple technical challenges, including (1) modeling latent non-linear dynamics and (2) solving circular dependencies caused by the presence of latent states. To tackle these challenging problems, we propose a new method, Latent Non-Linear equation modeling (LaNoLem), that can model a latent non-linear dynamical system and a novel alternating minimization algorithm for effectively estimating latent states and model parameters. In addition, we introduce criteria to control model complexity without human intervention. Compared with the state-of-the-art model, LaNoLem achieves competitive performance for estimating dynamics while outperforming other methods in prediction.