Impact of spatial and temporal properties of multivariate time series on graph inference.

Multivariate time series are most commonly observed in brain studies, where resting-state fMRI acquisitions provide observations of brain function over space and time. The brain can be modelled as a graph where nodes represent brain regions and edges correspond to functional connections between brain regions. In this talk I will show how temporal and spatial properties of the multivariate time series can drastically affect the inference of the graphs. Statistical properties will be illustrated for correlations. The impact of temporal properties is derived using complex wavelets, and a correction is proposed to account for long memory properties of the time series. Spatial properties are considered by proposing a novel nonparametric estimator of the correlation between groups of variables with arbitrary intra-group dependence and in the presence of noise. We illustrate these considerations with simulations as well as with real data using resting-state fMRI datasets from rats.