QR.admm: Quantile Regression (QR) use Alternating Direction Method of...

In cqrReg: Quantile, Composite Quantile Regression and Regularized Versions

Quantile Regression (QR) use Alternating Direction Method of Multipliers (ADMM) algorithm

Description

The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .

Usage

QR.admm(X,y,tau,rho,beta, maxit, toler)

Arguments

X	the design matrix
y	response variable
tau	quantile level
rho	augmented Lagrangian parameter
beta	initial value of estimate coefficient (default naive guess by least square estimation)
maxit	maxim iteration (default 200)
toler	the tolerance critical for stop the algorithm (default 1e-3)

Value

a list structure is with components

beta	the vector of estimated coefficient
b	intercept

Note

QR.admm(x,y,tau) work properly only if the least square estimation is good.

References

S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein.(2010) Distributed Optimization and Statistical Learning via the Alternating Direction.Method of Multipliers Foundations and Trends in Machine Learning, 3, No.1, 1–122

Koenker, Roger. Quantile Regression, New York, 2005. Print.

Examples

set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
QR.admm(x,y,0.1)

cqrReg documentation built on June 7, 2022, 9:06 a.m.