Help for package huge

Type:

Package

Title:

High-Dimensional Undirected Graph Estimation

Version:

2.0.0

Maintainer:

Tuo Zhao <tourzhao@gatech.edu>

Depends:

R (≥ 3.4.0)

Imports:

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

Suggests:

testthat (≥ 3.1.7)

LinkingTo:

Rcpp

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, the graphical lasso, or the TIGER (tuning-insensitive graph estimation and regression) method, and the first two 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

URL:

https://github.com/Gatech-Flash/huge

BugReports:

https://github.com/Gatech-Flash/huge/issues

Repository:

CRAN

NeedsCompilation:

yes

SystemRequirements:

C++17

RoxygenNote:

7.3.3

Encoding:

UTF-8

Packaged:

2026-07-25 00:52:04 UTC; tourzhao

Author:

Haoming Jiang [aut], Xinyu Fei [aut], Han Liu [aut], Kathryn Roeder [aut], John Lafferty [aut], Larry Wasserman [aut], Xingguo Li [aut], Tuo Zhao [aut, cre]

Date/Publication:

2026-07-26 16:30:07 UTC

High-Dimensional Undirected Graph Estimation

Description

A package for high-dimensional undirected graph estimation

Details

The package "huge" provides 9 main functions:
(1) the data generator creates random samples from multivariate normal distributions with different graph structures. Please refer to huge.generator.
(2) the nonparanormal (npn) transformation helps relax the normality assumption. Please refer to huge.npn.
(3) The correlation thresholding graph estimation. Please refer to huge.
(4) The Meinshausen-Buhlmann graph estimation. Please refer to huge.
(5) The graphical Lasso algorithm using lossless screening rule. Please refer to huge.
(6) The tuning-insensitive graph estimation (tiger). Please refer to huge.tiger.

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

Author(s)

Tuo Zhao, Han Liu, Haoming Jiang, Kathryn Roeder, John Lafferty, and Larry Wasserman
Maintainer: Tuo Zhao <tourzhao@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. Four 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,
  input.type = "auto"
)

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 the sample size and d is the dimension).

lambda

An optional numeric scalar or non-empty one-dimensional numeric path. For method = "mb", "glasso", or "tiger", values must be finite, strictly positive, and non-increasing; ties are allowed. For method = "ct", values must be finite and non-negative, zero is allowed, and thresholds are applied in the supplied order. Leave lambda = NULL to generate a path from nlambda and lambda.min.ratio.

nlambda

The number of regularization/thresholding parameters. The default value is 20 for method = "ct" and 10 for method = "mb", "glasso" or "tiger".

lambda.min.ratio

If method = "mb", "glasso" or "tiger", it is the smallest value for lambda, as a fraction of the upperbound (MAX) of the regularization/thresholding parameter which makes all estimates equal to 0. The program can automatically generate lambda as a sequence of length = nlambda starting from MAX to lambda.min.ratio*MAX in log scale. If method = "ct", it is 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.ratio evenly.The default value is 0.1 when method = "mb", "glasso" or "tiger", and 0.05 when method = "ct".

method

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

scr

If scr = TRUE, the lossy screening rule is applied to preselect the neighborhood before the graph estimation. The default value is FALSE. NOT applicable when method = "ct" or "tiger".

scr.num

The neighborhood size after the lossy screening rule (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 and method = "mb".

cov.output

If cov.output = TRUE, the output will include 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 take much memory under high-dimensional setting. The default value is FALSE.

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", the edge is selected when either node i or node j is selected as the neighbor for each other. The default value is "or". ONLY applicable when method = "mb" or "tiger".

verbose

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

input.type

How to interpret x: "auto" preserves symmetry-based detection, "data" forces an observation matrix, and "covariance" requires a square covariance or correlation matrix. Use "data" for square symmetric observation matrices. For glasso covariance input, "auto" retains the historical diagonal-sensitive default lambda scale; use "covariance" for a scale based only on off-diagonal entries. Glasso may accept an indefinite pairwise covariance estimate when regularization produces a certified positive-definite result; CT, MB, and TIGER require positive semidefiniteness.

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

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 d matrix with each column containing the indices of the remaining neighbors of the corresponding variable after the lossy screening. ONLY applicable when scr = TRUE.

lambda

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

sym

The sym from the input. ONLY applicable when method = "mb" or "tiger".

scr

The scr from the input. ONLY applicable when method = "mb" or "glasso".

path

A list of d by d adjacency matrices of estimated graphs as a graph path corresponding to lambda.

sparsity

The sparsity levels of the graph path.

icov

A list of d by d precision matrices as an alternative graph path (numerical path) corresponding to lambda. ONLY applicable when method = "glasso" or "tiger".

cov

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 = "mb" or "tiger", it is a d 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 icov.

loglik

A nlambda dimensional vector containing the likelihood scores along the graph path (icov). ONLY applicable when method = "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 to huge.select.

