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Type:

Package

Title:

High-Dimensional Undirected Graph Estimation

Version:

1.3.5

Author:

Haoming Jiang, Xinyu Fei, Han Liu, Kathryn Roeder, John Lafferty, Larry Wasserman, Xingguo Li, and Tuo Zhao

Maintainer:

Haoming Jiang <jianghm.ustc@gmail.com>

Depends:

R (≥ 3.0.0)

Imports:

Matrix, igraph, MASS, grDevices, graphics, methods, stats,utils, Rcpp

LinkingTo:

Rcpp, RcppEigen

Description:

Provides a general framework for high-dimensional undirected graph estimation. It integrates data preprocessing, neighborhood screening, graph estimation, and model selection techniques into a pipeline. In preprocessing stage, the nonparanormal(npn) transformation is applied to help relax the normality assumption. In the graph estimation stage, the graph structure is estimated by Meinshausen-Buhlmann graph estimation or the graphical lasso, and both methods can be further accelerated by the lossy screening rule preselecting the neighborhood of each variable by correlation thresholding. We target on high-dimensional data analysis usually d >> n, and the computation is memory-optimized using the sparse matrix output. We also provide a computationally efficient approach, correlation thresholding graph estimation. Three regularization/thresholding parameter selection methods are included in this package: (1)stability approach for regularization selection (2) rotation information criterion (3) extended Bayesian information criterion which is only available for the graphical lasso.

License:

GPL-2

Repository:

CRAN

NeedsCompilation:

yes

RoxygenNote:

7.1.1

Encoding:

UTF-8

Packaged:

2021-06-30 19:55:18 UTC; jhaoming

Date/Publication:

2021-06-30 20:20:02 UTC

High-Dimensional Undirected Graph Estimation

Description

A package for high-dimensional undirected graph estimation

Details

Package:	huge
Type:	Package
Version:	1.2.7
Date:	2015-09-14
License:	GPL-2
LazyLoad:	yes

The package "huge" provides 8 main functions:
(1) the data generator creates random samples from multivariate normal distributions with different graph structures. Please refer tohuge.generator.
(2) the nonparanormal (npn) transformation helps relax the normality assumption. Please refer tohuge.npn.
(3) The correlation thresholding graph estimation. Please refer tohuge.
(4) The Meinshausen-Buhlmann graph estimation. Please refer tohuge.
(5) The graphical Lasso algorithm using lossless screening rule. Please refer andhuge.

**Both (4) and (5) can be further accelerated by the lossy screening rule preselecting the neighborhood of each node via thresholding sample correlation.
(6) The model selection using the stability approach to regularization selection. Please refer tohuge.select.
(7) The model selection using the rotation information criterion. Please refer tohuge.select.
(8) The model selection using the extended Bayesian information criterion. Please refer tohuge.select.

Author(s)

Tuo Zhao, Han Liu, Haoming Jiang, Kathryn Roeder, John Lafferty, and Larry Wasserman
Maintainers: Haoming Jiang<hjiang98@gatech.edu>;

References

1. T. Zhao and H. Liu. The huge Package for High-dimensional Undirected Graph Estimation in R.Journal of Machine Learning Research, 2012
2. H. Liu, F. Han, M. Yuan, J. Lafferty and L. Wasserman. High Dimensional Semiparametric Gaussian Copula Graphical Models.Annals of Statistics,2012
3. D. Witten and J. Friedman. New insights and faster computations for the graphical lasso.Journal of Computational and Graphical Statistics, to appear, 2011.4. Han Liu, Kathryn Roeder and Larry Wasserman. Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models.Advances in Neural Information Processing Systems, 2010.
5. R. Foygel and M. Drton. Extended bayesian information criteria for gaussian graphical models.Advances in Neural Information Processing Systems, 2010.
6. H. Liu, J. Lafferty and L. Wasserman. The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs.Journal of Machine Learning Research, 2009
7. J. Fan and J. Lv. Sure independence screening for ultra-high dimensional feature space (with discussion).Journal of Royal Statistical Society B, 2008.
8. O. Banerjee, L. E. Ghaoui, A. d'Aspremont: Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data.Journal of Machine Learning Research, 2008.
9. J. Friedman, T. Hastie and R. Tibshirani. Regularization Paths for Generalized Linear Models via Coordinate Descent.Journal of Statistical Software, 2008.
10. J. Friedman, T. Hastie and R. Tibshirani. Sparse inverse covariance estimation with the lasso,Biostatistics, 2007.
11. N. Meinshausen and P. Buhlmann. High-dimensional Graphs and Variable Selection with the Lasso.The Annals of Statistics, 2006.

