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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.<\/jats:p>","DOI":"10.1093\/biomet\/asaa066","type":"journal-article","created":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T11:40:51Z","timestamp":1598614851000},"page":"425-442","source":"Crossref","is-referenced-by-count":11,"title":["Estimating differential latent variable graphical models with applications to brain connectivity"],"prefix":"10.1093","volume":"108","author":[{"given":"S","family":"Na","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Chicago, 5747 South Ellis Avenue, Chicago, Illinois 60637, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7353-3404","authenticated-orcid":false,"given":"M","family":"Kolar","sequence":"additional","affiliation":[{"name":"Booth School of Business, University of Chicago, 5807 South Woodlawn Avenue, Chicago, Illinois 60637, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O","family":"Koyejo","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Illinois at Urbana-Champaign, 201 North Goodwin Avenue, Urbana, Illinois 61801, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,9,4]]},"reference":[{"key":"2021051519493202200_B1","doi-asserted-by":"publisher","DOI":"10.3389\/fninf.2014.00014","article-title":"Machine learning for neuroimaging with scikit-learn","volume":"8","author":"Abraham,","year":"2014","journal-title":"Front. 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