blockwise_coordinate_descent_general: Blockwise coordinate descent

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

Description

Implement blockwise coordinate descent algorithm. Best penalty value is evaluated through cross-validation.

Usage

blockwise_coordinate_descent_general(
  Z,
  y,
  n,
  p,
  p1,
  p2,
  p3,
  center.Z = TRUE,
  scale.Z = TRUE,
  center.y = TRUE,
  scale.y = TRUE,
  lambda.factor = ifelse(dim(Z)[1] < dim(Z)[2], 0.01, 0.001),
  step = 100,
  K = 4,
  mu = 10,
  tau = NULL,
  etol = 1e-04,
  optTol = 1e-05,
  earlyStopping_max = 10,
  penalty = c("lasso", "SCAD"),
  mode = "ADMM"
)

Arguments

Z	Corrupted design matrix (with additive error or missing data)
y	Response vector
n	Number of samples of the design matrix
p	Number of features of the matrix
p1	Number of uncorrupted predictors
p2	Number of corrupted predictors containing additive error
p3	Number of corrupted predictors containing missingness
center.Z	If TRUE, centers Z matrix without taking into account NAs values, and then change NAs to 0 value (in the missing data setting).
scale.Z	If TRUE, divides Z columns by their standard deviation
center.y	If TRUE, centers y
scale.y	If TRUE, divides y by its standard deviation
lambda.factor	Range of the lambda interval we are going to explore
step	Number of values of lambda in the interval we are going to test
K	Number of folds for the cross-validation
mu	Penalty parameter for the ADMM algorithm
tau	Standard deviation for the additive error matrix in the additive error setting (NULL in the missing data setting)
etol	Tolerance parameter for the ADMM algorithm
optTol	Tolerance parameter for the convergence of the error in the pathwise coordinate descent
earlyStopping_max	Number of iterations allowed when error starts increasing
penalty	Type of penalty used : can be lasso penalty or SCAD penalty
mode	ADMM or HM

Details

It is highly recommended to use center.Z = TRUE for the algorithm to work in the case of missing data. Otherwise the algorithm will not work the way it is intended. It is recommended to use center.Z = TRUE, scale.Z = TRUE, center.y = TRUE and scale.y = TRUE for both convergence and interpretability reasons. The use of center.Z = TRUE in the additive error setting can be subject to discussion, as it may introduce bias in the algorithm. For computing speed reasons, if model is not converging or running slow, consider changing mu, decreasing etol or optTol or decreasing earlyStopping_max

Value

list containing

• lambda.opt optimal value of lambda corresponding to minimum error

• lambda.sd Value of lambda corresponding to error higher than minimum error by one standard deviation

• beta.opt Value of beta corresponding to lambda.opt

• beta.sd Value of beta corresponding to lambda.sd

• data_error Dataframe containing errors and their standard deviation for each iteration of the algorithm

• data_beta Dataframe containing the values of beta for each iteration of the algorithm

• earlyStopping Integer containing the value of iteration when early stopping happens

• vnames Column names of Z matrix

• mean.Z Mean of Z matrix without the NAs values

• sd.Z Standard deviation of Z matrix without the NAs values

• mean.y Mean of y matrix

• sd.y Standard deviation of y matrix

See Also

https://arxiv.org/pdf/1510.07123.pdf

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