Examples

#generate data
L = huge.generator(n = 50, d = 12, graph = "hub", g = 4)

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

Graph estimation via correlation thresholding (ct)

Description

See more details in huge

Usage

huge.ct(
  x,
  nlambda = NULL,
  lambda.min.ratio = NULL,
  lambda = NULL,
  verbose = TRUE,
  input.type = "auto"
)

Arguments

x

nlambda

The number of regularization/thresholding parameters. The default value is 20 for method = "ct" and 10 for method = "mb", "glasso" or "tiger".

lambda.min.ratio

lambda

A numeric scalar or non-empty one-dimensional numeric input of finite, non-negative thresholds. Values are applied in the supplied order, and zero is allowed. Leave lambda = NULL to generate a path from nlambda and lambda.min.ratio.

verbose

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

input.type

How to interpret x: "auto" preserves symmetry-based detection, "data" forces an observation matrix, and "covariance" requires a square covariance or correlation matrix.

Details

The default path targets increasing numbers of undirected edges and defines each graph by the strict rule abs(correlation) > lambda. Equal-weight edges are never split, so ties can make the realized sparsity smaller than the nominal target. Reusing the returned lambda values therefore reconstructs the same path. When lambda = NULL, nlambda must be a positive integer and lambda.min.ratio must lie in (0, 1]. Supplying lambda overrides those two arguments.

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), as an integer of at least 2. The default value is 200.

d

The positive integer number of variables (dimension). The default value is 50.

graph

The graph structure with 5 options: "random", "hub", "cluster", "band" and "scale-free".

v

A finite positive number used for the off-diagonal elements of the precision matrix, controlling the magnitude of partial correlations with u. The default value is 0.3.

u

A finite positive number added to the diagonal elements of the precision matrix to control the magnitude of partial correlations. The default value is 0.1.

g

A finite positive integer. For "cluster" or "hub" graph, g is the number of clusters or hubs; values above d are treated as d. The default is about d/20 if d >= 40 and min(2, d) otherwise. For "band" graph, g is the bandwidth and defaults to 1; values above d - 1 add no edges. Not applicable to "random" or "scale-free" graph.

prob

For "random" or "cluster" graph, a finite number in [0, 1] giving the probability that a pair of nodes has an edge. The default is min(1, 3/d) for "random". For "cluster", the default is min(1, 6*g/d) if d/g <= 30 and 0.3 otherwise. Not applicable to "hub", "band", or "scale-free" graph.

vis

A single non-missing logical. If TRUE, visualize the adjacency matrix, graph pattern, covariance matrix, and empirical correlation matrix. The default is FALSE.

verbose

A single non-missing logical. If FALSE, tracing output is disabled. The default is TRUE.

Details

Given the adjacency matrix theta, the graph patterns are generated as below:

(I) "random": Each pair of off-diagonal elements are randomly set theta[i,j]=theta[j,i]=1 for i!=j with probability prob, and 0 otherwise. It results in about d*(d-1)*prob/2 edges in the graph.

(II)"hub":The row/columns are evenly partitioned into g disjoint groups. Each group is associated with a "center" row i in that group. Each pair of off-diagonal elements are set theta[i,j]=theta[j,i]=1 for i!=j if j also belongs to the same group as i and 0 otherwise. It results in d - g edges in the graph.

(III)"cluster":The row/columns are evenly partitioned into g disjoint groups. Each pair of off-diagonal elements are set theta[i,j]=theta[j,i]=1 for i!=j with the probability probif both i and j belong to the same group, and 0 otherwise. It results in about g*(d/g)*(d/g-1)*prob/2 edges in the graph.

(IV)"band": Let b=min(g,d-1). The off-diagonal elements are set to be theta[i,j]=1 if 1<=|i-j|<=b and 0 otherwise. It results in (2d-1-b)*b/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 in d-1 edges for d>=2; for d=1, the graph is empty.

The adjacency matrix theta has all diagonal elements equal to 0. To obtain a positive definite precision matrix, the smallest eigenvalue of theta*v (denoted by e) is computed. Then we set the precision matrix equal to theta*v+(|e|+0.1+u)I. The covariance matrix is then computed to generate multivariate normal data. Every graph type returns an empty graph with zero sparsity when d=1.

