transformed {PACLasso}

Transform Data to Fit PaC Implementation (Equality Constraints)

Description

This function is called internally by lars.c to compute the transformed versions of the X, Y, and constraint matrix data, as shown in the PaC paper.

Usage

transformed(x, y, C.full, b, lambda, beta0, eps = 10^-8)

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

lambda

value of lambda

beta0

initial guess for beta coefficient vector

eps

value close to zero used to verify SVD decomposition. Default is 10^-8

Value

x transformed x data to be used in the PaC algorithm

y transformed y data to be used in the PaC algorithm

Y_star transformed Y* value to be used in the PaC algorithm

a2 index of A used in the calculation of beta2 (the non-zero coefficients)

beta1 beta1 values

beta2 beta2 values

C constraint matrix

C2 subset of constraint matrix corresponding to non-zero coefficients

active.beta index of non-zero coefficient values

beta2.index index of non-zero coefficient values

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

random_data = generate.data(n = 500, p = 20, m = 10)
transform_fit = transformed(random_data$x, random_data$y, random_data$C.full,
random_data$b, lambda = 0.01, beta0 = rep(0,20))
dim(transform_fit$x)
head(transform_fit$y)
dim(transform_fit$C)
transform_fit$active.beta