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Recovering shared structure from multiple networks with unknown edge distributions

Keith Levin, Asad Lodhia, Elizaveta Levina; 23(3):1−48, 2022.


In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across networks; for example, brain connectivity networks in neuroscience. We consider the setting where the observed networks have a shared expectation, but may differ in the noise structure on their edges. Our approach exploits the shared mean structure to denoise edge-level measurements of the observed networks and estimate the underlying population-level parameters. We also explore the extent to which edge-level errors influence estimation and downstream inference. In the process, we establish a finite-sample concentration inequality for the low-rank eigenvalue truncation of a random weighted adjacency matrix, which may be of independent interest. The proposed approach is illustrated on synthetic networks and on data from an fMRI study of schizophrenia.

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