orderedLasso: Fit an ordered lasso

In orderedLasso: Ordered Lasso and Time-Lag Sparse Regression

Description

One of the main functions. Ordered Lasso builds a regression model with an L1-constraint imposed on the coefficients. The coefficients are re-written as negative and positive parts and the model requires positive and negative parts are monotone non-increasing and positive.

Usage

orderedLasso(x, y, lambda, intercept = TRUE, b0 = NULL, beta_pos = NULL,
  beta_neg = NULL, method = c("Solve.QP", "GG"), strongly.ordered = FALSE,
  standardize = TRUE, trace = FALSE, niter = 500, iter.gg = 100,
  epsilon = 1e-08)

Arguments

x	A matrix of predictors, where the rows are the samples and the columns are the predictors
y	A vector of observations, where length(y) equals nrow(x)
lambda	Regularization parameter(>0)
intercept	TRUE if there is an intercept in the model.
b0	Initial value for the intercept.
beta_pos	Optional vector of initialization of the positive part of the coefficients.
beta_neg	Optional vector of initialization of the negative part of the coefficients.
method	Two options available, Solve.QP and Generalized Gradient. Solve.QP uses the package quadprog to solve a quadratic programming problem. GG stands for genearlized gradient. GG uses proximal genearalized gradient algorithm to solve the problem. Detailed can be seen in the paper refered in the description.
strongly.ordered	An option which allows users to order the coefficients in absolute value. The coefficients returned by the orderedLasso may not be monotone non-increasing in absolute value even though the positive parts and negative parts are monotone non-increasing. Details can be seen in the paper referred in the Description. Strongly.ordered options returns the coefficients monotone non-increasing in absolute value.
standardize	Standardize the data matrix x
trace	Output option; trace = TRUE gives verbose output
niter	Maximum number of iterations; default 500.
iter.gg	Number of iterations of genearalized gradient; default 100
epsilon	Error tolerance parameter for convergence criterion ; default 1e-05.

Value

bp	Estimated coefficients- positive part
bn	Estimated coefficients- negative part
beta	Estimated coefficients, which are equal to bp - bn
b0	Estimated intercept, if there is one in the model.
fitted	Fitted values of y
type	Type of model fit, "gaussian"
call	The call to orderedLasso

Examples

set.seed(3)
n = 50
b = c(7,3,1,0)
p = length(b)
x = matrix(rnorm(n*p),nrow = n)
sigma = 4
y = x %*% b + sigma * rnorm(n, 0, 1)
result1 = orderedLasso(x,y, lambda = 1, intercept =TRUE, standardize = TRUE,
          method = "GG", strongly.ordered = TRUE)
result2 = orderedLasso(x,y, lambda = 1, intercept = TRUE, standardize =TRUE,
          strongly.ordered = TRUE)
print(result1)
print(result2)

Example output

Loading required package: Matrix
Call
orderedLasso(x = x, y = y, lambda = 1, intercept = TRUE, method = "GG", 
    strongly.ordered = TRUE, standardize = TRUE)

       beta_pos beta_neg       beta beta.ordered
[1,] 6.23014945        0 6.23014945   6.23014945
[2,] 3.16808611        0 3.16808611   3.16808611
[3,] 0.59988916        0 0.59988916   0.59988916
[4,] 0.05781525        0 0.05781525   0.05781525

beta_zero = 0.379694 beta.ordered_zero =  0.379694
Call
orderedLasso(x = x, y = y, lambda = 1, intercept = TRUE, strongly.ordered = TRUE, 
    standardize = TRUE)

       beta_pos     beta_neg       beta beta.ordered
[1,] 6.23001551 4.503967e-20 6.23001551   6.23001551
[2,] 3.16801566 0.000000e+00 3.16801566   3.16801566
[3,] 0.59987131 0.000000e+00 0.59987131   0.59987131
[4,] 0.05782413 0.000000e+00 0.05782413   0.05782413

beta_zero = 0.3796877 beta.ordered_zero =  0.3796877

orderedLasso documentation built on May 2, 2019, 6:36 a.m.