nclreg: Optimize a nonconvex loss with regularization

In mpath: Regularized Linear Models

Optimize a nonconvex loss with regularization

Description

Fit a linear model via penalized nonconvex loss function. The regularization path is computed for the lasso (or elastic net penalty), scad (or snet) and mcp (or mnet penalty), at a grid of values for the regularization parameter lambda. The name refers to NonConvex Loss with REGularization.

Usage

## S3 method for class 'formula'
nclreg(formula, data, weights, offset=NULL, contrasts=NULL, ...)
## S3 method for class 'matrix'
nclreg(x, y, weights, offset=NULL, ...)
## Default S3 method:
nclreg(x,  ...)

Arguments

formula	symbolic description of the model, see details.
data	argument controlling formula processing via model.frame.
weights	optional numeric vector of weights. If standardize=TRUE, weights are renormalized to weights/sum(weights). If standardize=FALSE, weights are kept as original input
x	input matrix, of dimension nobs x nvars; each row is an observation vector
y	response variable. Quantitative for rfamily="clossR" and -1/1 for classification.
offset	Not implemented yet
contrasts	the contrasts corresponding to levels from the respective models
...	Other arguments passing to nclreg_fit

Details

The sequence of robust models implied by lambda is fit by majorization-minimization along with coordinate descent. Note that the objective function is

weights*loss + λ*penalty,

if standardize=FALSE and

\frac{weights}{∑(weights)}*loss + λ*penalty,

if standardize=TRUE.

Value

An object with S3 class "nclreg" for the various types of models.

call	the call that produced this object
b0	Intercept sequence of length length(lambda)
beta	A nvars x length(lambda) matrix of coefficients.
lambda	The actual sequence of lambda values used
nobs	number of observations
risk	if type.path="nonactive", a matrix with number of rows iter and number of columns nlambda, loss values along the regularization path. If type.path="fast", a vector of length nlambda, loss values along the regularization path
pll	if type.path="nonactive", a matrix with number of rows iter and number of columns nlambda, penalized loss values along the regularization path. If type.path="fast", a vector of length nlambda, penalized loss values along the regularization path
fitted.values	predicted values depending on standardize, internal use only

Author(s)

Zhu Wang <[e-mail]>

References

Zhu Wang (2021), MM for Penalized Estimation, TEST, doi: 10.1007/s11749-021-00770-2

See Also

print, predict, coef and plot methods, and the cv.nclreg function.

Examples

#binomial
x=matrix(rnorm(100*20),100,20)
g2=sample(c(-1,1),100,replace=TRUE)
### different solution paths via a combination of type.path, decreasing and type.init
fit1=nclreg(x,g2,s=1,rfamily="closs",type.path="active",decreasing=TRUE,type.init="bst")
fit2=nclreg(x,g2,s=1,rfamily="closs",type.path="active",decreasing=FALSE,type.init="bst")
fit3=nclreg(x,g2,s=1,rfamily="closs",type.path="nonactive",decreasing=TRUE,type.init="bst")
fit4=nclreg(x,g2,s=1,rfamily="closs",type.path="nonactive",decreasing=FALSE,type.init="bst")
fit5=nclreg(x,g2,s=1,rfamily="closs",type.path="active",decreasing=TRUE,type.init="ncl")
fit6=nclreg(x,g2,s=1,rfamily="closs",type.path="active",decreasing=FALSE,type.init="ncl")
fit7=nclreg(x,g2,s=1,rfamily="closs",type.path="nonactive",decreasing=TRUE,type.init="ncl")
fit8=nclreg(x,g2,s=1,rfamily="closs",type.path="nonactive",decreasing=FALSE,type.init="ncl")

mpath documentation built on Jan. 7, 2023, 1:17 a.m.