Reviews: Direct Estimation of Differential Functional Graphical Models

The authors describe a method for estimating the difference between two functional graphical models using time-varying data. This is done by first modelling the functional graphical models as multi-variate Gaussian processes, and then defining the differential graph as arising from the difference between the covariance functions estimated for both processes. Optimization is done via a proximal gradient approach, and the method is evaluated under 3 different data generating mechanisms, before being applied to an EEG dataset. As I am not an expert in functional data analysis, I cannot vouch for the originality except to say that I have not come across a similar method. The quality of the method and experiments is high, and the inclusion of theoretical consistency results is welcomed.