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Version:	1.6.1
Date:	2025-03-05
Title:	Extending Lasso Model Fitting to Big Data
Maintainer:	Patrick Breheny <patrick-breheny@uiowa.edu>
Description:	Extend lasso and elastic-net model fitting for large data sets that cannot be loaded into memory. Designed to be more memory- and computation-efficient than existing lasso-fitting packages like 'glmnet' and 'ncvreg', thus allowing the user to analyze big data with limited RAM <doi:10.32614/RJ-2021-001>.
License:	GPL-3
URL:	https://pbreheny.github.io/biglasso/,https://github.com/pbreheny/biglasso
BugReports:	https://github.com/pbreheny/biglasso/issues
Depends:	R (≥ 3.2.0), bigmemory (≥ 4.5.0), Matrix, ncvreg
Imports:	Rcpp (≥ 0.12.1), methods
LinkingTo:	Rcpp, RcppArmadillo (≥ 0.8.600), bigmemory, BH
VignetteBuilder:	knitr
Suggests:	glmnet, knitr, parallel, rmarkdown, survival, tinytest
RoxygenNote:	7.3.2
Encoding:	UTF-8
NeedsCompilation:	yes
Packaged:	2025-03-05 17:32:37 UTC; pbreheny
Author:	Yaohui Zeng [aut], Chuyi Wang [aut], Tabitha Peter [aut], Patrick Breheny [aut, cre]
Repository:	CRAN
Date/Publication:	2025-03-05 18:10:14 UTC

Extending Lasso Model Fitting to Big Data

Description

Extend lasso and elastic-net linear, logistic and cox regression models forultrahigh-dimensional, multi-gigabyte data sets that cannot be loaded intoavailable RAM. This package utilizes memory-mapped files to store themassive data on the disk and only read those into memory whenever necessaryduring model fitting. Moreover, some advanced feature screening rules areproposed and implemented to accelerate the model fitting. As a result, thispackage is much more memory- and computation-efficient and highly scalableas compared to existing lasso-fitting packages such asglmnet andncvreg, thus allowing forpowerful big data analysis even with only an ordinary laptop.

Details

Penalized regression models, in particular the lasso, have been extensivelyapplied to analyzing high-dimensional data sets. However, due to the memorylimit, existing R packages are not capable of fitting lasso models forultrahigh-dimensional, multi-gigabyte data sets which have been increasinglyseen in many areas such as genetics, biomedical imaging, genome sequencingand high-frequency finance.

This package aims to fill the gap by extending lasso model fitting to BigData in R. Version >= 1.2-3 represents a major redesign where the sourcecode is converted into C++ (previously in C), and new feature screeningrules, as well as OpenMP parallel computing, are implemented. Some keyfeatures ofbiglasso are summarized as below:

1. itutilizes memory-mapped files to store the massive data on the disk, onlyloading data into memory when necessary during model fitting. Consequently,it's able to seamlessly data-larger-than-RAM cases.

2. it is built uponpathwise coordinate descent algorithm with warm start, active set cycling,and feature screening strategies, which has been proven to be one of fastestlasso solvers.

3. in incorporates our newly developed hybrid and adaptivescreening that outperform state-of-the-art screening rules such asthe sequential strong rule (SSR) and the sequential EDPP rule (SEDPP) withadditional 1.5x to 4x speedup.

4. the implementation is designed to be asmemory-efficient as possible by eliminating extra copies of the data createdby other R packages, making it at least 2x more memory-efficient thanglmnet.

5. the underlying computation is implemented in C++, andparallel computing with OpenMP is also supported.

For more information:

• Benchmarking results:https://github.com/pbreheny/biglasso

• Tutorial:https://pbreheny.github.io/biglasso/articles/biglasso.html

• Technical paper:https://arxiv.org/abs/1701.05936

Note

The input design matrix X must be abigmemory::big.matrix() object.This can be created by the functionas.big.matrix in the R packagebigmemory.If the data (design matrix) is very large (e.g. 10 GB) and stored in an externalfile, which is often the case for big data, X can be created by calling thefunctionsetupX().In this case, there are several restrictions about the data file:

1. the data file must be a well-formated ASCII-file, witheach row corresponding to an observation and each column a variable;

2. the data file must contain only one single type. Current version onlysupportsdouble type;

3. the data file must contain only numericvariables. If there are categorical variables, the user needs to createdummy variables for each categorical varable (by adding additional columns).