High-dimensional undirected graph estimation

Description

The main function for high-dimensional undirected graph estimation. Three graph estimation methods, including (1) Meinshausen-Buhlmann graph estimation (mb) (2) graphical lasso (glasso) (3) correlation thresholding graph estimation (ct) and (4) tuning-insensitive graph estimation (tiger), are available for data analysis.

Usage

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

Arguments

x

There are 2 options: (1)x is ann byd data matrix (2) ad byd sample covariance matrix. The program automatically identifies the input matrix by checking the symmetry. (n is the sample size andd is the dimension).

lambda

A sequence of decreasing positive numbers to control the regularization whenmethod = "mb","glasso" or"tiger", or the thresholding inmethod = "ct". Typical usage is to leave the inputlambda = NULL and have the program compute its ownlambda sequence based onnlambda andlambda.min.ratio. Users can also specify a sequence to override this. Whenmethod = "mb","glasso" or"tiger", use with care - it is better to supply a decreasing sequence values than a single (small) value.

nlambda

The number of regularization/thresholding parameters. The default value is30 formethod = "ct" and10 formethod = "mb","glasso" or"tiger".

lambda.min.ratio

Ifmethod = "mb","glasso" or"tiger", it is the smallest value forlambda, as a fraction of the upperbound (MAX) of the regularization/thresholding parameter which makes all estimates equal to0. The program can automatically generatelambda as a sequence of length =nlambda starting fromMAX tolambda.min.ratio*MAX in log scale. Ifmethod = "ct", it is the largest sparsity level for estimated graphs. The program can automatically generatelambda as a sequence of length =nlambda, which makes the sparsity level of the graph path increases from0 tolambda.min.ratio evenly.The default value is0.1 whenmethod = "mb","glasso" or"tiger", and 0.05method = "ct".

method

Graph estimation methods with 4 options:"mb","ct","glasso" and"tiger". The default value is"mb".

scr

Ifscr = TRUE, the lossy screening rule is applied to preselect the neighborhood before the graph estimation. The default value isFALSE. NOT applicable whenmethod = "ct", "mb", or "tiger".

scr.num

The neighborhood size after the lossy screening rule (the number of remaining neighbors per node). ONLY applicable whenscr = TRUE. The default value isn-1. An alternative value isn/log(n). ONLY applicable whenscr = TRUE andmethod = "mb".

cov.output

Ifcov.output = TRUE, the output will include a path of estimated covariance matrices. ONLY applicable whenmethod = "glasso". Since the estimated covariance matrices are generally not sparse, please use it with care, or it may take much memory under high-dimensional setting. The default value isFALSE.

sym

Symmetrize the output graphs. Ifsym = "and", the edge between nodei and nodej is selected ONLY when both nodei and nodej are selected as neighbors for each other. Ifsym = "or", the edge is selected when either nodei or nodej is selected as the neighbor for each other. The default value is"or". ONLY applicable whenmethod = "mb" or "tiger".

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Details

The graph structure is estimated by Meinshausen-Buhlmann graph estimation or the graphical lasso, and both methods can be further accelerated via the lossy screening rule by preselecting the neighborhood of each variable by correlation thresholding. We target on high-dimensional data analysis usually d >> n, and the computation is memory-optimized using the sparse matrix output. We also provide a highly computationally efficient approaches correlation thresholding graph estimation.

Value

An object with S3 class"huge" is returned:

data

Then byd data matrix ord byd sample covariance matrix from the input

cov.input

An indicator of the sample covariance.

ind.mat

Thescr.num byk matrix with each column corresponding to a variable inind.group and contains the indices of the remaining neighbors after the GSS. ONLY applicable whenscr = TRUE andapprox = FALSE

lambda

The sequence of regularization parameters used in mb or thresholding parameters in ct.

sym

Thesym from the input. ONLY applicable whenmethod = "mb" or"tiger".

scr

Thescr from the input. ONLY applicable whenmethod = "mb" or"glasso".

path

A list ofk byk adjacency matrices of estimated graphs as a graph path corresponding tolambda.

