huge (version 1.0.3)

huge: High-dimensional undirected graph estimation

Description

The main function for high-dimensional undirected graph estimation. Three graph estimation methods, including Meinshausen & Buhlmann Graph Estimation via Lasso (MBGEL), Graphical Lasso (GLASSO) and Graph Estimation via Correlation Thresholding (GECT), are available for data analysis.

Usage

huge(x, lambda = NULL, nlambda = NULL, lambda.min.ratio = NULL, method = "mbgel", scr = NULL, scr.num = NULL, cov.output = FALSE, sym = "or", verbose = TRUE)

Arguments

x

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

lambda

A sequence of decresing positive numbers to control the regularization in MBGEL and GLASSO, or the thresholding in GECT. Typical usage is to leave the input lambda = NULL and have the program compute its own lambda sequence based

nlambda

The number of regularization/thresholding paramters. The default value is 30 if method = "gect" and 10 if method = "mbgel" or method = "glasso".

lambda.min.ratio

If method = "mbgel" or method = "glasso", it is the smallest value for lambda, as a fraction of the uppperbound (MAX) of the regularization/thresholding parameter which makes all estimates equal to

method

Graph estimation methods with 3 options: "mbgel", "gect" and "glasso". The defaulty value is "mbgel".

scr

If scr = TRUE, Graph Sure Screening (GSS) is applied to preselect the neighborhood before MBGEL. The default value is TRUE for n and FALSE for n>=d. ONLY applicable when method = "mb

scr.num

The neighborhood size after the GSS (the number of remaining neighbors per node). ONLY applicable when scr = TRUE. The default value is n-1. An alternative value is n/log(n). ONLY applicable when scr = TRUE

cov.output

If cov.output = TRUE, the outpu will inlcude a path of estimated covariance matrices. ONLY applicable when method = "glasso". Since the estimated covariance matrices are generally not sparse, please use it with care, or it may ta

sym

Symmetrize the output graphs. If sym = "and", the edge between node i and node j is selected ONLY when both node i and node j are selected as neighbors for each other. If sym = "or"

verbose

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

Value

• An object with S3 class "huge" is returned:
• data
  The n by d data matrix or d by d sample covariance matrix from the input
• cov.input
  An indicator of the sample covariance.
• ind.mat
  The scr.num by k matrix with each column correspondsing to a variable in ind.group and contains the indices of the remaining neighbors after the GSS. ONLY applicable when scr = TRUE and approx = FALSE
• lambda
  The sequence of regularization parameters used in MBGEL or thresholding parameters in GECT.
• sym
  The sym from the input. ONLY applicable when method = "mbgel".
• scr
  The scr from the input. ONLY applicable when method = "mbgel".
• path
  A list of k by k adjacency matrices of estimated graphs as a graph path corresponding to lambda.
• sparsity
  The sparsity levels of the graph path.
• wi
  A list of d by d precision matrices as an alternative graph path (numerical path) corresponding to lambda. ONLY applicable when {method = "glasso"}
• w
  A list of d by d estimated covariance matrices corresponding to lambda. ONLY applicable when cov.output = TRUE and {method = "glasso"}
• method
  The method used in the graph estimation stage.
• df
  If method = "mbgel", it is a k by nlambda matrix. Each row contains the number of nonzero coefficients along the lasso solution path. If method = "glasso", it is a nlambda dimensional vector containing the number of nonzero coefficients along the graph path wi.
• loglik
  A nlambda dimensional vector containing the likelihood scores along the graph path (wi). ONLY applicable when method = "glasso"

Details

The graph stucture is estimated using Meinshausen & Buhlmann Graph Estimation via Lasso (MBGEL) by default and it can be further accelerated by Graph SURE Screening (GSS) subroutine which preselects the graph neighborhood of each variable. In the case d >> n, the computation is memory optimized and is targeted on larger-scale problems. We also provide two alternative approaches for the graph estimation stage:(1) Graph Estimation via Correlation Thresholding (GECT) which is highly efficient and (2) A slightly modified Graphical Lasso (GLASSO) procedure in which the memory usage is optimized using sparse matrix output.

References

1.Tuo Zhao and Han Liu. HUGE: A Package for High-dimensional Undirected Graph Estimation. Technical Report, Carnegie Mellon University, 2010 2.Han Liu, John Lafferty and Larry Wasserman. The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs. Journal of Machine Learning Research (JMLR), 2009 3.Jianqing Fan and Jinchi Lv. Sure independence screening for ultra-high dimensional feature space (with discussion). Journal of Royal Statistical Society B, 2008. 4.Jerome Friedman, Trevor Hastie and Rob Tibshirani. Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 2008. 5.Onureena Banerjee, Laurent El Ghaoui, Alexandre d'Aspremont: Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data. Journal of Machine Learning Research (JMLR), 2008. 6.Jerome Friedman, Trevor Hastie and Robert Tibshirani. Sparse inverse covariance estimation with the lasso. Biostatistics, 2007. 7.Nicolai Meinshausen and Peter Buhlmann. High-dimensional Graphs and Variable Selection with the Lasso. The Annals of Statistics, 2006.

See Also

huge.generator, huge.select, huge.plot, huge.roc, and huge-package.

Examples

#generate data
L = huge.generator(n = 200, d = 80, graph = "hub")

#graph path estimation using MBGEL
out1 = huge(L$data)
out1
plot(out1)				 #Not aligned	
plot(out1, align = TRUE) #Aligned
huge.plot(out1$path[[3]])

#graph path estimation using the sample covariance matrix as the input.
out1 = huge(cor(L$data))
out1
plot(out1)				 #Not aligned	
plot(out1, align = TRUE) #Aligned
huge.plot(out1$path[[3]])

#graph path estimation using GECT
out2 = huge(L$data,method = "gect")
out2
plot(out2)

#graph path estimation using GLASSO
out3 = huge(L$data, method = "glasso")
out3
plot(out3)