Package 'flare' reference manual

Title:	Family of Lasso Regression
Description:	Provides implementations of a family of Lasso variants, including Dantzig Selector, LAD Lasso, SQRT Lasso, and Lq Lasso, for estimating high-dimensional sparse linear models. We adopt the alternating direction method of multipliers and convert the original optimization problem into a sequence of L1-penalized least-squares minimization problems that are efficiently solved by linearization and multi-stage screening. In addition to sparse linear model estimation, we provide extensions of these methods to sparse Gaussian graphical model estimation, including TIGER and CLIME, using either L1 or adaptive penalties. Missing values can be tolerated for Dantzig selector and CLIME. Computation is memory-optimized using sparse matrix output. For more information, see <https://www.jmlr.org/papers/volume16/li15a/li15a.pdf>.
Authors:	Xingguo Li [aut], Tuo Zhao [aut, cre], Lie Wang [aut], Xiaoming Yuan [aut], Han Liu [aut]
Maintainer:	Tuo Zhao <[email protected]>
License:	GPL-2
Version:	1.8
Built:	2026-05-21 06:44:38 UTC
Source:	https://github.com/cran/flare

flare: A Family of Lasso Regression Methods

Description

The package "flare" provides a family of regression methods (Lasso, Dantzig Selector, LAD Lasso, SQRT Lasso, and Lq Lasso) and their extensions to sparse precision matrix estimation (TIGER and CLIME using L1) in high dimensions. We adopt the alternating direction method of multipliers and convert the original optimization problem into a sequence of L1-penalized least squares minimization problems with linearization and multi-stage screening of variables. Missing values can be tolerated for Dantzig selector in the design matrix and response vector, and for CLIME in the data matrix. Computation is memory-optimized using sparse matrix output. In addition, we provide convenient tools for regularization parameter selection and visualization.

Details

Package:	flare
Type:	Package
Version:	1.8
Date:	2026-02-19
License:	GPL-2

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang , Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

References

1. E. Candes and T. Tao. The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics, 2007.
2. A. Belloni, V. Chernozhukov and L. Wang. Pivotal recovery of sparse signals via conic programming. Biometrika, 2012.
3. L. Wang. L1 penalized LAD estimator for high dimensional linear regression. Journal of Multivariate Analysis, 2012.
4. J. Liu and J. Ye. Efficient L1/Lq Norm Regularization. Technical Report, 2010.
5. T. Cai, W. Liu and X. Luo. A constrained $\ell_1$ minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011.
6. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning, 2011.
7. H. Liu and L. Wang. TIGER: A tuning-insensitive approach for optimally estimating large undirected graphs. Technical Report, 2012.
8. B. He and X. Yuan. On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers. Technical Report, 2012.

Extract Model Coefficients for an object with S3 class `"slim"`

Description

Extract estimated regression coefficient vectors from the solution path.

Usage

## S3 method for class 'slim'
coef(object, lambda.idx = c(1:3), beta.idx = c(1:3), ...)
## S3 method for class 'slim'
coef(object, lambda.idx = c(1:3), beta.idx = c(1:3), ...)

Arguments

object

An object with S3 class "slim"

lambda.idx

The indices of the regularization parameters in the solution path to display. The default values are c(1:3).

beta.idx

The indices of estimated regression coefficient vectors in the solution path to display. The default values are c(1:3).

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

The Bardet-Biedl syndrome Gene expression data from Scheetz et al. (2006)

Description

Gene expression data (20 genes for 120 samples) from the microarray experiments of mammalianeye tissue samples of Scheetz et al. (2006).

Usage

data(eyedata)data(eyedata)

Format

The format is a list containing conatins a matrix and a vector. 1. x - an 120 by 200 matrix, which represents the data of 120 rats with 200 gene probes. 2. y - a 120-dimensional vector of, which represents the expression level of TRIM32 gene.

Details

This data set contains 120 samples with 200 predictors

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

References

1. T. Scheetz, k. Kim, R. Swiderski, A. Philp, T. Braun, K. Knudtson, A. Dorrance, G. DiBona, J. Huang, T. Casavant, V. Sheffield, E. Stone .Regulation of gene expression in the mammalian eye and its relevance to eye disease. Proceedings of the National Academy of Sciences of the United States of America, 2006.

