Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach

E consider a stationary discrete-time vector process or time series. Such a process could model, e.g., the time evolution of air pollutant concentrations [1], [2] or medical diagnostic data obtained in electrocorticography (ECoG) [3]. One specific way of representing the dependence structure of a vector process is via a graphical model [4], where the nodes of the graph represent the individual scalar process components, and the edges represent statistical relations between the individual process components. More precisely, the (undirected) edges of a conditional independence graph (CIG) associated with a process represent conditional independence statements about the process components [4], [1]. In particular, two nodes in the CIG are connected by an edge if and only if the two corresponding process components are conditionally dependent, given the remaining process components. Note that the so defined CIG for time series extends the basic notion of a CIG for random vectors by considering dependencies between entire time series instead of dependencies between scalar random variables [5], [6]. In this work, we investigate the problem of graphical model selection (GMS), i.e., that of inferring the CIG of a time series, given a finite-length observation. A. Jung is with the Institute of Telecommunications, Vienna University of Technology, 1040-Vienna, Austria email: ajung@nt.tuwien.ac.at.