gslope: Graphical SLOPE
In StatsIMUWr/gslope: Graphical SLOPE

Description Usage Arguments Details Value References Examples

View source: R/gslope.R

Computes precision matrix for graph models using graphical SLOPE.

gslope(
  data,
  lambda = NULL,
  scaled = FALSE,
  mu = 1.1,
  max_iter = 10000,
  epsilon = 1e-04,
  threshold = 1e-04,
  alpha = 0.05
)

`data`	a matrix containing observations of variables of interest.
`lambda`	vector of regularizers for SLOPE. By default computed based on Benjamini-Hochberg's method.
`scaled`	logical. The data need to be scaled so that it has mean = 0 and variance = 1. If TRUE, build-in data scaling will be omitted.
`mu`	correction for lambda scaling in ADMM algorithm.
`max_iter`	maximum number of iterations allowed in ADMM algorithm. Default 10 000.
`epsilon`	a value used to determine accuracy of the ADMM algorithm. Default 10e-4.
`threshold`	a value used to determine which variables in graphical model are not linked by an edge. The larger the value, the more variables will be unlinked. Default 10e-4.
`alpha`	significance level.

gslope selects high probability graph structure for graphical model with likelihood-based methods combined with ordered L1-regularization. Namely, it solves - using ADMM algorithm - the following maximization problem:

log det Θ - tr(S Θ) - λ(Θ), subject to Θ \in S+,

where S is a sample covariance matrix, λ(Θ) is a series of regularizers for SLOPE and S+ denotes a set of symmetric, semidefinite matrices.

returns a list containing following components:

precision_matrix a precision matrix revealing graph structure for the data.
covariance_matrix covariance matrix equal to the inverse of the presicion matrix.
scaled_precision_matrix An element with coordinates (k,l) is given by formula:
k_lm=-Cov(X_l,X_m|X_(V\ {l,m}))/(Var(X_l|X_(V\ {l,m}))^(1/2)*Var(X_m|X_(V\ {l,m}))^(1/2)).
lambda a vector of penalty parameters used in SLOPE.
iterations a number of iterations performed in ADMM algorithm.
graph an IGRAPH object returning set of edges between vertices in the model. For more details see ?igraph
clusters a sub-graph structure. Numbers associeted with vertex indicates which sub-graph the vertex belongs to. If all verices are marked with ones, then there is only one graph in the model. Size an number of clusters are additionaly provided in separate vectors. For more details see ?clusters.