Examples

data(eyedata)
image(x)
data(eyedata)
image(x)

Internal flare functions

Description

Internal flare functions

Usage

sugm.likelihood(Sigma, Omega)
sugm.tracel2(Sigma, Omega)
sugm.cv(obj, loss=c("likelihood", "tracel2"), fold=5)
part.cv(n, fold)
sugm.clime.ladm.scr(Sigma, lambda, nlambda, n, d, maxdf, rho, shrink, prec, 
                    max.ite, verbose)
sugm.tiger.ladm.scr(data, n, d, maxdf, rho, lambda, shrink, prec, 
                    max.ite, verbose)
slim.lad.ladm.scr.btr(Y, X, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                      intercept, verbose)
slim.sqrt.ladm.scr(Y, X, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                   intercept, verbose)
slim.dantzig.ladm.scr(Y, X, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                      intercept, verbose)
slim.lq.ladm.scr.btr(Y, X, q, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                     intercept, verbose)
slim.lasso.ladm.scr(Y, X, lambda, nlambda, n, d, maxdf, max.ite, prec, 
                    intercept, verbose)
sugm.likelihood(Sigma, Omega)
sugm.tracel2(Sigma, Omega)
sugm.cv(obj, loss=c("likelihood", "tracel2"), fold=5)
part.cv(n, fold)
sugm.clime.ladm.scr(Sigma, lambda, nlambda, n, d, maxdf, rho, shrink, prec, 
                    max.ite, verbose)
sugm.tiger.ladm.scr(data, n, d, maxdf, rho, lambda, shrink, prec, 
                    max.ite, verbose)
slim.lad.ladm.scr.btr(Y, X, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                      intercept, verbose)
slim.sqrt.ladm.scr(Y, X, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                   intercept, verbose)
slim.dantzig.ladm.scr(Y, X, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                      intercept, verbose)
slim.lq.ladm.scr.btr(Y, X, q, lambda, nlambda, n, d, maxdf, rho, max.ite, prec, 
                     intercept, verbose)
slim.lasso.ladm.scr(Y, X, lambda, nlambda, n, d, maxdf, max.ite, prec, 
                    intercept, verbose)

Arguments

Sigma

Covariance matrix.

Omega

Inverse covariance matrix.

obj

An object with S3 class returned from "sugm".

loss

Type of loss function for cross-validation.

fold

The number of folds for cross-validation.

n

The number of observations (sample size).

d

Dimension of data.

maxdf

Maximal degree of freedom.

lambda

Grid of positive values for the regularization parameter lambda.

nlambda

The number of the regularization parameter lambda.

shrink

Shrinkage of regularization parameter based on precision of estimation.

rho

Value of augmented Lagrangian multiplier.

prec

Stopping criterion.

max.ite

Maximal value of iterations.

data

n by d data matrix.

Y

Dependent variables in linear regression.

X

Design matrix in linear regression.

q

The vector norm used for the loss term.

intercept

Indicator of whether to include intercepts.

verbose

Tracing information printing is disabled if verbose = FALSE. The default value is TRUE.

Details

These are not intended for use by users.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Plot Function for "roc"

Description

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

Usage

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

Arguments

x

An object with S3 class "roc"

...

System reserved (No specific usage)

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Plot Function for "select"

Description

Plot the optimal graph by model selection.

Usage

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

Arguments

x

An object with S3 class "select"

...

System reserved (No specific usage)

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

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

Arguments

x

An object with S3 class "sim"

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Plot Function for "slim"

Description

Visualize the solution path of regression estimates corresponding to regularization parameters.

Usage

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

Arguments

x

An object with S3 class "slim".

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Plot Function for "sugm"

Description

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

Usage

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

Arguments

x

An object with S3 class "sugm"

align

If align = TRUE, the three plotted graphs are aligned.

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Prediction for an object with S3 class `"slim"`

Description

Predict responses for new design data.

Usage

## S3 method for class 'slim'
predict(object, newdata, lambda.idx = c(1:3), Y.pred.idx = c(1:5), ...)
## S3 method for class 'slim'
predict(object, newdata, lambda.idx = c(1:3), Y.pred.idx = c(1:5), ...)

Arguments

object

An object with S3 class "slim"

newdata

A matrix or data frame containing predictors used for prediction.

lambda.idx

The indices of regularization parameters in the solution path to display. The default values are c(1:3).

Y.pred.idx

The indices of the predicted response vectors in the solution path to be displayed. The default values are c(1:5).

...

