Resources on probabilistic graphical models

I started a Github repository resources-pgm where I will index some interesting resources on probabilistic graphical models. I will update it as I go along. For the moment, it is structured in books, articles and R packages. The content can also be found here.

Contents

• Books
• Papers
  • Gaussian graphical models
    • Review
    • Inference
  • Mixed graphical models
• R packages
  • Inference
• Optimization
• Variable selection

Books

• Probabilistic Graphical Models, D. Koller and N. Friedman, 2009
• Graphical models, S L Lauritzen, 1996
• Graphical Models with R, S. Højsgaard, D. Edwards, S. Lauritzen; 2012
• Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics, C. Sinoquet and R. Mourad, 2014

Papers

Gaussian graphical models

Review

• Structure Learning in Graphical Modeling, Drton and Maathuis 2017
• Estimation of covariance and precision matrix, network structure and a view towards systems biology, M. Kuismin, M. Sillanpää 2017, [Review of methods and their associated R packages]
• An Overview on the Estimation of Large Covariance and Precision Matrices, J. Fan, Y. Liao, H. Liu; 2015, [Review of covariance and precision matrices estimation]
• Getting Started in Probabilistic Graphical Models, E. M. Airoldi, 2007

Inference

Nodewise regression

• High-dimensional graphs and variable selection with the Lasso, N. Meinshausen and P. Buhlmann, 2006, [Neighborhood selection]

Likelihood optimization

• [BIG & QUIC: Sparse Inverse Covariance Estimation for a Million Variables], Hsieh et al. 2013
• The cluster graphical Lasso for improved estimation of gaussian graphical models, K. M. Tan and al., 2013, [The connected components returned by Graphical Lasso with regularization parameter $\lambda$ are the same that the clusters obtained through Single Linkage hierarchical clustering on empirical covariance with dendrogram cut at level $\lambda$.]
• Sparse inverse covariance estimation with the graphical Lasso, J. Friedman and al., 2008, [coordinate descent algorithm]

Fused graphical models

This section contains papers that do likelihood optimization or nodewise regression. The peculiarity is that the cost function includes a total variation term.

• [Estimation of sparse Gaussian graphical models with hidden clustering structure], Lin et al. 2020 (preprint)
• [Clustered Gaussian Graphical Model via Symmetric Convex clustering], Yao and Allen, 2019
• [The joint graphical lasso for inverse covariance estimation across multiple classes], Danaher et al., 2014
• [Local Neighborhood Fusion in Locally Constant Gaussian Graphical Models], Ganguly et al. 2014 (preprint)

Tricks

• Exact Covariance Thresholding into Connected Components for Large-Scale Graphical Lasso, R. Mazumder and T. Hastie, 2011 [block diagonal screening rule]

Mixed graphical models

• Anomaly Detection and Localisation using Mixed Graphical Models, R. Laby and al, 2016

R packages

Visualization

• igraph
• ggraph, [with ggplots]
• networkD3, [with javascript]

Inference

• glasso
• simone
• QUIC
• huge
• stabs, [stability selection]

The CRAN Task View: gRaphical Models in R also lists a good number of packages on R linked to graphical models.

Optimization

• [Optimization with sparsity-inducing penalties], Bach et al., 2011
• [Convex Optimization], Boyd and Vandenberghe, 2004

Variable selection

• [Statistical Learning with Sparsity], Hastie et al. 2016