mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data

We present the R-package mgm for the estimation of k-order Mixed Graphical Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package.

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

[2]  Larry A. Wasserman,et al.  The huge Package for High-dimensional Undirected Graph Estimation in R , 2012, J. Mach. Learn. Res..

[3]  Denny Borsboom,et al.  Multicausal systems ask for multicausal approaches: A network perspective on subjective well-being in individuals with autism spectrum disorder , 2017, Autism : the international journal of research and practice.

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

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

[6]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[7]  Denny Borsboom,et al.  Data from ‘Critical Slowing Down as a Personalized Early Warning Signal for Depression’ , 2017 .

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

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

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

[11]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[12]  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).

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

[14]  S. Geer,et al.  On asymptotically optimal confidence regions and tests for high-dimensional models , 2013, 1303.0518.

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

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

[17]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[18]  E. Salmon.  Gene Expression During the Life Cycle of Drosophila melanogaster , 2002 .

[19]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

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

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

[22]  Larry A. Wasserman,et al.  Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models , 2010, NIPS.

[23]  Rina Foygel,et al.  Extended Bayesian Information Criteria for Gaussian Graphical Models , 2010, NIPS.

[24]  Bernhard Pfaff,et al.  VAR, SVAR and SVEC Models: Implementation Within R Package vars , 2008 .

[25]  Denny Borsboom,et al.  Mental Disorders as Causal Systems , 2015 .

[26]  Pradeep Ravikumar,et al.  On Poisson Graphical Models , 2013, NIPS.

[27]  James D. B. Nelson,et al.  Estimating Dynamic Graphical Models from Multivariate Time-series Data , 2015, AALTD@PKDD/ECML.

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

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

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

[31]  Peter Bühlmann,et al.  High-Dimensional Statistics with a View Toward Applications in Biology , 2014 .

[32]  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 .

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

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

[37]  M. Eichler,et al.  A graphical vector autoregressive modelling approach to the analysis of electronic diary data , 2010, BMC medical research methodology.

[38]  Sander Begeer,et al.  Allemaal autisme, allemaal anders. NVA-enquête 2013 , 2013 .

[39]  Verena D. Schmittmann,et al.  Making Large-Scale Networks from fMRI Data , 2015, PloS one.

[40]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

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

[42]  N. Meinshausen,et al.  Stability selection , 2008, 0809.2932.

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

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

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

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

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

[48]  Ali Shojaie,et al.  Selection and estimation for mixed graphical models. , 2013, Biometrika.

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

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

[51]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

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

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

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

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

[56]  Verena D. Schmittmann,et al.  Qgraph: Network visualizations of relationships in psychometric data , 2012 .

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

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

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

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

[61]  Eiko I. Fried,et al.  Estimating Psychological Networks and their Stability: a Tutorial Paper , 2016 .