Future versions will try to address these restrictions.

Denote the number of observations and variables be, respectively,nandp. It's worth noting that the package is more suitable for widedata (ultrahigh-dimensional,⁠p >> n⁠) as compared to long data(⁠n >> p⁠). This is because the model fitting algorithm takes advantageof sparsity assumption of high-dimensional data. To just give the user someideas, below are some benchmarking results of the total computing time (inseconds) for solving lasso-penalized linear regression along a sequence of100 values of the tuning parameter. In all cases, assume 20 non-zerocoefficients equal +/- 2 in the true model. (Based on Version 1.2-3,screening rule "SSR-BEDPP" is used)

• For wide data case (p > n),⁠n = 1,000⁠:

  p	1,000	10,000	100,000	1,000,000
  Size ofX	9.5 MB	95 MB	950 MB	9.5 GB
  Elapsed time (s)	0.11	0.83	8.47	85.50

  %

• For long data case (⁠n >> p⁠),⁠p = 1,000⁠:%

  %n	1,000	10,000	100,000	1,000,000
  %Size ofX	9.5 MB	95 MB	950 MB	9.5 GB
  %Elapsed time (s)	2.50	11.43	83.69	1090.62
  %

Author(s)

Yaohui Zeng, Chuyi Wang, Tabitha Peter, and Patrick Breheny

References

• Zeng Y and Breheny P. (2021) The biglasso Package: A Memory- andComputation-Efficient Solver for Lasso Model Fitting with Big Data in R.R Journal,12: 6-19.doi:10.32614/RJ-2021-001

• Wang C and Breheny P. (2022) Adaptive hybrid screening for efficientlasso optimization.Journal of Statistical Computation and Simulation,92: 2233-2256.doi:10.1080/00949655.2021.2025376

• Tibshirani, R., Bien, J., Friedman, J., Hastie, T., Simon, N., Taylor, J.,and Tibshirani, R. J. (2012). Strong rules for discarding predictors inlasso-type problems.Journal of the Royal Statistical Society: SeriesB (Statistical Methodology),74(2), 245-266.

• Wang, J., Zhou, J., Wonka, P., and Ye, J. (2013). Lasso screening rules via dualpolytope projection.In Advances in Neural Information ProcessingSystems, pp. 1070-1078.

• Xiang, Z. J., and Ramadge, P. J. (2012).Fast lasso screening tests based on correlations.In Acoustics, Speechand Signal Processing (ICASSP), 2012 IEEE International Conference on (pp.2137-2140). IEEE.

• Wang, J., Zhou, J., Liu, J., Wonka, P., and Ye, J.(2014). A safe screening rule for sparse logistic regression.InAdvances in Neural Information Processing Systems, pp. 1053-1061.

Examples

## Not run: ## Example of reading data from external big data file, fit lasso model, ## and run cross validation in parallel# simulated design matrix, 1000 observations, 500,000 variables, ~ 5GB# there are 10 true variables with non-zero coefficient 2.xfname <- 'x_e3_5e5.txt' yfname <- 'y_e3_5e5.txt' # response vectortime <- system.time(  X <- setupX(xfname, sep = '\t') # create backing files (.bin, .desc))print(time) # ~ 7 minutes; this is just one-time operationdim(X)# the big.matrix then can be retrieved by its descriptor file (.desc) in any new R session. rm(X)xdesc <- 'x_e3_5e5.desc' X <- attach.big.matrix(xdesc)dim(X)y <- as.matrix(read.table(yfname, header = F))time.fit <- system.time(  fit <- biglasso(X, y, family = 'gaussian', screen = 'Hybrid'))print(time.fit) # ~ 44 seconds for fitting a lasso model along the entire solution path# cross validation in parallelseed <- 1234time.cvfit <- system.time(  cvfit <- cv.biglasso(X, y, family = 'gaussian', screen = 'Hybrid',                        seed = seed, ncores = 4, nfolds = 10))print(time.cvfit) # ~ 3 minutes for 10-fold cross validationplot(cvfit)summary(cvfit)## End(Not run)

Fit lasso penalized regression path for big data

Description

Extend lasso model fitting to big data that cannot be loaded into memory.Fit solution paths for linear, logistic or Cox regression models penalized bylasso, ridge, or elastic-net over a grid of values for the regularizationparameter lambda.

