glmlep: Fit a GLM wit LEP regularization

In glmlep: Fit GLM with LEP-Based Penalized Maximum Likelihood

Description

Fit a generalized linear model via penalized maximum likelihood. The regularization path is computed for the LEP penalty at a grid of values for the regularization parameter lambda. Fits linear, logistic and Cox regression models.

Usage

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)

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.

Details

The sequence of models implied by lambda is fit by a modified version of coordinate descent (MCD), see reference below. Note that n is the sample size and p is the dimension of variables.

Value

An object of class "glmlep", "*", where "*" is "gaulep" or "binlep" for the two types of models.

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.
EBIC	The EBIC value for each value of lambda. Note tha the EBIC value is defined as
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. [e-mail]

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
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 <- glmlep(x,y,family="gaussian")

glmlep documentation built on May 1, 2019, 9:14 p.m.