mglasso: Inference of Multiscale Gaussian Graphical Model.

In mglasso: Multiscale Graphical Lasso

Inference of Multiscale Gaussian Graphical Model.

Description

Cluster variables using L2 fusion penalty and simultaneously estimates a gaussian graphical model structure with the addition of L1 sparsity penalty.

Usage

mglasso(
  x,
  lambda1 = 0,
  fuse_thresh = 0.001,
  maxit = NULL,
  distance = c("euclidean", "relative"),
  lambda2_start = 1e-04,
  lambda2_factor = 1.5,
  precision = 0.01,
  weights_ = NULL,
  type = c("initial"),
  compact = TRUE,
  verbose = FALSE
)

Arguments

x	Numeric matrix (n x p). Multivariate normal sample with n independent observations.
lambda1	Positive numeric scalar. Lasso penalty.
fuse_thresh	Positive numeric scalar. Threshold for clusters fusion.
maxit	Integer scalar. Maximum number of iterations.
distance	Character. Distance between regression vectors with permutation on symmetric coefficients.
lambda2_start	Numeric scalar. Starting value for fused-group Lasso penalty (clustering penalty).
lambda2_factor	Numeric scalar. Step used to update fused-group Lasso penalty in a multiplicative way..
precision	Tolerance for the stopping criterion (duality gap).
weights_	Matrix of weights.
type	If "initial" use classical version of MGLasso without weights.
compact	Logical scalar. If TRUE, only save results when previous clusters are different from current.
verbose	Logical scalar. Print trace. Default value is FALSE.

Details

Estimates a gaussian graphical model structure while hierarchically grouping variables by optimizing a pseudo-likelihood function combining Lasso and fuse-group Lasso penalties. The problem is solved via the COntinuation with NEsterov smoothing in a Shrinkage-Thresholding Algorithm (Hadj-Selem et al. 2018). Varying the fusion penalty λ_2 in a multiplicative fashion allow to uncover a seemingly hierarchical clustering structure. For λ_2 = 0, the approach is theoretically equivalent to the Meinshausen-Bühlmann (2006) neighborhood selection as resuming to the optimization of pseudo-likelihood function with \ell_1 penalty (Rocha et al., 2008). The algorithm stops when all the variables have merged into one cluster. The criterion used to merge clusters is the \ell_2-norm distance between regression vectors.

For each iteration of the algorithm, the following function is optimized :

1/2 ∑_{i=1}^p || X^i - X^{\ i} β^i ||_2 ^2 + λ_1 ∑_{i = 1}^p || β^i ||_1 + λ_2 ∑_{i < j} || β^i - τ_{ij}(β^j) ||_2.

where β^i is the vector of coefficients obtained after regression X^i on the others and τ_{ij} is a permutation exchanging β_j^i with β_i^j.

Value

A list-like object of class mglasso is returned.

out	List of lists. Each element of the list corresponds to a clustering level. An element named levelk contains the regression matrix beta and clusters vector clusters for a clustering in k clusters. When compact = TRUE out has as many elements as the number of unique partitions. When set to FALSE, the function returns as many items as the the range of values taken by lambda2.
l1	the sparsity penalty lambda1 used in the problem solving.

See Also

conesta() for the problem solver, plot_mglasso() for plotting the output of mglasso.

Examples

## Not run: 
reticulate::use_condaenv("rmglasso", required = TRUE)
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.covariance <- Matrix::bdiag(blocs)
mat.covariance

set.seed(11)
X <- mvtnorm::rmvnorm(n, mean = rep(0,p), sigma = as.matrix(mat.covariance))
X <- scale(X)

res <- mglasso(X, 0.1, lambda2_start = 0.1)
res$out[[1]]$clusters
res$out[[1]]$beta

## End(Not run)

mglasso documentation built on Sept. 8, 2022, 5:08 p.m.