lasso_covariance_block: Lasso in covariance form for the BD-CoCoLasso

In celiaescribe/BDcocolasso: Implementation of CoCoLasso and Block Descent CoCoLasso

Description

Solve the least squares loss with lasso penalty written in a form with the covariance matrix : \frac{1}{2} β^{'} Σ β - ρ^{'} β + λ \|β\|_1

Usage

lasso_covariance_block(
  n,
  p1,
  p2,
  X1,
  Z2,
  y,
  sigma1,
  sigma2,
  lambda,
  noise = c("additive", "missing", "HM"),
  ratio_matrix = NULL,
  control = list(maxIter = 1000, optTol = 10^(-5), zeroThreshold = 10^(-6)),
  beta1.start,
  beta2.start,
  penalty = c("lasso", "SCAD")
)

Arguments

n	Number of samples of the design matrix
p1	Number of uncorrupted predictors
p2	Number of corrupted predictors
X1	first block of the design matrix corresponding to uncorrupted features
Z2	second block of the design matrix corresponding to corrupted features
y	Response vector
sigma1	Covariance matrix for X1 : \frac{1}{n} X_1'X_1. This parameter is automatically furnished in blockwise_coordinate_descent
sigma2	Modified covariance matrix for Z2 through the CoCoLasso algorithm. This parameter is automatically furnished in blockwise_coordinate_descent
lambda	Penalty parameter
noise	Type of noise for Z2 : additive or missing
ratio_matrix	Observation matrix in the missing data setting (NULL otherwise)
control	Including control parameters : max of iterations, tolerance for the convergence of the error, zero threshold to put to zero small beta coefficients
beta1.start	Initial value for the coefficients of uncorrupted features
beta2.start	Initial value for the coefficients of corrupted features
penalty	Type of penalty used : can be lasso penalty or SCAD penalty

Value

list containing

• coefficients.beta1 : Coefficients corresponding to final beta1 after convergence of the algoritm

• coefficients.beta2 : Coefficients corresponding to final beta2 after convergence of the algoritm

• num.it : Number of iterations of algorithm

celiaescribe/BDcocolasso documentation built on Feb. 11, 2020, 11:41 p.m.