Arguments to be passed to methods.

Details

predict.slim produces predicted values of the responses of the newdata from the estimated beta values in the object, i.e.

$\hat{Y} = \hat{\beta}_0 + X_{new} \hat{\beta}.$

Value

Y.pred

A matrix of predicted response values based on the selected models.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Examples

## load library
library(flare)
## generate data
set.seed(123)
n = 100
d = 200
d1 = 10
rho0 = 0.3
lambda = c(3:1)*sqrt(log(d)/n)
Sigma = matrix(0,nrow=d,ncol=d)
Sigma[1:d1,1:d1] = rho0
diag(Sigma) = 1
mu = rep(0,d)
X = mvrnorm(n=2*n,mu=mu,Sigma=Sigma)
X.fit = X[1:n,]
X.pred = X[(n+1):(2*n),]
eps = rt(n=n,df=n-1)
beta = c(rep(sqrt(1/3),3),rep(0,d-3))
Y.fit = X.fit%*%beta+eps

## Regression with "dantzig".
out=slim(X=X.fit,Y=Y.fit,lambda=lambda,method = "lq",q=1)

## Display results
Y=predict(out,X.pred)
## load library
library(flare)
## generate data
set.seed(123)
n = 100
d = 200
d1 = 10
rho0 = 0.3
lambda = c(3:1)*sqrt(log(d)/n)
Sigma = matrix(0,nrow=d,ncol=d)
Sigma[1:d1,1:d1] = rho0
diag(Sigma) = 1
mu = rep(0,d)
X = mvrnorm(n=2*n,mu=mu,Sigma=Sigma)
X.fit = X[1:n,]
X.pred = X[(n+1):(2*n),]
eps = rt(n=n,df=n-1)
beta = c(rep(sqrt(1/3),3),rep(0,d-3))
Y.fit = X.fit%*%beta+eps

## Regression with "dantzig".
out=slim(X=X.fit,Y=Y.fit,lambda=lambda,method = "lq",q=1)

## Display results
Y=predict(out,X.pred)

Print Function for an object with S3 class `"roc"`

Description

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

Usage

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

Arguments

x

An object with S3 class "roc"

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Print Function for an object with S3 class `"select"`

Description

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

Usage

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

Arguments

x

An object with S3 class "select"

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Print Function for an object with 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, ...)
## S3 method for class 'sim'
print(x, ...)

Arguments

x

An object with S3 class "sim".

...

Arguments to be passed to methods.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Print Function for an object with S3 class `"slim"`

Description

Print a summary of the information about an object with S3 class "slim".

Usage

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

Arguments

x

An object with S3 class "slim".

...

Arguments to be passed to methods.

Details

This call simply outlines the options used for computing a slim object.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Print Function for an object with S3 class `"sugm"`

Description

Print a summary of information about an object with S3 class "sugm".

Usage

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

Arguments

x

An object with S3 class "sugm".

...

Arguments to be passed to methods.

Details

This call simply outlines the options used for computing a sugm object.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Sparse Linear Regression using Nonsmooth Loss Functions and L1 Regularization

Description

The function "slim" implements a family of Lasso variants for estimating high-dimensional sparse linear models, including Dantzig Selector, LAD Lasso, SQRT Lasso, and Lq Lasso. We adopt the alternating direction method of multipliers (ADMM) and convert the original optimization problem into a sequence of L1-penalized least squares minimization problems, which can be efficiently solved by combining linearization and multi-stage screening of variables. Missing values can be tolerated for Dantzig selector in the design matrix and response vector.

Usage

slim(X, Y, lambda = NULL, nlambda = NULL, 
     lambda.min.value = NULL, lambda.min.ratio = NULL, 
     rho = 1, method="lq", q = 2, res.sd = FALSE, 
     prec = 1e-5, max.ite = 1e5, verbose = TRUE)
slim(X, Y, lambda = NULL, nlambda = NULL, 
     lambda.min.value = NULL, lambda.min.ratio = NULL, 
     rho = 1, method="lq", q = 2, res.sd = FALSE, 
     prec = 1e-5, max.ite = 1e5, verbose = TRUE)

Arguments

Y

The $n$ -dimensional response vector.