sparsity

The sparsity levels of the graph path.

icov

A list ofd byd precision matrices as an alternative graph path (numerical path) corresponding tolambda. ONLY applicable whenmethod = "glasso" or"tiger".

cov

A list ofd byd estimated covariance matrices corresponding tolambda. ONLY applicable whencov.output = TRUE andmethod = "glasso"

method

The method used in the graph estimation stage.

df

Ifmethod = "mb" or"tiger", it is ak bynlambda matrix. Each row contains the number of nonzero coefficients along the lasso solution path. Ifmethod = "glasso", it is anlambda dimensional vector containing the number of nonzero coefficients along the graph pathicov.

loglik

Anlambda dimensional vector containing the likelihood scores along the graph path (icov). ONLY applicable whenmethod = "glasso". For an estimated inverse covariance Z, the program only calculates log(det(Z)) - trace(SZ) where S is the empirical covariance matrix. For the likelihood for n observations, please multiply by n/2.

Note

This function ONLY estimates the graph path. For more information about the optimal graph selection, please refer tohuge.select.

Examples

#generate dataL = huge.generator(n = 50, d = 12, graph = "hub", g = 4)#graph path estimation using mbout1 = huge(L$data)out1plot(out1)         #Not alignedplot(out1, align = TRUE) #Alignedhuge.plot(out1$path[[3]])#graph path estimation using the sample covariance matrix as the input.#out1 = huge(cor(L$data), method = "glasso")#out1#plot(out1)         #Not aligned#plot(out1, align = TRUE) #Aligned#huge.plot(out1$path[[3]])#graph path estimation using ct#out2 = huge(L$data,method = "ct")#out2#plot(out2)#graph path estimation using glasso#out3 = huge(L$data, method = "glasso")#out3#plot(out3)#graph path estimation using tiger#out4 = huge(L$data, method = "tiger")#out4#plot(out4)

Graph estimation via correlation thresholding (ct)

Description

See more details inhuge

Usage

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

Arguments

x

nlambda

The number of regularization/thresholding parameters. The default value is30 formethod = "ct" and10 formethod = "mb","glasso" or"tiger".

lambda.min.ratio

lambda

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Data generator

Description

Implements the data generation from multivariate normal distributions with different graph structures, including"random","hub","cluster","band" and"scale-free".

Usage

huge.generator(  n = 200,  d = 50,  graph = "random",  v = NULL,  u = NULL,  g = NULL,  prob = NULL,  vis = FALSE,  verbose = TRUE)

Arguments

n

The number of observations (sample size). The default value is200.

d

The number of variables (dimension). The default value is50.

graph

The graph structure with 4 options:"random","hub","cluster","band" and"scale-free".

v

The off-diagonal elements of the precision matrix, controlling the magnitude of partial correlations withu. The default value is0.3.

u

A positive number being added to the diagonal elements of the precision matrix, to control the magnitude of partial correlations. The default value is0.1.

g

For"cluster" or"hub" graph,g is the number of hubs or clusters in the graph. The default value is aboutd/20 ifd >= 40 and2 ifd < 40. For"band" graph,g is the bandwidth and the default value is1. NOT applicable to"random" graph.

prob

For"random" graph, it is the probability that a pair of nodes has an edge. The default value is3/d. For"cluster" graph, it is the probability that a pair of nodes has an edge in each cluster. The default value is6*g/d ifd/g <= 30 and0.3 ifd/g > 30. NOT applicable to"hub" or"band" graphs.

vis

Visualize the adjacency matrix of the true graph structure, the graph pattern, the covariance matrix and the empirical covariance matrix. The default value isFALSE

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Details

Given the adjacency matrixtheta, the graph patterns are generated as below:

(I)"random": Each pair of off-diagonal elements are randomly settheta[i,j]=theta[j,i]=1 fori!=j with probabilityprob, and0 other wise. It results in aboutd*(d-1)*prob/2 edges in the graph.

(II)"hub":The row/columns are evenly partitioned intog disjoint groups. Each group is associated with a "center" rowi in that group. Each pair of off-diagonal elements are settheta[i,j]=theta[j,i]=1 fori!=j ifj also belongs to the same group asi and0 otherwise. It results ind - g edges in the graph.