Usage

biglasso(  X,  y,  row.idx = 1:nrow(X),  penalty = c("lasso", "ridge", "enet"),  family = c("gaussian", "binomial", "cox", "mgaussian"),  alg.logistic = c("Newton", "MM"),  screen = c("Adaptive", "SSR", "Hybrid", "None"),  safe.thresh = 0,  update.thresh = 1,  ncores = 1,  alpha = 1,  lambda.min = ifelse(nrow(X) > ncol(X), 0.001, 0.05),  nlambda = 100,  lambda.log.scale = TRUE,  lambda,  eps = 1e-07,  max.iter = 1000,  dfmax = ncol(X) + 1,  penalty.factor = rep(1, ncol(X)),  warn = TRUE,  output.time = FALSE,  return.time = TRUE,  verbose = FALSE)

Arguments

Details

The objective function for linear regression or multiple responses linear regression(family = "gaussian" orfamily = "mgaussian") is

\frac{1}{2n}\textrm{RSS} + \lambda*\textrm{penalty},

where forfamily = "mgaussian"), a group-lasso type penalty is applied.For logistic regression(family = "binomial") it is

-\frac{1}{n} loglike +\lambda*\textrm{penalty},

, for cox regression,breslow approximation for ties is applied.

Several advanced feature screening rules are implemented. Forlasso-penalized linear regression, all the options ofscreen areapplicable. Our proposal adaptive rule -"Adaptive" - achieves highest speedupso it's the recommended one, especially for ultrahigh-dimensional large-scaledata sets. For cox regression and/or the elastic net penalty, only"SSR" is applicable for now. More efficient rules are under development.

Value

An object with S3 class"biglasso" for⁠"gaussian", "binomial", "cox"⁠ families, or an object with S3 class"mbiglasso" for"mgaussian" family, with following variables.

Author(s)

Yaohui Zeng, Chuyi Wang and Patrick Breheny

References

Zeng Y and Breheny P. (2021) The biglasso Package: A Memory- and Computation-Efficient Solver for Lasso Model Fitting with Big Data in R.R Journal,12: 6-19.doi:10.32614/RJ-2021-001

See Also

biglasso-package,setupX(),cv.biglasso(),plot.biglasso(),ncvreg::ncvreg()

Examples

## Linear regressiondata(colon)X <- colon$Xy <- colon$yX.bm <- as.big.matrix(X)# lasso, defaultpar(mfrow=c(1,2))fit.lasso <- biglasso(X.bm, y, family = 'gaussian')plot(fit.lasso, log.l = TRUE, main = 'lasso')# elastic netfit.enet <- biglasso(X.bm, y, penalty = 'enet', alpha = 0.5, family = 'gaussian')plot(fit.enet, log.l = TRUE, main = 'elastic net, alpha = 0.5')## Logistic regressiondata(colon)X <- colon$Xy <- colon$yX.bm <- as.big.matrix(X)# lasso, defaultpar(mfrow = c(1, 2))fit.bin.lasso <- biglasso(X.bm, y, penalty = 'lasso', family = "binomial")plot(fit.bin.lasso, log.l = TRUE, main = 'lasso')# elastic netfit.bin.enet <- biglasso(X.bm, y, penalty = 'enet', alpha = 0.5, family = "binomial")plot(fit.bin.enet, log.l = TRUE, main = 'elastic net, alpha = 0.5')## Cox regressionset.seed(10101)N <- 1000; p <- 30; nzc <- p/3X <- matrix(rnorm(N * p), N, p)beta <- rnorm(nzc)fx <- X[, seq(nzc)] %*% beta/3hx <- exp(fx)ty <- rexp(N, hx)tcens <- rbinom(n = N, prob = 0.3, size = 1)  # censoring indicatory <- cbind(time = ty, status = 1 - tcens)  # y <- Surv(ty, 1 - tcens) with library(survival)X.bm <- as.big.matrix(X)fit <- biglasso(X.bm, y, family = "cox")plot(fit, main = "cox")## Multiple responses linear regressionset.seed(10101)n=300; p=300; m=5; s=10; b=1x = matrix(rnorm(n * p), n, p)beta = matrix(seq(from=-b,to=b,length.out=s*m),s,m)y = x[,1:s] %*% beta + matrix(rnorm(n*m,0,1),n,m)x.bm = as.big.matrix(x)fit = biglasso(x.bm, y, family = "mgaussian")plot(fit, main = "mgaussian")

Direct interface to biglasso fitting, no preprocessing

Description

This function is intended for users who know exactly what they're doing andwant complete control over the fitting process. It

• does NOT add an intercept

• does NOT standardize the design matrix

• does NOT set up a path for lambda (the lasso tuning parameter)all of the above are critical steps in data analysis. However, a direct APIhas been provided for use in situations where the lasso fitting process isan internal component of a more complicated algorithm and standardizationmust be handled externally.