X

The $n$ by $d$ design matrix.

lambda

A sequence of decreasing, positive, finite numbers controlling regularization. Typical usage is to leave lambda = NULL and let the program compute the sequence based on nlambda, lambda.min.value, and lambda.min.ratio.

nlambda

The number of values used in lambda. Default value is 5.

lambda.min.value

The minimum value in the generated lambda sequence when lambda is not supplied. The default is $\sqrt{\log(d)/n}$ for non-Dantzig methods.

lambda.min.ratio

A multiplier for lambda.max used to generate lambda.min.value when method = "dantzig" and lambda.min.value is not provided. The default is 0.5 for Dantzig selector.

rho

The penalty parameter used in ADMM. The default value is 1.

method

Dantzig selector is applied if method = "dantzig" and $L_q$ Lasso is applied if method = "lq". Standard Lasso is provided if method = "lasso". The default value is "lq".

q

The loss function used in Lq Lasso. It is only applicable when method = "lq" and must be in [1,2]. The default value is 2.

res.sd

Whether the response variable is standardized. The default value is FALSE.

prec

Stopping criterion. The default value is 1e-5.

max.ite

The iteration limit. The default value is 1e5.

verbose

Tracing information printing is disabled if verbose = FALSE. The default value is TRUE.

Details

Standard Lasso

$\min {\frac{1}{2n}}|| Y - X \beta ||_2^2 + \lambda || \beta ||_1$

Dantzig selector solves the following optimization problem

$\min || \beta ||_1, \quad \textrm{s.t. } || X'(Y - X \beta) ||_{\infty} < \lambda$

$L_q$ loss Lasso solves the following optimization problem

$\min n^{-\frac{1}{q}}|| Y - X \beta ||_q + \lambda || \beta ||_1$

where $1<= q <=2$ . Lq Lasso is equivalent to LAD Lasso and SQRT Lasso when $q=1$ and $q=2$ , respectively.

Value

An object with S3 class "slim" is returned:

beta

A matrix of regression estimates whose columns correspond to regularization parameters.

intercept

The value of intercepts corresponding to regularization parameters.

Y

The value of Y used in the program.

X

The value of X used in the program.

lambda

The sequence of regularization parameters lambda used in the program.

nlambda

The number of values used in lambda.

method

The method from the input.

df

The number of nonzero coefficients at each value of lambda.

ite

Iteration counts returned by the underlying optimization solver.

verbose

The verbose from the input.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

References

1. E. Candes and T. Tao. The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics, 2007.
2. A. Belloni, V. Chernozhukov and L. Wang. Pivotal recovery of sparse signals via conic programming. Biometrika, 2012.
3. L. Wang. L1 penalized LAD estimator for high dimensional linear regression. Journal of Multivariate Analysis, 2012.
4. J. Liu and J. Ye. Efficient L1/Lq Norm Regularization. Technical Report, 2010.
5. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning, 2011.
6. B. He and X. Yuan. On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers. Technical Report, 2012.

Examples

## load library
library(flare)
## generate data
n = 50
d = 100
X = matrix(rnorm(n*d), n, d)
beta = c(3,2,0,1.5,rep(0,d-4))
eps = rnorm(n)
Y = X%*%beta + eps
nlamb = 5
ratio = 0.3

## Regression with "dantzig", general "lq" and "lasso" respectively
out1 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="dantzig")
out2 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lq",q=1)
out3 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lq",q=1.5)
out4 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lq",q=2)
out5 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lasso")

## Display results
print(out4)
plot(out4)
coef(out4)
## load library
library(flare)
## generate data
n = 50
d = 100
X = matrix(rnorm(n*d), n, d)
beta = c(3,2,0,1.5,rep(0,d-4))
eps = rnorm(n)
Y = X%*%beta + eps
nlamb = 5
ratio = 0.3

## Regression with "dantzig", general "lq" and "lasso" respectively
out1 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="dantzig")
out2 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lq",q=1)
out3 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lq",q=1.5)
out4 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lq",q=2)
out5 = slim(X=X,Y=Y,nlambda=nlamb,lambda.min.ratio=ratio,method="lasso")

## Display results
print(out4)
plot(out4)
coef(out4)

High-dimensional Sparse Undirected Graphical Models

Description

The function "sugm" estimates sparse undirected graphical models (Gaussian precision matrices) in high dimensions. Two procedures are implemented using a column-wise regression scheme: (1) Tuning-Insensitive Graph Estimation and Regression based on square-root Lasso ("tiger"); and (2) The Constrained L1 Minimization for Sparse Precision Matrix Estimation ("clime"). The optimization algorithm is based on the alternating direction method of multipliers (ADMM), linearization, and multi-stage screening. Missing values can be tolerated for CLIME when the input is a data matrix. Computation is memory-optimized using sparse matrix output.

