Partial separability and functional graphical models for multivariate Gaussian processes

Summary The covariance structure of multivariate functional data can be highly complex, especially if the dimension is large, making extensions statistical methods for standard to setting challenging. For example, Gaussian graphical models have recently been extended by applying coefficients truncated basis expansions. However, compared with data, a key difficulty that operator compact and thus not invertible. This paper addresses general problem modelling in particular. As first step, new notion separability proposed, termed partial separability, leading novel Karhunen–Loève-type expansion such data. Next, shown particularly useful providing well-defined model identified sequence finite-dimensional models, each identical fixed dimension. motivates simple efficient estimation procedure through application joint lasso. Empirical performance proposed method assessed simulation analysis brain connectivity during motor task.