Usage

biglasso_fit(  X,  y,  r,  init = rep(0, ncol(X)),  xtx,  penalty = "lasso",  lambda,  alpha = 1,  gamma,  ncores = 1,  max.iter = 1000,  eps = 1e-05,  dfmax = ncol(X) + 1,  penalty.factor = rep(1, ncol(X)),  warn = TRUE,  output.time = FALSE,  return.time = TRUE)

Arguments

Details

Note:

• Hybrid safe-strong rules are turned off forbiglasso_fit(), as these relyon standardization

• Currently, the function only works with linear regression(family = 'gaussian').

Value

An object with S3 class"biglasso" with following variables.

Author(s)

Tabitha Peter and Patrick Breheny

Examples

data(Prostate)X <- cbind(1, Prostate$X)xtx <- apply(X, 2, crossprod)/nrow(X)y <- Prostate$yX.bm <- as.big.matrix(X)init <- rep(0, ncol(X))fit <- biglasso_fit(X = X.bm, y = y, r=y, init = init, xtx = xtx,  lambda = 0.1, penalty.factor=c(0, rep(1, ncol(X)-1)), max.iter = 10000)fit$beta  fit <- biglasso_fit(X = X.bm, y = y, r=y, init = init, xtx = xtx, penalty='MCP',  lambda = 0.1, penalty.factor=c(0, rep(1, ncol(X)-1)), max.iter = 10000)fit$beta

Direct interface to biglasso fitting, no preprocessing, path version

Description

This function is intended for users who know exactly what they're doing andwant complete control over the fitting process. It

• does NOT add an intercept

• does NOT standardize the design matrixboth of the above are critical steps in data analysis. However, a direct APIhas been provided for use in situations where the lasso fitting process isan internal component of a more complicated algorithm and standardizationmust be handled externally.

Usage

biglasso_path(  X,  y,  r,  init = rep(0, ncol(X)),  xtx,  penalty = "lasso",  lambda,  alpha = 1,  gamma,  ncores = 1,  max.iter = 1000,  eps = 1e-05,  dfmax = ncol(X) + 1,  penalty.factor = rep(1, ncol(X)),  warn = TRUE,  output.time = FALSE,  return.time = TRUE)

Arguments

Details

biglasso_path() works identically tobiglasso_fit() except it offers theadditional option of fitting models across a path of tuning parameter values.

Note:

• Hybrid safe-strong rules are turned off forbiglasso_fit(), as these relyon standardization

• Currently, the function only works with linear regression(family = 'gaussian').

Value

An object with S3 class"biglasso" with following variables.

Author(s)

Tabitha Peter and Patrick Breheny

Examples

data(Prostate)X <- cbind(1, Prostate$X)xtx <- apply(X, 2, crossprod)/nrow(X)y <- Prostate$yX.bm <- as.big.matrix(X)init <- rep(0, ncol(X))fit <- biglasso_path(X = X.bm, y = y, r = y, init = init, xtx = xtx,  lambda = c(0.5, 0.1, 0.05, 0.01, 0.001),   penalty.factor=c(0, rep(1, ncol(X)-1)), max.iter=2000)fit$beta  fit <- biglasso_path(X = X.bm, y = y, r = y, init = init, xtx = xtx,  lambda = c(0.5, 0.1, 0.05, 0.01, 0.001), penalty='MCP',  penalty.factor=c(0, rep(1, ncol(X)-1)), max.iter = 2000)fit$beta

Gene expression data from colon-cancer patients

Description

The data file contains gene expression data of 62 samples (40 tumor samples,22 normal samples) from colon-cancer patients analyzed with an Affymetrixoligonucleotide Hum6000 array.

Format

A list of 2 variables included incolon:

• X: a 62-by-2000 matrix that records the gene expression data.Used as design matrix.

