Package 'hrqglas'

Extract coefficients from cv.hrq_glasso object

Description

Extract coefficients from cv.hrq_glasso object

Usage

## S3 method for class 'cv.hrq_glasso'
coef(object, s, ...)

Arguments

object	The model object cv.hrq_glasso object.
s	Value of lambda.
...	other input parameters.

Value

The function extract estimated coefficients from cv.hrq_glasso object.

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Extract coefficients from hrq_glasso object

Description

Extract coefficients from hrq_glasso object

Usage

## S3 method for class 'hrq_glasso'
coef(object, s, ...)

Arguments

object	The model object hrq_glasso object.
s	Value of lambda.
...	other input parameters.

Value

The function extract estimated coefficients from hrq_glasso object.

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Cross-validation for quantile regression with group lasso

Description

K fold cross-validation is conducted. Four types of loss (squared error (se), absolute error (ae) quantile check loss (check) and huber loss (he)) can be specified as the CV criterion.

Usage

cv.hrq_glasso(
  x,
  y,
  group.index,
  tau = 0.5,
  k = 5,
  loss = "check",
  method = "quantile",
  folds = NULL,
  ...
)

Arguments

x	Design matrix
y	Response variable
group.index	A vector of group index, e.g., (1,1,1,2,2,2,3,3)
tau	Percentage
k	Number of folders.
loss	The loss function used for computing the cross-validation error. Supported losses include squared error (se), absolute error (ae), quantile check loss (check) and huber loss (he).
method	Choice for mean or quantile regression. Default is quantile.
folds	A vector of folder index for all observations. The procedure random splits if this argument is not specified.
...	Other inputs of function hrq_glasso().

Value

The full solution path is returned. It also returns the vector of CV score as well as the optimal values in terms of min and 1se. Corresponding lambda values are also returned.

beta	The estimated coefficients for all lambdas, stored in sparse matrix format, where each column corresponds to a lambda.
lambda	The sequence of lambdas.
lambda.min	The optimal lambda that minimizes the CV error
lambda.1se	The largest lambda such that CV error is within 1 standard error of the minimum CV error.
cv.all	The vector of all values of CV error for all lambdas.
cv.min	The value of CV error corresponding to lambda.min.
cv.1se	The value of CV error corresponding to lambda.1se.
folds	The vector of indices for k folds split.
cvup	CV error + 1 standard error
cvlo	CV error + 1 standard error
n.grp	The number of selected groups for each lambda.

Examples

n<- 100
p<- 10
x0<- matrix(rnorm(n*p),n,p)
X<- cbind(x0, x0^2, x0^3)[,order(rep(1:p,3))]
y<- -2+X[,1]+0.5*X[,2]-X[,3]-0.5*X[,7]+X[,8]-0.2*X[,9]+rt(n,2)
group<- rep(1:p, each=3)
fitcv<- cv.hrq_glasso(x=X, y=y, group.index=group, method="quantile")
plot(fitcv)

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Robust group variable selection for quantile and mean regression

Description

This function conducts group-wise (with known groups) variable selection for quantile and robust mean regression with the group lasso penalty. The Huber loss is used for both types of regression model, where the quantile check function is approximated by Huber loss. A full solution path is generated unless a single value of the shrinkage parameter is specified.

Usage

hrq_glasso(
  x,
  y,
  group.index,
  tau = 0.5,
  lambda = NULL,
  weights = NULL,
  w.lambda = NULL,
  gamma = 0.2,
  max_iter = 200,
  apprx = "huber",
  lambda.discard = TRUE,
  method = "quantile",
  scalex = TRUE,
  epsilon = 1e-04,
  beta0 = NULL
)

