huge (version 1.0.2)

huge.GECT: Graph Estimation via Correlation Thresholding (GECT)

Description

Implements Graph Estimation via Correlation Thresholding (GECT) which approximates the graph by thresholding sample correlations.

Usage

huge.GECT(x, nlambda = NULL, lambda.min.ratio = NULL, lambda = NULL, verbose = TRUE)

Arguments

x

There are 2 options for the input:(1) The n by d data matrix. (2) A d by d sample covariance covariance matrix. The program automatically identifies the input matrix by checking the symmetry.(n

lambda

A sequence of decresing positive numbers to control the thresholding in GECT. Typical usage is to leave the input lambda = NULL and have the program compute its own lambda sequence based on nlambda and lambda.m

nlambda

The number of thresholding paramters. The default value is 20.

lambda.min.ratio

The largest sparsity level for estimated graphs. The program can automatically generate lambda as a sequence of length = nlambda, which makes the sparsity level of the graph path increases from 0 to lambda.min.

verbose

If verbose = FALSE, printing the tracing information is disabled. The default value is TRUE.

Value

• An object with S3 class "GECT" is returned:
• path
  A list of k by k adjacency matrices (in sparse matrix representation) of estimated graphs as the solution path corresponding to lambda.
• cov.input
  An indicator of the sample covariance.
• lambda
  The sequence of thresholding parameters used in GECT.
• sparsity
  The sparsity levels of the graph path.

Details

Under the assumption of sparsity, Graph Estimation via Correlation Thresholding (GECT) is the most efficient way to study the underlying structure of Gaussian graphical models regardless the expected sparsity level. As an approximation of paritial correlation graph estimation, GECT also performs well. It can generate some dense graphs, while the sparsity level generated by L1 regularization methods usually depends on the sample size.

References

1.Tuo Zhao and Han Liu. HUGE: A Package for High-dimensional Undirected Graph Estimation. Technical Report, Carnegie Mellon University, 2010 2.Jerome Friedman, Trevor Hastie and Rob Tibshiran. Applications of the lasso and grouped lasso to the estimation of sparse graphical models, Technical Report, Stanford University, 2010

See Also

huge and huge-package

Examples

# generate data
L = huge.generator(graph = "hub", g = 5)

# the Graph Estimation via Correlation Threholding (GECT)
out = huge.GECT(L$data, nlambda = 20)
plot(out)