• y: a binary vector of length 62 recording the sample status: 1 =tumor; 0 = normal. Used as response vector.

Source

The raw data can be found on Bioconductor:https://bioconductor.org/packages/release/data/experiment/html/colonCA.html.

References

• U. Alon et al. (1999): Broad patterns of geneexpression revealed by clustering analysis of tumor and normal colon tissueprobed by oligonucleotide arrays.Proc. Natl. Acad. Sci. USA96, 6745-6750.https://www.pnas.org/doi/abs/10.1073/pnas.96.12.6745.

Examples

data(colon)X <- colon$Xy <- colon$ystr(X)dim(X)X.bm <- as.big.matrix(X, backingfile = "") # convert to big.matrix objectstr(X.bm)dim(X.bm)

Cross-validation for biglasso

Description

Perform k-fold cross validation for penalized regression models over a gridof values for the regularization parameter lambda.

Usage

cv.biglasso(  X,  y,  row.idx = 1:nrow(X),  family = c("gaussian", "binomial", "cox", "mgaussian"),  eval.metric = c("default", "MAPE", "auc", "class"),  ncores = parallel::detectCores(),  ...,  nfolds = 5,  seed,  cv.ind,  trace = FALSE,  grouped = TRUE)

Arguments

Details

The function callsbiglassonfolds times, each time leavingout 1/nfolds of the data. The cross-validation error is based on theresidual sum of squares whenfamily="gaussian" and the binomialdeviance whenfamily="binomial".

The S3 class objectcv.biglasso inherits classncvreg::cv.ncvreg(). So S3functions such as⁠"summary", "plot"⁠ can be directly applied to thecv.biglasso object.

Value

An object with S3 class"cv.biglasso" which inherits fromclass"cv.ncvreg". The following variables are contained in theclass (adopted fromncvreg::cv.ncvreg()).

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),plot.cv.biglasso(),summary.cv.biglasso(),setupX()

Examples

## Not run: ## cv.biglassodata(colon)X <- colon$Xy <- colon$yX.bm <- as.big.matrix(X)## logistic regressioncvfit <- cv.biglasso(X.bm, y, family = 'binomial', seed = 1234, ncores = 2)par(mfrow = c(2, 2))plot(cvfit, type = 'all')summary(cvfit)## End(Not run)

Internal biglasso functions

Description

Internal biglasso functions

Usage

loss.biglasso(y, yhat, family, eval.metric, grouped = TRUE)

Arguments

Details

These are not intended for use by users.loss.biglasso calculates thevalue of the loss function for the given predictions (used for cross-validation).

Author(s)

Yaohui Zeng and Patrick Breheny

Plot coefficients from a "biglasso" object

Description

Produce a plot of the coefficient paths for a fittedbiglasso() object.

Usage

## S3 method for class 'biglasso'plot(x, alpha = 1, log.l = TRUE, ...)

Arguments

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),cv.biglasso()

Examples

## See examples in "biglasso"

Plots the cross-validation curve from a "cv.biglasso" object

Description

Plot the cross-validation curve from acv.biglasso() object,along with standard error bars.

Usage

## S3 method for class 'cv.biglasso'plot(  x,  log.l = TRUE,  type = c("cve", "rsq", "scale", "snr", "pred", "all"),  selected = TRUE,  vertical.line = TRUE,  col = "red",  ...)

Arguments

Details

Error bars representing approximate 68\along with the estimates at value oflambda. Forrsq andsnr, these confidence intervals are quite crude, especially near.

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),cv.biglasso()

Examples

## See examples in "cv.biglasso"

Plot coefficients from a "mbiglasso" object

Description

Produce a plot of the coefficient paths for a fitted multiple responsesmbiglasso object.

Usage

## S3 method for class 'mbiglasso'plot(x, alpha = 1, log.l = TRUE, norm.beta = TRUE, ...)

Arguments

Author(s)

Chuyi Wang

See Also

biglasso()

Examples

## See examples in "biglasso"

Model predictions based on a fittedbiglasso object

Description

Extract predictions (fitted reponse, coefficients, etc.) from afittedbiglasso() object.

