PACLasso (version 1.0.0)

lars.c: Constrained LARS Coefficient Function (Equality Constraints)

Description

This function computes the PaC constrained LASSO coefficient paths following the methodology laid out in the PaC paper. This function could be called directly as a standalone function, but the authors recommend using lasso.c for any implementation. This is because lasso.c has additional checks for errors across the coefficient paths and allows for users to go forwards and backwards through the paths if the paths are unable to compute in a particular direction for a particular run.

Usage

lars.c(x, y, C.full, b, l.min = -2, l.max = 6, step = 0.2,
  beta0 = NULL, verbose = F, max.it = 12, intercept = T,
  normalize = T, forwards = T)

Arguments

x

independent variable matrix of data to be used in calculating PaC coefficient paths

y

response vector of data to be used in calculating PaC coefficient paths

C.full

complete constraint matrix C (with constraints of the form C.full*beta=b)

b

constraint vector b

l.min

lowest value of lambda to consider (used as 10^l.min). Default is -2

l.max

largest value of lambda to consider (used as 10^l.max). Default is 6

step

step size increase in lambda attempted at each iteration (by a factor of 10^step). Default is 0.2

beta0

initial guess for beta coefficient vector. Default is NULL (indicating initial vector should be calculated by algorithm)

verbose

should function print output at each iteration (TRUE) or not (FALSE). Default is FALSE

max.it

maximum number of times step size is halved before the algorithm terminates and gives a warning. Default is 12

intercept

should intercept be included in modeling (TRUE) or not (FALSE). Default is TRUE.

normalize

should x data be normalized. Default is TRUE

forwards

if forwards = F, then the algorithm starts at 10^l.max and moves backwards (without the forward step). If forwards = T, algorithm starts at 10^l.min and works forward. Default is FALSE

Value

coefs A p by length(lambda) matrix with each column corresponding to the beta estimate for that lambda

lambda the grid of lambdas used to calculate the coefficients on the coefficient path

intercept vector with each element corresponding to intercept for corresponding lambda

error did the algorithm terminate due to too many iterations (TRUE or FALSE)

b2index the index of the beta2 values identified by the algorithm at each lambda

References

Gareth M. James, Courtney Paulson, and Paat Rusmevichientong (JASA, 2019) "Penalized and Constrained Optimization." (Full text available at http://www-bcf.usc.edu/~gareth/research/PAC.pdf)

Examples

# NOT RUN {
random_data = generate.data(n = 500, p = 20, m = 10)
lars_fit = lars.c(random_data$x, random_data$y, random_data$C.full, random_data$b)
lars_fit$lambda
lars_fit$error
### The coefficients for the first lambda value
lars_fit$coefs[1,]
### Example of code where path is unable
### to be finished (only one iteration)
lars_err = lars.c(random_data$x, random_data$y, random_data$C.full,
random_data$b, max.it = 1)
lars_err$error
lars_err$lambda
# }