(III)"cluster":The row/columns are evenly partitioned intog disjoint groups. Each pair of off-diagonal elements are settheta[i,j]=theta[j,i]=1 fori!=j with the probabilityprobif bothi andj belong to the same group, and0 other wise. It results in aboutg*(d/g)*(d/g-1)*prob/2 edges in the graph.

(IV)"band": The off-diagonal elements are set to betheta[i,j]=1 if1<=|i-j|<=g and0 other wise. It results in(2d-1-g)*g/2 edges in the graph.

(V)"scale-free": The graph is generated using B-A algorithm. The initial graph has two connected nodes and each new node is connected to only one node in the existing graph with the probability proportional to the degree of the each node in the existing graph. It results ind edges in the graph.

The adjacency matrixtheta has all diagonal elements equal to0. To obtain a positive definite precision matrix, the smallest eigenvalue oftheta*v (denoted bye) is computed. Then we set the precision matrix equal totheta*v+(|e|+0.1+u)I. The covariance matrix is then computed to generate multivariate normal data.

Value

An object with S3 class "sim" is returned:

data

Then byd matrix for the generated data

sigma

The covariance matrix for the generated data

omega

The precision matrix for the generated data

sigmahat

The empirical covariance matrix for the generated data

theta

The adjacency matrix of true graph structure (in sparse matrix representation) for the generated data

Examples

## band graph with bandwidth 3L = huge.generator(graph = "band", g = 3)plot(L)## random sparse graphL = huge.generator(vis = TRUE)## random dense graphL = huge.generator(prob = 0.5, vis = TRUE)## hub graph with 6 hubsL = huge.generator(graph = "hub", g = 6, vis = TRUE)## hub graph with 8 clustersL = huge.generator(graph = "cluster", g = 8, vis = TRUE)## scale-free graphsL = huge.generator(graph="scale-free", vis = TRUE)

The graphical lasso (glasso) using sparse matrix output

Description

See more details inhuge

Usage

huge.glasso(  x,  lambda = NULL,  lambda.min.ratio = NULL,  nlambda = NULL,  scr = NULL,  cov.output = FALSE,  verbose = TRUE)

Arguments

x

lambda

lambda.min.ratio

nlambda

The number of regularization/thresholding parameters. The default value is30 formethod = "ct" and10 formethod = "mb","glasso" or"tiger".

scr

Ifscr = TRUE, the lossy screening rule is applied to preselect the neighborhood before the graph estimation. The default value isFALSE. NOT applicable whenmethod = "ct", "mb", or "tiger".

cov.output

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Graph inference

Description

Implements the inference for high dimensional graphical models, including Gaussian and Nonparanormal graphical modelsWe consider the problems of testing the presence of a single edge and the hypothesis is that the edge is absent.

Usage

huge.inference(data, T, adj, alpha = 0.05, type = "Gaussian", method = "score")

Arguments

data

The inputn byd data matrix(n is the sample size andd is the dimension).

T

The estimated inverse of correlation matrix of the data.

adj

The adjacency matrix corresponding to the graph.

alpha

The significance level of hypothesis.The default value is0.05.

type

The type of input data. There are 2 options:"Gaussian" and"Nonparanormal". The default value is"Gaussian".

method

When using nonparanormal graphical model. Test method with 2 options:"score" and"wald". The default value is"score".

Details

For Nonparanormal graphical model we provide Score test method and Wald Test. However it is really slow for inferencing on Nonparanormal model, especially for large data.

Value

An object is returned:

data

Then byd data matrix from the input.

p

Thed byd p-value matrix of hypothesis.

error

The type I error of hypothesis at alpha significance level.

References

1.Q Gu, Y Cao, Y Ning, H Liu. Local and global inference for high dimensional nonparanormal graphical models.
2.J Jankova, S Van De Geer. Confidence intervals for high-dimensional inverse covariance estimation.Electronic Journal of Statistics, 2015.

