cv.glmlep {glmlep}

Cross-validation for glmlep.

Description

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

Usage

cv.glmlep(x, y, family = c("gaussian", "binomial"), lambda = NULL, 
lambda.min = ifelse(n < p, 0.05, 0.001), nlambda = 100, lambda2 = 0, 
kappa = ifelse(n < p, 0.1, 0.05), pen.fac = rep(1, p), tol = 1e-06, 
max.ite = 1000, foldid, nfolds = 5, cv.seed = 100)

Arguments

x

The design matrix, without an intercept.

y

The response vector. Quantitative for family="gaussian". For family="binomial" should be a vector with two levels.

family

Response type (see above)

lambda

A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care. Do not supply a single value for lambda. Supply instead a decreasing sequence of lambda values. glmnet relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.

lambda.min

Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.001, close to zero. If nobs < nvars, the default is 0.05.

nlambda

The number of lambda values; default is 100.

lambda2

The tuning parameter for additional L_2 penalty. Use for better grouping effect. The default is 0.

kappa

The scale tuning parameter of the LEP penalty. One can specify it to get the desired estimates because of the homotopy of LEP function to the L_0 function. If nobs > nvars, the default is 0.05, close to zero. If nobs < nvars, the default is 0.1.

pen.fac

Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude). Note: the penalty factors are internally rescaled to sum to nobs, and the lambda sequence will reflect this change.

tol

Convergence tolerance for MCD. Each inner MCD loop continues until the change in the estimates is less than tol. default is 1E-6.

max.ite

Maximum number of passes over the data for all lambda values; default is 10^3.

foldid

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

nfolds

Number of folds - default is 5.

cv.seed

The seed for cross-validation. This could be used for simulation replicability.

Details

The function runs glmlep nfolds+1 times; the first to get the lambda sequence and the final estimate, and then the remainder to compute the fit with each of the folds omitted. The loss is accumulated, and the average loss over the folds is computed. Note that cv.glmlep does NOT search for values for kappa. A specific value should be supplied, else kappa=0.05 is assumed by default. If users would like to cross-validate kappa as well, they should call cv.glmlep with a pre-computed vector foldid, and then use this same fold vector in separate calls to cv.glmlep with different values of kappa. Note that n is the sample size and p is the dimension of variables.

Value

An object of class "cv.glmlep" is returned, which is a list with the ingredients of the cross-validation fit.

beta

A nrow(x) x length(lambda) matrix of estimated coefficient.

lambda

The sequence of regularization parameter values used

df

The degree of freedom for each value of lambda.

loss

The -2*log-likelihood value for each value of lambda.

lambda.min

The value of lambda with the minimum EBIC.

beta.min

The coefficient with the minimum EBIC.

call

The call that produces this object

Author(s)

Canhong Wen, Hao Lin, Shaoli Wang and Xueqin Wang.

Maintainer: Canhong Wen <[e-mail]>

References

Wen, C., Wang, X., & Wang, S. (2013). Laplace Error Penalty based variable selection in ultra high-dimension. In press.

Examples

## generate data from multivariate normal distribution
require(mvtnorm)
n = 100;
beta <- c(3,1.5,0,0,2,0,0,0)

set.seed(100)
p=length(beta);
corr_data=diag(rep(1,p));
x=as.matrix(rmvnorm(n,rep(0,p),corr_data))
noise=rnorm(n);

## Gaussian
y <- tcrossprod(x,t(beta)) + noise;
fit <- cv.glmlep(x,y,family="gaussian")