Neural Information Processing Systems http://nips.cc/

We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than multivariate scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time. In these problems, not only can the number of functions measured per sample be large, but each function is itself an infinite dimensional object, making estimation of model parameters challenging. We develop a method that directly estimates the difference of graphs, avoiding separate estimation of each graph, and show it is consistent in certain high-dimensional settings. We illustrate finite sample properties of our method through simulation studies. Finally, we apply our method to EEG data to uncover differences in functional brain connectivity between alcoholics and control subjects.

We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than multivariate scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time.

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.

The paper introduces a method for directly estimating the difference between two functional undirected graphical models, instead of doing it naively, and then combining them, the proposed method is novel, non-trivial, and leads to robust inferences. The authors provide extensive simulations to corroborate with their findings. Further, I like that even though some of the tools are well-studied and basic (e.g., fPCA), the authors generalized some key components in non-trivial fashion to make the whole thing to work. Having said that, and not taking any points from the technical contributions of the paper, I would be curious to see whether these new results would translate to the directed case, which is more related to causal inference. Acad., of Sci, 2016]), which defines and builds exactly on a combined representation that overlaps two causal diagrams, which was called selection diagram.

We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than multivariate scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time. In these problems, not only can the number of functions measured per sample be large, but each function is itself an infinite dimensional object, making estimation of model parameters challenging. We develop a method that directly estimates the difference of graphs, avoiding separate estimation of each graph, and show it is consistent in certain high-dimensional settings.

We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than multivariate scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time. In these problems, not only can the number of functions measured per sample be large, but each function is itself an infinite dimensional object, making estimation of model parameters challenging. We develop a method that directly estimates the difference of graphs, avoiding separate estimation of each graph, and show it is consistent in certain high-dimensional settings.