Examples

#generate dataL = huge.generator(n = 50, d = 12, graph = "hub", g = 4)#graph path estimation using glassoest = huge(L$data, method = "glasso")#inference of Gaussian graphical model at 0.05 significance levelT = tail(est$icov, 1)[[1]]out1 = huge.inference(L$data, T, L$theta)#inference of Nonparanormal graphical model using score test at 0.05 significance levelT = tail(est$icov, 1)[[1]]out2 = huge.inference(L$data, T, L$theta, type = "Nonparanormal")#inference of Nonparanormal graphical model using wald test at 0.05 significance levelT = tail(est$icov, 1)[[1]]out3 = huge.inference(L$data, T, L$theta, type = "Nonparanormal", method = "wald")#inference of Nonparanormal graphical model using wald test at 0.1 significance levelT = tail(est$icov, 1)[[1]]out4 = huge.inference(L$data, T, L$theta, 0.1, type = "Nonparanormal", method = "wald")

Meinshausen & Buhlmann graph estimation

Description

See more details inhuge

Usage

huge.mb(  x,  lambda = NULL,  nlambda = NULL,  lambda.min.ratio = NULL,  scr = NULL,  scr.num = NULL,  idx.mat = NULL,  sym = "or",  verbose = TRUE)

Arguments

x

lambda

nlambda

The number of regularization/thresholding parameters. The default value is30 formethod = "ct" and10 formethod = "mb","glasso" or"tiger".

lambda.min.ratio

scr

Ifscr = TRUE, the lossy screening rule is applied to preselect the neighborhood before the graph estimation. The default value isFALSE. NOT applicable whenmethod = "ct", "mb", or "tiger".

scr.num

idx.mat

Index matrix for screening.

sym

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Nonparanormal(npn) transformation

Description

Implements the Gausianization to help relax the assumption of normality.

Usage

huge.npn(x, npn.func = "shrinkage", npn.thresh = NULL, verbose = TRUE)

Arguments

x

Then byd data matrix representingn observations ind dimensions

npn.func

The transformation function used in the npn transformation. Ifnpn.func = "truncation", the truncated ECDF is applied. Ifnpn.func = "shrinkage", the shrunken ECDF is applied. The default is"shrinkage". Ifnpn.func = "skeptic", the nonparanormal skeptic is applied.

npn.thresh

The truncation threshold used in nonparanormal transformation, ONLY applicable whennpn.func = "truncation". The default value is1/(4*(n^0.25)*sqrt(pi*log(n))).

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Details

The nonparanormal extends Gaussian graphical models to semiparametric Gaussian copula models.Motivated by sparse additive models, the nonparanormal method estimates the Gaussian copula by marginally transforming the variables using smooth functions.Computationally, the estimation of a nonparanormal transformation is very efficient and only requires one pass of the data matrix.

Value

data

Ad byd nonparanormal correlation matrix ifnpn.func = "skeptic", and An byd data matrix representingn observations ind transformed dimensions other wise.

Examples

# generate nonparanormal dataL = huge.generator(graph = "cluster", g = 5)L$data = L$data^5# transform the data using the shrunken ECDFQ = huge.npn(L$data)# transform the non-Gaussian data using the truncated ECDFQ = huge.npn(L$data, npn.func = "truncation")# transform the non-Gaussian data using the truncated ECDFQ = huge.npn(L$data, npn.func = "skeptic")

Graph visualization

Description

Implements the graph visualization using adjacency matrix. It can automatic organize 2D embedding layout.

Usage

huge.plot(  G,  epsflag = FALSE,  graph.name = "default",  cur.num = 1,  location = NULL)

Arguments

G

The adjacency matrix corresponding to the graph.

epsflag

Ifepsflag = TRUE, save the plot as an eps file in the target directory. The default value isFALSE.

graph.name

The name of the output eps files. The default value is "default".

cur.num

The number of plots saved as eps files. Only applicale whenepsflag = TRUE. The default value is 1.

location

Target directory. The default value is the current working directory.

Details

The user can changecur.num to plot several figures and select the best one. The implementation is based on the popular package "igraph".

Examples

## visualize the hub graphL = huge.generator(graph = "hub")huge.plot(L$theta)## visualize the band graphL = huge.generator(graph = "band",g=5)huge.plot(L$theta)## visualize the cluster graphL = huge.generator(graph = "cluster")huge.plot(L$theta)## plot 5 graphs and save the plots as eps files in the tempdir()huge.plot(L$theta, epsflag = TRUE, cur.num = 5, location = tempdir())

Draw ROC Curve for a graph path

Description

Draws ROC curve for a graph path according to the true graph structure.

Usage

huge.roc(path, theta, verbose = TRUE)

Arguments

path

A graph path.

theta

The true graph structure.

