Recovering shared structure from multiple networks with unknown edge distributions

Keith Levin; Asad Lodhia; Elizaveta Levina

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arXiv · 1906.07265

Recovering shared structure from multiple networks with unknown edge distributions

Keith Levin·Asad Lodhia·Elizaveta Levina

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Abstract

In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction between brain regions that have been aligned to a common template. 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. We establish a finite-sample concentration inequality for the low-rank eigenvalue truncation of a random weighted adjacency matrix that 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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Keith Levin, Asad Lodhia, Elizaveta Levina. 2019-06-13. Recovering shared structure from multiple networks with unknown edge distributions. https://arxiv.org/abs/1906.07265

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