Value

An object with S3 class "sim" is returned:

data

The n by d matrix for the generated data

sigma

The covariance matrix for the generated data

omega

The precision matrix for the generated data

sigmahat

The empirical correlation matrix for the generated data

theta

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

sparsity

The proportion of possible off-diagonal entries present in the graph; zero when d=1

Examples

## band graph with bandwidth 3
L = huge.generator(graph = "band", g = 3)
plot(L)

## random sparse graph
L = huge.generator(vis = TRUE)

## random dense graph
L = huge.generator(prob = 0.5, vis = TRUE)

## hub graph with 6 hubs
L = huge.generator(graph = "hub", g = 6, vis = TRUE)

## hub graph with 8 clusters
L = huge.generator(graph = "cluster", g = 8, vis = TRUE)

## scale-free graphs
L = huge.generator(graph="scale-free", vis = TRUE)

The graphical lasso (glasso) using sparse matrix output

Description

See more details in huge

Usage

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

Arguments

x

lambda

A numeric scalar or non-empty one-dimensional numeric input defining a finite, strictly positive, non-increasing regularization path; tied values are allowed. Leave lambda = NULL to generate a path from nlambda and lambda.min.ratio.

lambda.min.ratio

nlambda

The number of regularization/thresholding parameters. The default value is 20 for method = "ct" and 10 for method = "mb", "glasso" or "tiger".

scr

If scr = TRUE, the lossy screening rule is applied to preselect the neighborhood before the graph estimation. The default value is FALSE.

cov.output

verbose

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

input.type

How to interpret x: "auto" preserves symmetry-based detection, "data" forces an observation matrix, and "covariance" requires a square covariance or correlation matrix. For covariance input with lambda = NULL, "auto" retains the historical diagonal-sensitive lambda scale; use "covariance" for a scale based only on off-diagonal entries. Indefinite pairwise covariance estimates are accepted only when regularization produces a certified positive-definite result.

Graph inference

Description

Implements the inference for high dimensional graphical models, including Gaussian and Nonparanormal graphical models We 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

A finite numeric n by d data matrix with at least two observations and no constant columns.

T

A finite d by d estimate of the inverse correlation matrix with a positive diagonal.

adj

A finite numeric or logical d by d adjacency matrix corresponding to the graph.

alpha

The significance level in (0, 1]. The default value is 0.05.

type

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

method

For a Nonparanormal model, the test method: "score" or "wald". The default is "score". Ignored for Gaussian inference.

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. Gaussian inference supports one variable, while Nonparanormal inference requires at least two. Nonparanormal score-test diagonal p-values do not represent edges and may be undefined; every tested off-diagonal p-value must be finite.

Value

An object is returned:

data

The n by d data matrix from the input.

p

The d by d 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 data
L = huge.generator(n = 50, d = 12, graph = "hub", g = 4)

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

#inference of Gaussian graphical model at 0.05 significance level
T = 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 level
T = 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 level
T = 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 level
T = 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 in huge

Usage

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

Arguments

x

lambda

nlambda

The number of regularization/thresholding parameters. The default value is 20 for method = "ct" and 10 for method = "mb", "glasso" or "tiger".

lambda.min.ratio

scr

If scr = TRUE, the lossy screening rule is applied to preselect the neighborhood before the graph estimation. The default value is FALSE.

scr.num

The neighborhood size after the lossy screening rule (the number of remaining neighbors per node). It must be an integer between 1 and d - 1. ONLY applicable when scr = TRUE. The default value is n-1. An alternative value is n/log(n). ONLY applicable when scr = TRUE and method = "mb".

idx.mat

A scr.num by d index matrix for screening. Column m must contain distinct, zero-based indices in 0:(d - 1) and must exclude the response index m - 1.

sym

verbose

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

input.type

How to interpret x: "auto" preserves symmetry-based detection, "data" forces an observation matrix, and "covariance" requires a square covariance or correlation matrix.

Nonparanormal(npn) transformation

Description

Implements the Gaussianization to help relax the assumption of normality.

Usage

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

Arguments

x

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

npn.func

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

npn.thresh

The truncation threshold used in nonparanormal transformation, ONLY applicable when npn.func = "truncation". The default value is 1/(4*(n^0.25)* sqrt(pi*log(n))).

verbose

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

na.last

for controlling the treatment of NAs. If TRUE, missing values in the data are put last; if FALSE, they are put first; if NA, they are removed; if "keep" they are kept with rank NA. See also rank.

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

A d by d nonparanormal correlation matrix if npn.func = "skeptic", and A n by d data matrix representing n observations in d transformed dimensions otherwise.

