Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation
This work addresses graph learning for time series data, which is important for fields like neuroscience or finance, but it appears incremental as it builds on existing sparse estimation techniques.
The paper tackles the problem of inferring conditional independence graphs from high-dimensional multivariate Gaussian time series by formulating it as a multi-attribute graph estimation problem, and it outperforms existing frequency-domain methods in edge detection accuracy.
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.