huge (version 1.0.1)

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

Description

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

Usage

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

Arguments

x

The n by d data matrix representing n observations in d dimensions

lambda

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

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.
• lambda
  The sequence of thresholding parameters used in the GECT.
• sparsity
  The sparsity levels of the graph path.

Details

Under the assumption of sparsity, the GECT is the most efficient way to study the underlying structure of Gaussian graphical models. As an approximation of paritial correlation graph estimation, the 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)
summary(out)
plot(out)