@article{discovery10059558,
         journal = {Frontiers in Genetics},
            year = {2018},
       publisher = {FRONTIERS MEDIA SA},
           title = {Learning Subject-Specific Directed Acyclic Graphs With Mixed Effects Structural Equation Models From Observational Data},
          volume = {9},
            note = {{\copyright} 2018 Li, Xie, McColgan, Tabrizi, Scahill, Zeng and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (http://creativecommons.org/licenses/by/4.0/). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.},
           month = {October},
            issn = {1664-8021},
             url = {https://doi.org/10.3389/fgene.2018.00430},
        abstract = {The identification of causal relationships between random variables from large-scale
observational data using directed acyclic graphs (DAG) is highly challenging. We
propose a new mixed-effects structural equation model (mSEM) framework to estimate
subject-specific DAGs, where we represent joint distribution of random variables in the
DAG as a set of structural causal equations with mixed effects. The directed edges
between nodes depend on observed exogenous covariates on each of the individual
and unobserved latent variables. The strength of the connection is decomposed into
a fixed-effect term representing the average causal effect given the covariates and a
random effect term representing the latent causal effect due to unobserved pathways.
The advantage of such decomposition is to capture essential asymmetric structural
information and heterogeneity between DAGs in order to allow for the identification
of causal structure with observational data. In addition, by pooling information across
subject-specific DAGs, we can identify causal structure with a high probability and
estimate subject-specific networks with a high precision. We propose a penalized
likelihood-based approach to handle multi-dimensionality of the DAG model. We propose
a fast, iterative computational algorithm, DAG-MM, to estimate parameters in mSEM and
achieve desirable sparsity by hard-thresholding the edges. We theoretically prove the
identifiability of mSEM. Using simulations and an application to protein signaling data,
we show substantially improved performances when compared to existing methods and
consistent results with a network estimated from interventional data. Lastly, we identify
gray matter atrophy networks in regions of brain from patients with Huntington's disease
and corroborate our findings using white matter connectivity data collected from an
independent study.},
        keywords = {graphical models, network analysis, causal structure discovery, heterogeneity, regularization},
          author = {Li, X and Xie, S and McColgan, P and Tabrizi, SJ and Scahill, R and Zeng, D and Wang, Y}
}