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This repository provides an implementation of the MGLasso (Multiscale Graphical Lasso) algorithm: an approach for estimating sparse Gaussian Graphical Models with the addition of a group-fused Lasso penalty.
MGLasso is described in the paper Inference of Multiscale Gaussian Graphical Model. MGLasso has these contributions:
We simultaneously infer a network and estimate a clustering structure by combining the neighborhood selection approach (Meinshausen and Bühlman, 2006) and convex clustering (Hocking et al. 2011).
We use a continuation with Nesterov smoothing in a shrinkage-thresholding algorithm (CONESTA, Hadj-Selem et al. 2018) to solve the optimization problem.
To solve the MGLasso problem, we seek the regression vectors \(\beta^i\) that minimize
$J{\lambda_1, \lambda_2}(\boldsymbol{\beta}; \mathbf{X} ) =
\frac{1}{2}
\sum{i=1}p
\left \lVert
\mathbf{X}i - \mathbf{X}{\setminus i} \boldsymbol{\beta}i
\right \rVert2 2 +
\lambda_1
\sum{i = 1}p
\left \lVert
\boldsymbol{\beta}i \right \rVert1 +
\lambda_2
\sum{i < j}
\left \lVert
\boldsymbol{\beta}i - \tau_{ij}(\boldsymbol{\beta}j)
\right \rVert_2.$
MGLasso package is based on the python implementation of the solver CONESTA available in pylearn-parsimony library.
reticulate package and Miniconda if no conda distribution available on the OS.install.packages('reticulate')
reticulate::install_miniconda()
MGLasso, its python dependencies and configure the conda environment rmglasso.# install.packages('mglasso')
remotes::install_github("desanou/mglasso")
library(mglasso)
install_pylearn_parsimony(envname = "rmglasso", method = "conda")
reticulate::use_condaenv("rmglasso", required = TRUE)
reticulate::py_config()
The conesta_solver is delay loaded. See reticulate::import_from_path for details.
An example of use is given below.
We simulate a \(3\)-block diagonal model where each block contains \(3\) variables. The intra-block correlation level is set to \(0.85\) while the correlations outside the blocks are kept to \(0\).
library(Matrix)
n = 50
K = 3
p = 9
rho = 0.85
blocs <- list()
for (j in 1:K) {
bloc <- matrix(rho, nrow = p/K, ncol = p/K)
for(i in 1:(p/K)) { bloc[i,i] <- 1 }
blocs[[j]] <- bloc
}
mat.correlation <- Matrix::bdiag(blocs)
corrplot::corrplot(as.matrix(mat.correlation), method = "color", tl.col="black")
set.seed(11)
X <- mvtnorm::rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.correlation))
colnames(X) <- LETTERS[1:9]
mglasso()We set the sparsity level \(\lambda_1\) to \(0.2\) and rescaled it with the size of the sample.
X <- scale(X)
res <- mglasso(X, lambda1 = 0.2*n, lambda2_start = 0.1, fuse_thresh = 1e-3, verbose = FALSE)
To launch a unique run of the objective function call the conesta function.
temp <- mglasso::conesta(X, lam1 = 0.2*n, lam2 = 0.1)
We plot the clustering path of mglasso method on the 2 principal components axis of \(X\). The path is drawn on the predicted \(X\)'s.
library(ggplot2)
library(ggrepel)
mglasso:::plot_clusterpath(as.matrix(X), res)
As the the fusion penalty increases from level9 to level1 we observe a progressive fusion of adjacent edges.
plot_mglasso(res)
Edmond, Sanou; Christophe, Ambroise; Geneviève, Robin; (2022): Inference of Multiscale Gaussian Graphical Model. ArXiv. Preprint. https://doi.org/10.48550/arXiv.2202.05775
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.