Conditional Gaussian Graphical Models for Functional Variables with Partially Separable Operators

Functional graphical modelling is gaining increasing attention in recent years. In this paper, we contribute to the literature by extending the notion of conditional Gaussian graphical model to a functional setting. We propose a double-penalized estimator and an efficient algorithm to recover the edge-set encoding both the conditional covariance structure of the response functions and the effects of the predictor functions on the conditional distribution.