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Details

To avoid the horizontal oscillation, false positive rates is automatically sorted in the ascent order and true positive rates also follow the same order.

Value

An object with S3 class "roc" is returned:

F1

The F1 scores along the graph path.

tp

The true positive rates along the graph path

fp

The false positive rates along the graph paths

AUC

Area under the ROC curve

Note

For a lasso regression, the number of nonzero coefficients is at mostn-1. Ifd>>n, even when regularization parameter is very small, the estimated graph may still be sparse. In this case, the AUC may not be a good choice to evaluate the performance.

Examples

#generate dataL = huge.generator(d = 200, graph = "cluster", prob = 0.3)out1 = huge(L$data)#draw ROC curveZ1 = huge.roc(out1$path,L$theta)#Maximum F1 scoremax(Z1$F1)

Model selection for high-dimensional undirected graph estimation

Description

Implements the regularization parameter selection for high dimensional undirected graph estimation. The optional approaches are rotation information criterion (ric), stability approach to regularization selection (stars) and extended Bayesian information criterion (ebic).

Usage

huge.select(  est,  criterion = NULL,  ebic.gamma = 0.5,  stars.thresh = 0.1,  stars.subsample.ratio = NULL,  rep.num = 20,  verbose = TRUE)

Arguments

est

An object with S3 class"huge".

criterion

Model selection criterion."ric" and"stars" are available for all 3 graph estimation methods.ebic is only applicable whenest$method = "glasso" inhuge(). The default value is"ric".

ebic.gamma

The tuning parameter for ebic. The default value is 0.5. Only applicable whenest$method = "glasso" andcriterion = "ebic".

stars.thresh

The variability threshold in stars. The default value is0.1. An alternative value is0.05. Only applicable whencriterion = "stars".

stars.subsample.ratio

The subsampling ratio. The default value is10*sqrt(n)/n whenn>144 and0.8 whenn<=144, wheren is the sample size. Only applicable whencriterion = "stars".

rep.num

The number of subsamplings whencriterion = "stars" or rotations whencriterion = "ric". The default value is20. NOT applicable whencriterion = "ebic".

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Details

Stability approach to regularization selection (stars) is a natural way to select optimal regularization parameter for all three estimation methods. It selects the optimal graph by variability of subsamplings and tends to overselect edges in Gaussian graphical models. Besides selecting the regularization parameters, stars can also provide an additional estimated graph by merging the corresponding subsampled graphs using the frequency counts. The subsampling procedure in stars may NOT be very efficient, we also provide the recent developed highly efficient, rotation information criterion approach (ric). Instead of tuning over a grid by cross-validation or subsampling, we directly estimate the optimal regularization parameter based on random Rotations. However, ric usually has very good empirical performances but suffers from underselections sometimes. Therefore, we suggest if user are sensitive of false negative rates, they should either consider increasingr.num or applying the stars to model selection. Extended Bayesian information criterion (ebic) is another competitive approach, but theebic.gamma can only be tuned by experience.

Value

An object with S3 class "select" is returned:

refit

The optimal graph selected from the graph path

opt.icov

The optimal precision matrix from the path only applicable whenmethod = "glasso"

opt.cov

The optimal covariance matrix from the path only applicable whenmethod = "glasso" andest$cov is available.

merge

The graph path estimated by merging the subsampling paths. Only applicable when the inputcriterion = "stars".

variability

The variability along the subsampling paths. Only applicable when the inputcriterion = "stars".

ebic.scores

Extended BIC scores for regularization parameter selection. Only applicable whencriterion = "ebic".

opt.index

The index of the selected regularization parameter. NOT applicable when the inputcriterion = "ric"

opt.lambda

The selected regularization/thresholding parameter.

opt.sparsity

The sparsity level of"refit".

and anything else included in the inputest

Note

The model selection is NOT available when the data input is the sample covariance matrix.