Arguments

x	Design matrix (in matrix format)
y	Response variable
group.index	A vector of group index, e.g., (1,1,1,2,2,2,3,3)
tau	Percentile
lambda	Shrinkage parameter, default is NULL so that the algorithm chooses a sequence.
weights	Observation weights, default is NULL
w.lambda	Weights for Shrinkage parameter of each group, default is NULL
gamma	Huber parameter. An initial value is 0.2, while the algorithm adaptively tunes the value in each iteration.
max_iter	Maximum number of iteration
apprx	Approximation method. Default is huber. The other option is tanh which uses the hypertangent function to approximate the first order derivative of absolute loss.
lambda.discard	Default is TRUE, meaning that the solution path stops if the relative deviance changes sufficiently small. It usually happens near the end of solution path. However, the program returns at least 70 models along the solution path.
method	Choice for mean or quantile regression. Default is quantile.
scalex	Standardize design matrix. Default is TRUE.
epsilon	The epsilon level convergence. Default is 1e-4.
beta0	Initial estimates. Default is NULL.

Value

It returns a sequence of estimated coefficients for quantile regression with group feature selection corresponding to a sequence of lambda. The estimated coefficients are in the sparse matrix format. Returned values also include the sequence of lambda, the null deviance, values of penalized loss, and unpenalized loss across the sequence of lambda.

beta	The estimated coefficients for all lambdas, stored in sparse matrix format, where each column corresponds to a lambda.
lambda	The sequence of lambdas.
null.dev	The null deviance.
pen.loss	The value of penalized loss for each lambda.
loss	The value of unpenalized loss for each lambda.
index.grp	Group indices that correspond to the estimated coefficient matrix beta.
n.grp	The number of selected groups for each lambda.

References

Sherwood, B., and Li, S. (2021) An Efficient Approach to Feature Selection and Estimation for Quantile Regression with Grouped Variables. Working paper.

Yang, Y., and Zou, H., (2015) A Fast Unified Algorithm for Solving Group-lasso Penalize Learning Problems, Statistics and Computing, 25 1129-1141. doi:10.1007/s11222-014-9498-5.

Examples

n<- 100
p<- 10
x0<- matrix(rnorm(n*p),n,p)
X<- cbind(x0, x0^2, x0^3)[,order(rep(1:p,3))]
y<- -2+X[,1]+0.5*X[,2]-X[,3]-0.5*X[,7]+X[,8]-0.2*X[,9]+rt(n,2)
group<- rep(1:p, each=3)
fit<- hrq_glasso(X, y, group)
fit$beta[,8]

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Generating plots for cross-validation

Description

Generating plots for cross-validation

Usage

## S3 method for class 'cv.hrq_glasso'
plot(x, ...)

Arguments

x	The object of function cv.hrq_glasso.
...	other input parameters for the generic function plot.

Value

Cross-validation plot for the entire solution path.

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Prediction for cv.hrq_glasso object

Description

Prediction for cv.hrq_glasso object

Usage

## S3 method for class 'cv.hrq_glasso'
predict(object, newX, s, ...)

Arguments

object	The model object of cv.hrq_glasso.
newX	New design matrix.
s	Value of lambda. If missing, the default is the lambda.min.
...	other input parameters.

Value

The function returns predicted values based on the fitted model from cv.hrq_glasso.

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Prediction for the hrq_glasso object

Description

This function provides the prediction of the hrq_glasso object.

Usage

## S3 method for class 'hrq_glasso'
predict(object, newX, s = NULL, ...)

Arguments

object	The model object of hrq_glasso.
newX	New design matrix.
s	Value of lambda. Default is NULL, so that the function provides prediction at all lambdas used in hrq_glasso.
...	other input parameters.

Value

The function returns predicted values based on the fitted model from hrq_glasso.

Examples

n<- 100
p<- 10
x0<- matrix(rnorm(n*p),n,p)
X<- cbind(x0, x0^2, x0^3)[,order(rep(1:p,3))]
y<- -2+X[,1]+0.5*X[,2]-X[,3]-0.5*X[,7]+X[,8]-0.2*X[,9]+rt(n,2)
group<- rep(1:p, each=3)
fit<- hrq_glasso(X, y, group)
pred<- predict(fit, newX=X, s=0.3)

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