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Differential network analysis: A statistical perspective

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Abstract Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and in response to external stimuli. In biology and medicine, these changes have been found to be predictive of complex diseases. They have also been used to gain insight into mechanisms of disease initiation and progression. Primarily motivated by biological applications, this article provides a review of recent statistical machine learning methods for inferring networks and identifying changes in their structures. This article is categorized under: Data: Types and Structure > Graph and Network Data Statistical Models > Graphical Models
Illustration of different notions of difference in networks. Top: hypothetical networks for two populations; here, networks correspond to two GGMs and adjacency matrices A1 and A2 correspond to (true) partial correlations among nodes. Bottom: differential networks based on differences in values of adjacency matrices (left); differences in supports of the adjacency matrices (center); and differences in signs of adjacency matrices (right)
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Differential network analysis in subtypes of breast cancer. The two networks show edges identified as significant in only one breast cancer subtypes (left: ER+; right: ER−). They correspond to interactions among a subset of m = 358 cancer‐related genes, and are inferred using gene expression measurements from the Cancer Genome Atlas (TCGA)
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Statistical Models > Graphical Models
Data: Types and Structure > Graph and Network Data

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