Graph learning is an active research domain in statistics, highlighted by well-known models such as Gaussian graphical models for i.i.d. data and autoregressive models for time series. In this talk, we will present two new models developed to address distinct analytical challenges.  

The first model tackles a non-classical data setting where the data points are probability distributions. Here, the graph is inferred to represent the dependence structure of a set of distributional time series. Leveraging Wasserstein space theory, we develop a novel autoregressive model, which is then applied to a demographic dataset.  

The second model is designed to meet an application-driven need: inferring a functional connectivity graph for a single subject’s brain fMRI time series while quantifying uncertainty. We adopt a Bayesian modeling approach to infer these graphs, with posterior distributions over edges providing uncertainty estimates. In particular, we introduce a prior for correlation matrices that facilitates the integration of expert knowledge. The model is applied to a rat fMRI dataset, where two follow-up analyses—edge detection and subject comparison—are conducted. The results highlight the robustness gained through uncertainty quantification.