  In many applications, a dataset can be considered as a set of observed
signals that live on an unknown underlying graph structure. Some of these
signals may be seen as white noise that has been filtered on the graph topology
by a graph filter. Hence, the knowledge of the filter and the graph provides
valuable information about the underlying data generation process and the
complex interactions that arise in the dataset. We hence introduce a novel
graph signal processing framework for jointly learning the graph and its
generating filter from signal observations. We cast a new optimisation problem
that minimises the Wasserstein distance between the distribution of the signal
observations and the filtered signal distribution model. Our proposed method
outperforms state-of-the-art graph learning frameworks on synthetic data. We
then apply our method to a temperature anomaly dataset, and further show how
this framework can be used to infer missing values if only very little
information is available.