Examples

# generate nonparanormal data
L = huge.generator(graph = "cluster", g = 5)
L$data = L$data^5

# transform the data using the shrunken ECDF
Q = huge.npn(L$data)

# transform the non-Gaussian data using the truncated ECDF
Q = huge.npn(L$data, npn.func = "truncation")

# estimate the nonparanormal correlation matrix using the skeptic estimator
Q = 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

If epsflag = TRUE, save the plot as an eps file in the target directory. The default value is FALSE.

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 when epsflag = TRUE. The default value is 1.

location

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

Details

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

Examples

## visualize the hub graph
L = huge.generator(graph = "hub")
huge.plot(L$theta)

## visualize the band graph
L = huge.generator(graph = "band",g=5)
huge.plot(L$theta)

## visualize the cluster graph
L = 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, containing at least one edge and one absent off-diagonal edge.

verbose

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

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

ROC/AUC is undefined when theta contains only edges or only non-edges, so those one-class truth matrices are rejected. For a lasso regression, the number of nonzero coefficients is at most n-1. If d>>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 data
L = huge.generator(d = 200, graph = "cluster", prob = 0.3)
out1 = huge(L$data)

#draw ROC curve
Z1 = huge.roc(out1$path,L$theta)

#Maximum F1 score
max(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,
  num.cores = 1
)

Arguments

est

An object with S3 class "huge".

criterion

Model selection criterion. "ric" is available for all four estimation methods, "stars" for "mb", "ct", and "glasso", and "ebic" only for "glasso". Defaults are "ric" for "mb" and "tiger", "stars" for "ct", and "ebic" for "glasso".

ebic.gamma

The tuning parameter for ebic. The default value is 0.5. Only applicable when est$method = "glasso" and criterion = "ebic".

stars.thresh

The variability threshold in stars. The default value is 0.1. An alternative value is 0.05. Only applicable when criterion = "stars".

stars.subsample.ratio

The subsampling ratio. The default value is 10*sqrt(n)/n when n>144 and 0.8 when n<=144, where n is the sample size. Only applicable when criterion = "stars".

rep.num

The number of subsamplings when criterion = "stars" or rotations when criterion = "ric". The default value is 20. NOT applicable when criterion = "ebic".

verbose

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

num.cores

The number of CPU cores used to fit the stars subsamplings in parallel via parallel::mclapply. The default value is 1 (serial). At most two forked workers are used, and this argument is ignored on Windows. Each forked worker limits huge's native OpenMP code to one thread, but an external threaded BLAS may still create additional threads; num.cores = 1 is the portable choice when a bounded thread budget or fork safety matters. Results are identical to the serial path for the same random seed. Only applicable when criterion = "stars".

Details

Stability approach to regularization selection (stars) selects the optimal graph by variability of subsamplings and tends to overselect edges in Gaussian graphical models. It is available for "mb", "ct", and "glasso". TIGER can certify different lambda-path prefixes on different subsamples, so TIGER with stars is rejected until a common certified-prefix protocol is available; use "ric" for TIGER. 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 increasing rep.num or applying the stars to model selection where supported. Extended Bayesian information criterion (ebic) is another competitive approach, but the ebic.gamma can only be tuned by experience.

For criterion = "stars", est$lambda must be non-increasing; tied values are allowed.

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 when method = "glasso"

opt.cov

The optimal covariance matrix from the path only applicable when method = "glasso" and est$cov is available.

merge

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

variability

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

ebic.score

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

opt.index

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

opt.lambda

The selected regularization/thresholding parameter.

opt.sparsity

The sparsity level of "refit".

and anything else included in the input est

Note

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

Examples

#generate data
L = 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 ric
out.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 ebic
out.select = huge.select(out.glasso,criterion = "ebic")
plot(out.select)

Tuning-insensitive graph estimation

Description

See more details in huge

Usage

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

Arguments

x

lambda

A numeric scalar or non-empty one-dimensional numeric input defining a finite, strictly positive, non-increasing regularization path. Tied values are allowed. Leave lambda = NULL to generate the path from nlambda and lambda.min.ratio in C++.

nlambda

The number of regularization/thresholding parameters. The default value is 20 for method = "ct" and 10 for method = "mb", "glasso" or "tiger".

lambda.min.ratio

sym

verbose

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

input.type

Details

Raw observations are centered and normalized, while covariance input is converted to a correlation matrix, inside the shared C++ core. When lambda = NULL, the same native correlation matrix determines the returned default lambda path. A user-supplied path must be finite, strictly positive, and non-increasing; tied values are allowed and are used unchanged. If smaller generated values cannot be certified to the solver's KKT tolerance, the function warns and returns the longest certified path prefix. A user-supplied value that cannot be certified raises an error.

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

If align = TRUE, 3 plotted graphs are aligned to the same sparsity levels. The default value is FALSE.

...

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 correlation 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

Package {huge}

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

Details

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