Usage

## S3 method for class 'biglasso'predict(  object,  X,  row.idx = 1:nrow(X),  type = c("link", "response", "class", "coefficients", "vars", "nvars"),  lambda,  which = 1:length(object$lambda),  ...)## S3 method for class 'mbiglasso'predict(  object,  X,  row.idx = 1:nrow(X),  type = c("link", "response", "coefficients", "vars", "nvars"),  lambda,  which = 1:length(object$lambda),  k = 1,  ...)## S3 method for class 'biglasso'coef(object, lambda, which = 1:length(object$lambda), drop = TRUE, ...)## S3 method for class 'mbiglasso'coef(object, lambda, which = 1:length(object$lambda), intercept = TRUE, ...)

Arguments

Value

The object returned depends ontype.

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),cv.biglasso()

Examples

## Logistic regressiondata(colon)X <- colon$Xy <- colon$yX.bm <- as.big.matrix(X, backingfile = "")fit <- biglasso(X.bm, y, penalty = 'lasso', family = "binomial")coef <- coef(fit, lambda=0.05, drop = TRUE)coef[which(coef != 0)]predict(fit, X.bm, type="link", lambda=0.05)[1:10]predict(fit, X.bm, type="response", lambda=0.05)[1:10]predict(fit, X.bm, type="class", lambda=0.1)[1:10]predict(fit, type="vars", lambda=c(0.05, 0.1))predict(fit, type="nvars", lambda=c(0.05, 0.1))

Model predictions based on a fittedcv.biglasso() object

Description

Extract predictions from a fittedcv.biglasso() object.

Usage

## S3 method for class 'cv.biglasso'predict(  object,  X,  row.idx = 1:nrow(X),  type = c("link", "response", "class", "coefficients", "vars", "nvars"),  lambda = object$lambda.min,  which = object$min,  ...)## S3 method for class 'cv.biglasso'coef(object, lambda = object$lambda.min, which = object$min, ...)

Arguments

Value

The object returned depends ontype.

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),cv.biglasso()

Examples

## Not run: ## predict.cv.biglassodata(colon)X <- colon$Xy <- colon$yX.bm <- as.big.matrix(X, backingfile = "")fit <- biglasso(X.bm, y, penalty = 'lasso', family = "binomial")cvfit <- cv.biglasso(X.bm, y, penalty = 'lasso', family = "binomial", seed = 1234, ncores = 2)coef <- coef(cvfit)coef[which(coef != 0)]predict(cvfit, X.bm, type = "response")predict(cvfit, X.bm, type = "link")predict(cvfit, X.bm, type = "class")predict(cvfit, X.bm, lambda = "lambda.1se")## End(Not run)

Set up design matrix X by reading data from big data file

Description

Set up the design matrix X as abig.matrix object based on externalmassive data file stored on disk that cannot be fullly loaded into memory.The data file must be a well-formated ASCII-file, and contains only onesingle type. Current version only supportsdouble type. Otherrestrictions about the data file are described inbiglasso-package. This function reads the massive data, andcreates abig.matrix object. By default, the resultingbig.matrix is file-backed, and can be shared across processors ornodes of a cluster.

Usage

setupX(  filename,  dir = getwd(),  sep = ",",  backingfile = paste0(unlist(strsplit(filename, split = "\\."))[1], ".bin"),  descriptorfile = paste0(unlist(strsplit(filename, split = "\\."))[1], ".desc"),  type = "double",  ...)

Arguments

Details

For a data set, this function needs to be called only one time to set up thebig.matrix object with two backing files (.bin, .desc) created incurrent working directory. Once set up, the data can be "loaded" into any(new) R session by callingattach.big.matrix(discriptorfile).

This function is a simple wrapper ofbigmemory::read.big.matrix(). Seebigmemory for moredetails.

Value

Abig.matrix object corresponding to a file-backedbigmemory::big.matrix(). It's ready to be used as the design matrixX inbiglasso() andcv.biglasso().

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),ncvreg::cv.ncvreg(),biglasso-package

Examples

## see the example in "biglasso-package"

Summarizing inferences based on cross-validation

Description

Summary method forcv.biglasso objects.

Usage

## S3 method for class 'cv.biglasso'summary(object, ...)## S3 method for class 'summary.cv.biglasso'print(x, digits, ...)

Arguments

Value

summary.cv.biglasso produces an object with S3 class"summary.cv.biglasso". The class has its own print method and containsthe following list elements:

Author(s)

Yaohui Zeng and Patrick Breheny

See Also

biglasso(),cv.biglasso(),plot.cv.biglasso(),biglasso-package

Examples

## See examples in "cv.biglasso" and "biglasso-package"