Estimating differential latent variable graphical models with applications to brain connectivity

S. Na, M. Kolar, O. Koyejo

Research output: Contribution to journalArticlepeer-review


Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, and thus are of particular interest for scientific investigations. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

Original languageEnglish (US)
Pages (from-to)425-442
Number of pages18
Issue number2
StatePublished - Jun 1 2021
Externally publishedYes


  • Alternating projected gradient descent
  • Differential network
  • Functional connectivity
  • Latent variable Gaussian graphical model

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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