PenalisedGraphical {sharp}

Graphical LASSO

Description

Runs the graphical LASSO algorithm for estimation of a Gaussian Graphical Model (GGM). This function is not using stability.

Usage

PenalisedGraphical(
  xdata,
  pk = NULL,
  Lambda,
  Sequential_template = NULL,
  scale = TRUE,
  start = "cold",
  output_omega = FALSE,
  ...
)

Arguments

xdata

matrix with observations as rows and variables as columns.

pk

optional vector encoding the grouping structure. Only used for multi-block stability selection where pk indicates the number of variables in each group. If pk=NULL, single-block stability selection is performed.

Lambda

matrix of parameters controlling the level of sparsity.

Sequential_template

logical matrix encoding the type of procedure to use for data with multiple blocks in stability selection graphical modelling. For multi-block estimation, the stability selection model is constructed as the union of block-specific stable edges estimated while the others are weakly penalised (TRUE only for the block currently being calibrated and FALSE for other blocks). Other approaches with joint calibration of the blocks are allowed (all entries are set to TRUE).

scale

logical indicating if the correlation (scale=TRUE) or covariance (scale=FALSE) matrix should be used as input of glassoFast if implementation=PenalisedGraphical. Otherwise, this argument must be used in the function provided in implementation.

start

character string indicating if the algorithm should be initialised at the estimated (inverse) covariance with previous penalty parameters (start="warm") or not (start="cold"). Using start="warm" can speed-up the computations, but could lead to convergence issues (in particular with small Lambda_cardinal). Only used for implementation=PenalisedGraphical (see argument "start" in glassoFast).

output_omega

logical indicating if the estimated precision matrices should be stored and returned.

...

additional parameters passed to the function provided in implementation.

Details

The use of the procedure from Equation (4) or (5) is controlled by the argument "Sequential_template".

Value

An array with binary and symmetric adjacency matrices along the third dimension.

References

Friedman J, Hastie T, Tibshirani R (2008). “Sparse inverse covariance estimation with the graphical lasso.” Biostatistics, 9(3), 432–441.

See Also

GraphicalModel

Other underlying algorithm functions: CART(), ClusteringAlgo(), PenalisedOpenMx(), PenalisedRegression()

Examples

# Data simulation
set.seed(1)
simul <- SimulateGraphical()

# Running graphical LASSO
myglasso <- PenalisedGraphical(
  xdata = simul$data,
  Lambda = matrix(c(0.1, 0.2), ncol = 1)
)

# Returning estimated precision matrix
myglasso <- PenalisedGraphical(
  xdata = simul$data,
  Lambda = matrix(c(0.1, 0.2), ncol = 1),
  output_omega = TRUE
)