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A random covariance model for bi-level graphical modeling with application to resting-state fMRI data.

Lin ZhangAndrew DiLerniaKarina QuevedoJazmin CamchongKelvin LimWei Pan
Published in: Biometrics (2020)
We consider a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level graphical models is of interest. Such a problem arises from many applications, including multi-subject neuro-imaging and genomics data analysis. We propose a novel and efficient statistical method, the random covariance model, to learn the group- and individual-level graphical models simultaneously. The proposed method can be nicely interpreted as a random covariance model that mimics the random effects model for mean structures in linear regression. It accounts for similarity between individual graphical models, identifies group-level connections that are shared by individuals, and simultaneously infers multiple individual-level networks. Compared to existing multiple graphical modeling methods that only focus on individual-level graphical modeling, our model learns the group-level structure underlying the multiple individual graphical models and enjoys computational efficiency that is particularly attractive for practical use. We further define a measure of degrees-of-freedom for the complexity of the model useful for model selection. We demonstrate the asymptotic properties of our method and show its finite-sample performance through simulation studies. Finally, we apply the method to our motivating clinical data, a multi-subject resting-state functional magnetic resonance imaging dataset collected from participants diagnosed with schizophrenia, identifying both individual- and group-level graphical models of functional connectivity.
Keyphrases
  • functional connectivity
  • resting state
  • magnetic resonance imaging
  • data analysis
  • dna methylation
  • computed tomography
  • single cell
  • magnetic resonance
  • bipolar disorder
  • big data
  • genome wide
  • copy number