Granger Causal Inference from Indirect Low-Dimensional Measurements with Application to MEG Functional Connectivity Analysis

We consider the problem of determining Granger causal influences among sources that are indirectly observed through low-dimensional and noisy linear projections. Commonly used methods proceed in a two-stage fashion, by first solving an inverse problem to localize the sources, and then inferring the Granger causal influences from the estimated sources. The inferred Granger causal links thus inherit the various biases that are used in source localization techniques, in the form of spatiotemporal priors designed in favor of spatial localization. In addition, this approach does not account for the structural properties of the underlying functional networks such as sparsity of the links. We address these issues by modeling the source dynamics as sparse vector autoregressive processes and estimate the model parameters directly from the observations, with no recourse to intermediate source localization. We evaluate the performance of the proposed methodology using both simulated and experimentally-recorded MEG data.