A0839
Title: Spectral differential network analysis for high-dimensional time series
Authors: Michael Hellstern - University of Washington (United States) [presenting]
Ali Shojaie - University of Washington (United States)
Byol Kim - University of Washington (United States)
Abstract: Analyzing multivariate time series networks is popular in many fields, from neuroscience to seismology and signal processing. In particular, partial spectral coherence is a common choice of the network due to its representation as the frequency domain correlation between two variables after removing the best linear predictor of all other variables. In many applications, it is often of interest to study how these networks change across different conditions. For example, in neuroscience, one might be interested in how the brain network changes before and after stimulation. Estimates of differential networks typically rely on estimating the network in each condition and naively taking their difference. In high dimensions, establishing consistency of these estimates requires the restrictive assumption of the sparsity of each network. A direct estimator of the difference in inverse spectral densities of time series in two conditions is proposed. Using an L1 penalty on the difference, consistency is established only by requiring the difference to be sparse. This is a more realistic assumption if, for example, there are minimal differences in the networks between conditions. The difference estimator is further debiased to obtain asymptotically valid inference.
