glmnet (version 1.7.4)

cv.glmnet: Cross-validation for glmnet

Description

Does k-fold cross-validation for glmnet, produces a plot, and returns a value for lambda

Usage

cv.glmnet(x, y, weights, offset, lambda, type.measure, ..., nfolds, foldid, grouped)

Arguments

x

x matrix as in glmnet.

y

response y as in glmnet.

weights

Observation weights; defaults to 1 per observation

offset

Offset vector (matrix) as in glmnet

lambda

Optional user-supplied lambda sequence; default is NULL, and glmnet chooses its own sequence

...

Other arguments that can be passed to glmnet.

nfolds

number of folds - default is 10. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3

foldid

an optional vector of values between 1 and nfold identifying what fold each observation is in. If supplied, nfold can be missing.

type.measure

loss to use for cross-validation. Currently five options, not all available for all models. The default is type.measure="deviance", which uses squared-error for gaussian models (a.k.a type.measure="mse" there), deviance

grouped

This is an experimental argument, with default TRUE, and can be ignored by most users. For all models except the "cox", this refers to computing nfolds separate statistics, and then using their mean

Value

• an object of class "cv.glmnet" is returned, which is a list with the ingredients of the cross-validation fit.
• lambda
  the values of lambda used in the fits.
• cvm
  The mean cross-validated error - a vector of length length(lambda).
• cvsd
  estimate of standard error of cvm.
• cvup
  upper curve = cvm+cvsd.
• cvlo
  lower curve = cvm-cvsd.
• nzero
  number of non-zero coefficients at each lambda.
• name
  a text string indicating type of measure (for plotting purposes).
• glmnet.fit
  a fitted glmnet object for the full data.
• lambda.min
  value of lambda that gives minimum cvm.
• lambda.1se
  largest value of lambda such that error is within 1 standard error of the minimum.

Details

The function runs glmnet nfolds+1 times; the first to get the lambda sequence, and then the remainder to compute the fit with each of the folds omitted. The error is accumulated, and the average error and standard deviation over the folds is computed. Note that cv.glmnet does NOT search for values for alpha. A specific value should be supplied, else alpha=1 is assumed by default. If users would like to cross-validate alpha as well, they should call cv.glmnet with a pre-computed vector foldid, and then use this same fold vector in separate calls to cv.glmnet with different values of alpha.

References

Friedman, J., Hastie, T. and Tibshirani, R. (2008) Regularization Paths for Generalized Linear Models via Coordinate Descent, http://www.stanford.edu/~hastie/Papers/glmnet.pdf Journal of Statistical Software, Vol. 33(1), 1-22 Feb 2010 http://www.jstatsoft.org/v33/i01/ Simon, N., Friedman, J., Hastie, T., Tibshirani, R. (2011) Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent, Journal of Statistical Software, Vol. 39(5) 1-13 http://www.jstatsoft.org/v39/i05/

See Also

glmnet and plot, predict, and coef methods for "cv.glmnet" object.

Examples

set.seed(1010)
n=1000;p=100
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)
beta=rnorm(nzc)
fx= x[,seq(nzc)] %*% beta
eps=rnorm(n)*5
y=drop(fx+eps)
px=exp(fx)
px=px/(1+px)
ly=rbinom(n=length(px),prob=px,size=1)
set.seed(1011)
cvob1=cv.glmnet(x,y)
plot(cvob1)
coef(cvob1)
predict(cvob1,newx=x[1:5,], s="lambda.min")
title("Gaussian Family",line=2.5)
set.seed(1011)
cvob1a=cv.glmnet(x,y,type.measure="mae")
plot(cvob1a)
title("Gaussian Family",line=2.5)
set.seed(1011)
par(mfrow=c(2,2),mar=c(4.5,4.5,4,1))
cvob2=cv.glmnet(x,ly,family="binomial")
plot(cvob2)
title("Binomial Family",line=2.5)
frame()
set.seed(1011)
cvob3=cv.glmnet(x,ly,family="binomial",type.measure="class")
plot(cvob3)
title("Binomial Family",line=2.5)
set.seed(1011)
cvob3a=cv.glmnet(x,ly,family="binomial",type.measure="auc")
plot(cvob3a)
title("Binomial Family",line=2.5)
set.seed(1011)
mu=exp(fx/10)
y=rpois(n,mu)
cvob4=cv.glmnet(x,y,family="poisson")
plot(cvob4)
title("Poisson Family",line=2.5)
# Multinomial
n=1000;p=30
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)
beta3=matrix(rnorm(30),10,3)
beta3=rbind(beta3,matrix(0,p-10,3))
f3=x%*% beta3
p3=exp(f3)
p3=p3/apply(p3,1,sum)
g3=rmult(p3)
set.seed(10101)
cvfit=cv.glmnet(x,g3,family="multinomial")
plot(cvfit)
title("Multinomial Family",line=2.5)
set.seed(10101)
cvfit=cv.glmnet(x,g3,family="mult",type="mse")
plot(cvfit)
title("Multinomial Family",line=2.5)
set.seed(10101)
cvfit=cv.glmnet(x,g3,family="mult",type="class")
plot(cvfit)
# Cox
beta=rnorm(nzc)
fx=x[,seq(nzc)]%*%beta/3
hx=exp(fx)
ty=rexp(n,hx)
tcens=rbinom(n=n,prob=.3,size=1)# censoring indicator
y=cbind(time=ty,status=1-tcens) # y=Surv(ty,1-tcens) with library(survival)
foldid=sample(rep(seq(10),length=n))
fit1_cv=cv.glmnet(x,y,family="cox",foldid=foldid)
plot(fit1_cv)
title("Cox Family",line=2.5)