mgm: Structure Estimation for Time-Varying Mixed Graphical Models in high-dimensional Data

We present the R-package mgm for the estimation of both stationary and time-varying mixed graphical models and mixed vector autoregressive models in high-dimensional data. Variables of mixed type (continuous, count, categorical) are ubiquitous in datasets in many disciplines, however, available methods cannot incorporate (nominal) categorical variables and suffer from possible information loss due to transformations of non-Gaussian continuous variables. In addition, we extend both models to the time-varying case in which the true model changes over time, under the assumption that change is a smooth function of time. Time-varying models offer a rich description of temporally evolving systems as they provide information about organizational processes, information diffusion, vulnerabilities and the potential impact of interventions. Next to introducing the theory of the implemented methods and explaining the software package, we provide performance benchmarks and applications to two medical datasets.

[1]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[2]  Alexandre d'Aspremont,et al.  Model Selection Through Sparse Max Likelihood Estimation Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data , 2022 .

[3]  Hiro Y. Toda,et al.  Statistical inference in vector autoregressions with possibly integrated processes , 1995 .

[4]  N. Meinshausen,et al.  High-dimensional graphs and variable selection with the Lasso , 2006, math/0608017.

[5]  Eric P. Xing,et al.  Sparsistent Estimation of Time-Varying Discrete Markov Random Fields , 2009, 0907.2337.

[6]  Mathias Drton,et al.  High-dimensional Ising model selection with Bayesian information criteria , 2014, 1403.3374.

[7]  Shuning Wang,et al.  Multiple Gaussian graphical estimation with jointly sparse penalty , 2016, Signal Process..

[8]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[9]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[10]  Mladen Kolar,et al.  Estimating networks with jumps. , 2010, Electronic journal of statistics.

[11]  Martin J Wainwright,et al.  Graphical models, exponential families, and variational inference. [electronic resource] / Wainwright, Martin J , 2008 .

[12]  Claudia D. van Borkulo,et al.  A new method for constructing networks from binary data , 2014, Scientific Reports.

[13]  Jing Li,et al.  Learning brain connectivity of Alzheimer's disease by sparse inverse covariance estimation , 2010, NeuroImage.

[14]  Larry A. Wasserman,et al.  The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs , 2009, J. Mach. Learn. Res..

[15]  Pradeep Ravikumar,et al.  Graphical models via univariate exponential family distributions , 2013, J. Mach. Learn. Res..

[16]  Lourens J. Waldorp,et al.  Structure estimation for mixed graphical models in high-dimensional data , 2015, 1510.05677.

[17]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[18]  Le Song,et al.  KELLER: estimating time-varying interactions between genes , 2009, Bioinform..

[19]  P. Kuppens,et al.  Emotional Inertia and Psychological Maladjustment , 2010, Psychological science.

[20]  J. Lafferty,et al.  High-dimensional Ising model selection using ℓ1-regularized logistic regression , 2010, 1010.0311.

[21]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[22]  M. Drton,et al.  Bayesian model choice and information criteria in sparse generalized linear models , 2011, 1112.5635.

[23]  Pradeep Ravikumar,et al.  Mixed Graphical Models via Exponential Families , 2014, AISTATS.

[24]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[25]  Po-Ling Loh,et al.  Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses , 2012, NIPS.

[26]  A. Dobra,et al.  Copula Gaussian graphical models and their application to modeling functional disability data , 2011, 1108.1680.

[27]  Edward M. Reingold,et al.  Graph drawing by force‐directed placement , 1991, Softw. Pract. Exp..

[28]  James D. B. Nelson,et al.  High dimensional changepoint detection with a dynamic graphical lasso , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[29]  Christoforos Anagnostopoulos,et al.  Estimating time-varying brain connectivity networks from functional MRI time series , 2013, NeuroImage.

[30]  Xiaohui Chen,et al.  Inference of high-dimensional linear models with time-varying coefficients , 2015, 1506.03909.

[31]  Larry A. Wasserman,et al.  Time varying undirected graphs , 2008, Machine Learning.

[32]  Le Song,et al.  Estimating time-varying networks , 2008, ISMB 2008.

[33]  James D. B. Nelson,et al.  Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso , 2015, 1512.06171.

[34]  Bernhard Pfaff,et al.  Analysis of Integrated and Cointegrated Time Series with R , 2005 .

[35]  D. Borsboom,et al.  Network analysis: an integrative approach to the structure of psychopathology. , 2013, Annual review of clinical psychology.

[36]  D. Borsboom,et al.  A Network Approach to Psychopathology: New Insights into Clinical Longitudinal Data , 2013, PloS one.

[37]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[38]  Marieke Wichers,et al.  Critical Slowing Down as a Personalized Early Warning Signal for Depression , 2016, Psychotherapy and Psychosomatics.

[39]  S. Horvath,et al.  Evidence for anti-Burkitt tumour globulins in Burkitt tumour patients and healthy individuals. , 1967, British Journal of Cancer.