Usage

sugm(data, lambda = NULL, nlambda = NULL, lambda.min.ratio = NULL, 
     rho = NULL, method = "tiger", sym = "or", shrink = NULL, 
     prec = 1e-4, max.ite = 1e4, standardize = FALSE, 
     perturb = TRUE, verbose = TRUE)
sugm(data, lambda = NULL, nlambda = NULL, lambda.min.ratio = NULL, 
     rho = NULL, method = "tiger", sym = "or", shrink = NULL, 
     prec = 1e-4, max.ite = 1e4, standardize = FALSE, 
     perturb = TRUE, verbose = TRUE)

Arguments

data

There are two options for "clime": (1) an n by d data matrix, or (2) a d by d sample covariance matrix. The input type is identified by symmetry. For "tiger", covariance input is not supported and d $\ge$ 3 is required. For "clime", d $\ge$ 2 is required.

lambda

A sequence of decreasing, positive, finite numbers controlling regularization. Typical usage is lambda = NULL, in which case the sequence is generated from nlambda and lambda.min.ratio.

nlambda

The number of values used in lambda. Default value is 5.

lambda.min.ratio

The minimum value of generated lambda as a fraction of lambda.max. The default value is 0.4 for both "tiger" and "clime".

rho

Penalty parameter used in the optimization algorithm. The default value is 1.

method

"tiger" is applied if method = "tiger" and "clime" is applied if method="clime". Default value is "tiger".

sym

Symmetrization of 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".

shrink

Shrinkage of the regularization parameter based on estimation precision. The default value is 0.

prec

Stopping criterion. The default value is 1e-4.

max.ite

The iteration limit. The default value is 1e4.

standardize

Variables are standardized to have mean zero and unit standard deviation if standardize = TRUE. The default value is FALSE.

perturb

For "clime", if TRUE, adds $1/\sqrt{n}$ to the diagonal of Sigma; if FALSE, no perturbation is added; a numeric value can also be supplied directly. The default value is TRUE.

verbose

Tracing information printing is disabled if verbose = FALSE. The default value is TRUE.

Details

CLIME solves the following minimization problem

$\min || \Omega ||_1 \quad \textrm{s.t. } || S \Omega - I ||_\infty \le \lambda,$

where $||\cdot||_1$ and $||\cdot||_\infty$ are element-wise 1-norm and $\infty$ -norm respectively.

"tiger" solves the following minimization problem

$\min ||X-XB||_{2,1} + \lambda ||B||_1 \quad \textrm{s.t. } B_{jj} = 0,$

where $||\cdot||_{1}$ and $||\cdot||_{2,1}$ are element-wise 1-norm and $L_{2,1}$ -norm respectively.

Value

An object with S3 class "sugm" 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.

lambda

The sequence of regularization parameters lambda used in the program.

nlambda

The number of values used in lambda.

icov

A list of d by d precision matrices corresponding to regularization parameters.

sym

The sym from the input.

method

The method from the input.

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.

ite

Iteration counts returned by the underlying optimization solver.

df

A d by nlambda matrix containing nonzero counts along the estimated path.

standardize

The standardize from the input.

perturb

The perturb from the input.

verbose

The verbose from the input.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

References

1. T. Cai, W. Liu and X. Luo. A constrained L1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011.
2. H. Liu, L. Wang. TIGER: A tuning-insensitive approach for optimally estimating large undirected graphs. Technical Report, 2012.
3. B. He and X. Yuan. On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers. Technical Report, 2012.

Examples


## load package required
library(flare)

## generating data
n = 50
d = 50
D = sugm.generator(n=n,d=d,graph="band",g=1)
plot(D)

## sparse precision matrix estimation with method "clime"
out1 = sugm(D$data, method = "clime")
plot(out1)
sugm.plot(out1$path[[4]])

## sparse precision matrix estimation with method "tiger"
out2 = sugm(D$data, method = "tiger")
plot(out2)
sugm.plot(out2$path[[5]])
## load package required
library(flare)

## generating data
n = 50
d = 50
D = sugm.generator(n=n,d=d,graph="band",g=1)
plot(D)

## sparse precision matrix estimation with method "clime"
out1 = sugm(D$data, method = "clime")
plot(out1)
sugm.plot(out1$path[[4]])

## sparse precision matrix estimation with method "tiger"
out2 = sugm(D$data, method = "tiger")
plot(out2)
sugm.plot(out2$path[[5]])

Data generator for sparse undirected graph estimation.