Examples

#generate dataL = huge.generator(d = 20, graph="hub")out.mb = huge(L$data)out.ct = huge(L$data, method = "ct")out.glasso = huge(L$data, method = "glasso")#model selection using ricout.select = huge.select(out.mb)plot(out.select)#model selection using stars#out.select = huge.select(out.ct, criterion = "stars", stars.thresh = 0.05,rep.num=10)#plot(out.select)#model selection using ebicout.select = huge.select(out.glasso,criterion = "ebic")plot(out.select)

Tuning-insensitive graph estimation

Description

See more details inhuge

Usage

huge.tiger(  x,  lambda = NULL,  nlambda = NULL,  lambda.min.ratio = NULL,  sym = "or",  verbose = TRUE)

Arguments

x

lambda

nlambda

The number of regularization/thresholding parameters. The default value is30 formethod = "ct" and10 formethod = "mb","glasso" or"tiger".

lambda.min.ratio

sym

verbose

Ifverbose = FALSE, tracing information printing is disabled. The default value isTRUE.

Plot function for S3 class "huge"

Description

Plot sparsity level information and 3 typical sparse graphs from the graph path.

Usage

## S3 method for class 'huge'plot(x, align = FALSE, ...)

Arguments

x

An object with S3 class"huge"

align

Ifalign = FALSE, 3 plotted graphs are aligned

...

System reserved (No specific usage)

Plot function for S3 class "roc"

Description

Plot the ROC curve for an object with S3 class"roc".

Usage

## S3 method for class 'roc'plot(x, ...)

Arguments

x

An object with S3 class"roc"

...

System reserved (No specific usage)

Plot function for S3 class "select"

Description

Plot the optimal graph by model selection.

Usage

## S3 method for class 'select'plot(x, ...)

Arguments

x

An object with S3 class"select"

...

System reserved (No specific usage)

Plot function for S3 class "sim"

Description

Visualize the covariance matrix, the empirical covariance matrix, the adjacency matrix and the graph pattern of the true graph structure.

Usage

## S3 method for class 'sim'plot(x, ...)

Arguments

x

An object with S3 class"sim"

...

System reserved (No specific usage)

Print function for S3 class "huge"

Description

Print the information about the model usage, the graph path length, graph dimension, sparsity level.

Usage

## S3 method for class 'huge'print(x, ...)

Arguments

x

An object with S3 class"huge".

...

System reserved (No specific usage)

Print function for S3 class "roc"

Description

Print the information about true positive rates, false positive rates, the area under curve and maximum F1 score.

Usage

## S3 method for class 'roc'print(x, ...)

Arguments

x

An object with S3 class"roc".

...

System reserved (No specific usage)

Print function for S3 class "select"

Description

Print the information about the model usage, graph dimension, model selection criterion, sparsity level of the optimal graph.

Usage

## S3 method for class 'select'print(x, ...)

Arguments

x

An object with S3 class"select".

...

System reserved (No specific usage)

Print function for S3 class "sim"

Description

Print the information about the sample size, the dimension, the pattern and sparsity of the true graph structure.

Usage

## S3 method for class 'sim'print(x, ...)

Arguments

x

An object with S3 class"sim".

...

System reserved (No specific usage)

Stock price of S&P 500 companies from 2003 to 2008

Description

This data set consists of stock price and company information.

Usage

data(stockdata)

Format

The format is a list containing contains two matrices.1. data - 1258x452, represents the 452 stocks' close prices for 1258 trading days.2. info - 452x3:The 1st column: the query symbol for each company.The 2nd column: the category for each company.The 3rd column: the full name of each company.

Details

This data set can be used to perform high-dimensional graph estimation to analyze the relationships between S&P 500 companies.

Source

It was publicly available at finance.yahoo, which is now out of date

Examples

data(stockdata)image(stockdata$data)stockdata$info

Movatterモバイル変換

High-Dimensional Undirected Graph Estimation

Description

Details

Author(s)

References

See Also

High-dimensional undirected graph estimation

Description

Usage

Arguments

Details

Value

Note

See Also

Examples

Graph estimation via correlation thresholding (ct)

Description

Usage

Arguments

See Also

Data generator

Description

Usage

Arguments

Details

Value

See Also

Examples

The graphical lasso (glasso) using sparse matrix output

Description

Usage

Arguments

See Also

Graph inference

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Meinshausen & Buhlmann graph estimation

Description

Usage

Arguments

See Also

Nonparanormal(npn) transformation

Description

Usage

Arguments

Details

Value

See Also

Examples

Graph visualization

Description

Usage

Arguments

Details

See Also

Examples

Draw ROC Curve for a graph path

Description

Usage

Arguments

Details

Value

Note

See Also

Examples

Model selection for high-dimensional undirected graph estimation

Description

Usage

Arguments

Details

Value

Note

See Also