APML0 (version 0.10)

APML0-package: Augmented and Penalized Minimization Method L0

Description

Fit linear, logistic and Cox models regularized with L0, lasso (L1), elastic-net (L1 and L2), or net (L1 and Laplacian) penalty, and their adaptive forms, such as adaptive lasso / elastic-net and net adjusting for signs of linked coefficients. It solves L0 penalty problem by simultaneously selecting regularization parameters and performing hard-thresholding (or selecting number of non-zeros). This augmented and penalized minimization method provides an approximation solution to the L0 penalty problem, but runs as fast as L1 regularization problem.

The package uses one-step coordinate descent algorithm and runs extremely fast by taking into account the sparsity structure of coefficients. It could deal with very high dimensional data.

Details

Package:	APML0
Type:	Package
Version:	0.10
Date:	2020-1-19
License:	GPL (>= 2)

Functions: APML0, print.APML0

References

Li, X., Xie, S., Zeng, D., Wang, Y. (2018). Efficient l0-norm feature selection based on augmented and penalized minimization. Statistics in medicine, 37(3), 473-486. https://onlinelibrary.wiley.com/doi/full/10.1002/sim.7526 Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1), 1-122. http://dl.acm.org/citation.cfm?id=2185816 Friedman, J., Hastie, T., Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent, Journal of Statistical Software, Vol. 33(1), 1. http://www.jstatsoft.org/v33/i01/

Examples

# NOT RUN {
###  Linear model  ###
set.seed(1213)
N=100;p=30;p1=5
x=matrix(rnorm(N*p),N,p)
beta=rnorm(p1)
xb=x[,1:p1]%*%beta
y=rnorm(N,xb)

fiti=APML0(x,y,penalty="Lasso",nlambda=10) # Lasso
fiti2=APML0(x,y,penalty="Lasso",nlambda=10,nfolds=10) # Lasso
# attributes(fiti)



###  Logistic model  ###
set.seed(1213)
N=100;p=30;p1=5
x=matrix(rnorm(N*p),N,p)
beta=rnorm(p1)
xb=x[,1:p1]%*%beta
y=rbinom(n=N, size=1, prob=1.0/(1.0+exp(-xb)))

fiti=APML0(x,y,family="binomial",penalty="Lasso",nlambda=10) # Lasso
fiti2=APML0(x,y,family="binomial",penalty="Lasso",nlambda=10,nfolds=10) # Lasso
# attributes(fiti)



###  Cox model  ###
set.seed(1213)
N=100;p=30;p1=5
x=matrix(rnorm(N*p),N,p)
beta=rnorm(p1)
xb=x[,1:p1]%*%beta
ty=rexp(N, exp(xb))
td=rexp(N, 0.05)
tcens=ifelse(td<ty,1,0)  # censoring indicator
y=cbind(time=ty,status=1-tcens)

fiti=APML0(x,y,family="cox",penalty="Lasso",nlambda=10) # Lasso
fiti2=APML0(x,y,family="cox",penalty="Lasso",nlambda=10,nfolds=10) # Lasso
# attributes(fiti)
# }