Description

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

Usage

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

Arguments

n

The number of observations (sample size). The default value is $200$ .

d

The number of variables (dimension). For "hub" and "cluster", d $\ge$ 4 is required. For "random", "band" and "scale-free", d $\ge$ 3 is required. The default value is $50$ .

graph

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

v

The off-diagonal elements of the precision matrix, controlling the magnitude of partial correlations with u. The default value is 0.3.

u

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

g

For "cluster" or "hub" graph, g is the number of hubs or clusters in the graph. The default value is about d/20 if d $\ge$ 40 and 2 if d $<$ 40. For "band" graph, g is the bandwidth and the default value is $1$ . NOT applicable to "random" graph.

prob

For "random" graph, it is the probability that a pair of nodes has an edge. The default value is 3/d. For "cluster" graph, it is the probability that a pair of nodes has an edge in each cluster. The default value is 6 $*$ g/d if d/g $\le$ 30 and 0.3 if d/g $>$ 30. NOT applicable to "hub", "band", and "scale-free" graphs.

seed

Set seed for data generation. The default value is 1.

vis

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

verbose

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

Details

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

(I) "random": Each pair of off-diagonal elements is randomly set to 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 rows/columns are evenly partitioned into g disjoint groups. Each pair of off-diagonal elements is set to theta[i,j]=theta[j,i]=1 for i!=j with probability prob if 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": The off-diagonal elements are set to theta[i,j]=1 if 1<=|i-j|<=g and 0 otherwise. 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 in d edges in the graph.

The adjacency matrix theta has all diagonal elements equal to 0. To obtain a positive definite covariance matrix, the smallest eigenvalue of theta*v (denoted by e) is computed. Then we set the covariance matrix equal to cov2cor(solve(theta*v+(|e|+0.1+u)*I)) to generate multivariate normal data.

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 covariance matrix for the generated data

theta

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

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Examples

## load package required
library(flare)

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

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

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

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

## scale-free graphs
L = sugm.generator(graph="scale-free", vis = TRUE)
## load package required
library(flare)

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

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

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

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

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

Graph Visualization from an Adjacency Matrix

Description

Implements graph visualization using an adjacency matrix and automatically organizes a 2D embedding layout.

Usage

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

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 applicable 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".

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Examples

## load package required
library(flare)

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

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

## visualize the cluster graph
L = sugm.generator(graph = "cluster")
sugm.plot(L$theta)

## Not run: 
#show working directory
getwd()
#plot 5 graphs and save the plots as eps files in the working directory  
sugm.plot(L$theta, epsflag = TRUE, cur.num = 5)

## End(Not run)
## load package required
library(flare)

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

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

## visualize the cluster graph
L = sugm.generator(graph = "cluster")
sugm.plot(L$theta)

## Not run: 
#show working directory
getwd()
#plot 5 graphs and save the plots as eps files in the working directory  
sugm.plot(L$theta, epsflag = TRUE, cur.num = 5)

## End(Not run)

Draw ROC Curve for an object with S3 class `"sugm"`

Description

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

Usage

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

Arguments

path

A graph path.

theta

The true graph structure.

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 oder 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 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.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

Examples

## load package required
library(flare)

#generate data
L = sugm.generator(d = 30, graph = "random", prob = 0.1)
out1 = sugm(L$data, lambda=10^(seq(log10(.4), log10(0.03), length.out=20)))

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

#Maximum F1 score
max(Z1$F1)
## load package required
library(flare)

#generate data
L = sugm.generator(d = 30, graph = "random", prob = 0.1)
out1 = sugm(L$data, lambda=10^(seq(log10(.4), log10(0.03), length.out=20)))

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

#Maximum F1 score
max(Z1$F1)

Model selection for high-dimensional undirected graphical models

Description

Implements regularization parameter selection for high-dimensional undirected graphical models. Supported approaches are Stability Approach to Regularization Selection ("stars") and cross-validation ("cv").

