Simona Maria Cabuz

• Numerous real world systems of major interest are modeled as sets of analog continuous stochastic processes with delayed and varying causal relationships. Yet, studying their dynamics becomes often difficult, as it involves sensing, understanding and predicting a system of inter-dependent random variables in a given context and over time. In the present work we develop a systematic, rigorous and efficient framework to structurally characterize and forecast the future states of such systems in a scalable manner. In particular we use an improved maximum spanning tree method to capture the causal dependence structure based on directed information theory. To this end we address the sparsity problem in information causality estimation in general, and directed information in particular and propose a new method that identifies and eliminates redundant calculations. To predict the behavior of child nodes based on their inferred causal parents we use a linear model aiming to capture the closest approximation of functional relations. Further dependencies are accounted for using causal conditional information and potential links that improve child nodes estimation are added. The result is a comprehensive and scalable approach to understanding and predicting large sets of inter-dependent narrowband processes, as we demonstrate on several synthetic datasets.