The Sylvester Graphical Lasso (SyGlasso)
This is an incremental contribution that provides an alternative model for tensor graphical lasso, potentially benefiting researchers in fields like neuroscience analyzing tensor data.
The paper tackles the problem of modeling multiway dependencies in tensor-valued data by introducing the Sylvester graphical lasso (SyGlasso), which provides a generative and interpretable Kronecker sum model, and demonstrates its application in an EEG study to estimate brain connectivity and temporal dependencies for alcoholic and nonalcoholic subjects.
This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.