Usage

sugm.select(est, criterion = "stars", stars.subsample.ratio = NULL,
            stars.thresh = 0.1, rep.num = 20, fold = 5,
            loss="likelihood", verbose = TRUE)
sugm.select(est, criterion = "stars", stars.subsample.ratio = NULL,
            stars.thresh = 0.1, rep.num = 20, fold = 5,
            loss="likelihood", verbose = TRUE)

Arguments

est

An object with S3 class "sugm"

criterion

Model selection criterion. "stars" and "cv" are available for both graph estimation methods. The default value is "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. Must be in (0,1). Only applicable when criterion = "stars".

stars.thresh

The variability threshold in STARS. Must be in [0,1]. The default value is 0.1. Only applicable when criterion = "stars".

rep.num

The number of subsamples. Must be at least 1. The default value is 20.

fold

The number of folds used in cross-validation. Must be between 2 and n. The default value is 5. Only applicable when criterion = "cv".

loss

Loss used in cross-validation. Two losses are available: "likelihood" and "tracel2". Default is "likelihood". Only applicable when criterion = "cv".

verbose

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

Details

Stability Approach to Regularization Selection (STARS) selects an optimal regularization parameter by variability across subsamples, and tends to over-select edges in Gaussian graphical models. In addition to selecting regularization parameters, STARS can provide an additional merged graph estimate based on edge frequencies across subsamples. K-fold cross-validation is also available for selecting lambda, using the following losses:

$likelihood: Tr(\Sigma \Omega) - \log|\Omega|$

$tracel2: Tr(diag(\Sigma \Omega - I)^2).$

Value

An object with S3 class "select" is returned:

refit

The optimal graph selected from the graph path

opt.icov

The optimal precision matrix selected.

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".

opt.index

The index of the selected regularization parameter.

opt.lambda

The selected regularization/thresholding parameter.

opt.sparsity

The sparsity level of "refit".

loss

Cross-validation loss used for selection. Only applicable when criterion = "cv".

and anything else included in the input est.

Note

Model selection is not available when the data input is a sample covariance matrix.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[email protected]>

References

1. T. Cai, W. Liu and X. Luo. A constrained $\ell_1$ minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011.
2. B. He and X. Yuan. On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers. Technical Report, 2012.

Examples

## load package required
library(flare)

#generate data
L = sugm.generator(d = 10, graph="hub")
out1 = sugm(L$data)

#model selection using stars
#out1.select1 = sugm.select(out1, criterion = "stars", stars.thresh = 0.1)
#plot(out1.select1)

#model selection using cross validation
out1.select2 = sugm.select(out1, criterion = "cv")
plot(out1.select2)
## load package required
library(flare)

#generate data
L = sugm.generator(d = 10, graph="hub")
out1 = sugm(L$data)

#model selection using stars
#out1.select1 = sugm.select(out1, criterion = "stars", stars.thresh = 0.1)
#plot(out1.select1)

#model selection using cross validation
out1.select2 = sugm.select(out1, criterion = "cv")
plot(out1.select2)

Package 'flare'

Help Index

flare: A Family of Lasso Regression Methods

Description

Details

Author(s)

References

See Also

Extract Model Coefficients for an object with S3 class "slim"

Description

Usage

Arguments

Author(s)

See Also

The Bardet-Biedl syndrome Gene expression data from Scheetz et al. (2006)

Description

Usage

Format

Details

Author(s)

References

See Also

Examples

Internal flare functions

Description

Usage

Arguments

Details

Author(s)

See Also

Plot Function for "roc"

Description

Usage

Arguments

Author(s)

See Also

Plot Function for "select"

Description

Usage

Arguments

Author(s)

See Also

Plot Function for "sim"

Description

Usage

Arguments

Author(s)

See Also

Plot Function for "slim"

Description

Usage

Arguments

Author(s)

See Also

Plot Function for "sugm"

Description

Usage

Arguments

Author(s)

See Also

Prediction for an object with S3 class "slim"

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Print Function for an object with S3 class "roc"

Description

Usage

Arguments

Author(s)

See Also

Print Function for an object with S3 class "select"

Description

Usage

Arguments

Author(s)

Extract Model Coefficients for an object with S3 class `"slim"`

Prediction for an object with S3 class `"slim"`

Print Function for an object with S3 class `"roc"`

Print Function for an object with S3 class `"select"`

Print Function for an object with S3 class `"sim"`

Print Function for an object with S3 class `"slim"`

Print Function for an object with S3 class `"sugm"`

Draw ROC Curve for an object with S3 class `"sugm"`