Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation

Nonparametric approaches for graphical We consider the problem of inferring the conditional independence modeling of real time series in high-dimensional settings (p is graph (CIG) of a high-dimensional stationary multivariate Gaussian large and/or sample size n is of the order of p) have been formulated time series. In a time series graph, each component of the vector series in the form of group-lasso penalized log-likelihood in frequencydomain is represented by distinct node, and associations between components in [10]. Sparse-group lasso penalized log-likelihood approach are represented by edges between the corresponding nodes. in frequency-domain has been considered in [11-13]. We formulate the problem as one of multi-attribute graph estimation In this paper we investigate graph structure estimation for for random vectors where a vector is associated with each node of the stationary Gaussian multivariate time series using a time-domain graph. At each node, the associated random vector consists of a time approach, unlike [10-12] who, as noted earlier, use a frequencydomain series component and its delayed copies.