Package 'SALES'

Title: The (Adaptive) Elastic Net and Lasso Penalized Sparse Asymmetric Least Squares (SALES) and Coupled Sparse Asymmetric Least Squares (COSALES) using Coordinate Descent and Proximal Gradient Algorithms
Description: A coordinate descent algorithm for computing the solution paths of the sparse and coupled sparse asymmetric least squares, including the (adaptive) elastic net and Lasso penalized SALES and COSALES regressions.
Authors: Yuwen Gu <[email protected]>, Hui Zou <[email protected]>
Maintainer: Yuwen Gu <[email protected]>
License: GPL (>= 2)
Version: 1.0.2
Built: 2024-11-28 06:42:17 UTC
Source: CRAN

Help Index

Extract Model Coefficients

Description

coef is a generic function which extracts model coefficients from objects returned by modeling functions. coefficients is an alias for it.

Usage

coef(object, ...)

Arguments

object

an object for which the extraction of model coefficients is meaningful.
...

other arguments.

Value

Coefficients extracted from the model object object.

See Also

coef.ernet, coef.cpernet

Get coefficients from a cpernet object

Description

Computes the coefficients or returns a list of the indices of the nonzero coefficients at the requested values for lambda from a fitted cpernet object.

Usage

## S3 method for class 'cpernet'
coef(object, s = NULL, type = c("coefficients", "nonzero"), ...)

Arguments

object

fitted cpernet model object.
s

value(s) of the penalty parameter lambda at which predictions are to be made. Default is the entire sequence used to create the model.
type

type "coefficients" computes coefficients at the requested values for s. Type "nonzero" returns a list of the indices of nonzero coefficients for each value of s. Default is "coefficients".
...

not used. Other arguments to predict.

Details

s is the new vector at which predictions are requested. If s is not in the lambda sequence used for fitting the model, the coef function will use linear interpolation to make predictions. The new values are interpolated using a fraction of coefficients from both left and right lambda indices.

Value

The object returned depends on type.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cpernet, predict.cpernet, print.cpernet, plot.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2 <- cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
              pf.mean = pf, pf.scale = pf2, intercept = TRUE,
              standardize = FALSE, lambda2 = lambda2)

mean.coef <- as.vector(coef(m2, s = m2$lambda[50])[[1]])
scale.coef <- as.vector(coef(m2, s = m2$lambda[50])[[2]])

Get coefficients from a cv.cpernet object

Description

This function gets coefficients from a cross-validated cpernet model, using the fitted cv.cpernet object, and the optimal value chosen for lambda.

Usage

## S3 method for class 'cv.cpernet'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

object

fitted cv.cpernet object.
s

value(s) of the penalty parameter lambda at which predictions are required. Default is the value s="lambda.1se" stored on the CV object, it is the largest value of lambda such that error is within 1 standard error of the minimum. Alternatively s="lambda.min" can be used, it is the optimal value of lambda that gives minimum cross validation error cvm. If s is numeric, it is taken as the value(s) of lambda to be used.
...

not used. Other arguments to predict.

Details

This function makes it easier to use the results of cross-validation to get coefficients or make coefficient predictions.

Value

The object returned depends the ... argument which is passed on to the predict method for cpernet objects.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cv.cpernet, predict.cv.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2.cv <- cv.cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
                    pf.mean = pf, pf.scale = pf2,
                    standardize = FALSE, lambda2 = lambda2)
as.vector(coef(m2.cv, s = "lambda.min")$beta)
as.vector(coef(m2.cv, s = "lambda.min")$theta)

Get coefficients from a cv.ernet object

Description

This function gets coefficients from a cross-validated ernet model, using the fitted cv.ernet object, and the optimal value chosen for lambda.

Usage

## S3 method for class 'cv.ernet'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

object

fitted cv.ernet object.
s

value(s) of the penalty parameter lambda at which predictions are required. Default is the value s="lambda.1se" stored on the CV object, it is the largest value of lambda such that error is within 1 standard error of the minimum. Alternatively s="lambda.min" can be used, it is the optimal value of lambda that gives minimum cross validation error cvm. If s is numeric, it is taken as the value(s) of lambda to be used.
...

not used. Other arguments to predict.

Details

This function makes it easier to use the results of cross-validation to get coefficients or make coefficient predictions.

Value

The object returned depends the ... argument which is passed on to the predict method for ernet objects.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cv.ernet, predict.cv.ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1.cv <- cv.ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
                  pf2 = pf2, standardize = FALSE, intercept = FALSE,
                  lambda2 = lambda2)
as.vector(coef(m1.cv, s = "lambda.min"))

Get coefficients from an ernet object

Description

Computes the coefficients or returns a list of the indices of the nonzero coefficients at the requested values for lambda from a fitted ernet object.

Usage

## S3 method for class 'ernet'
coef(object, s = NULL, type = c("coefficients", "nonzero"), ...)

Arguments

object

fitted ernet model object.
s

value(s) of the penalty parameter lambda at which predictions are to be made. Default is the entire sequence used to create the model.
type

type "coefficients" computes coefficients at the requested values for s. Type "nonzero" returns a list of the indices of nonzero coefficients for each value of s. Default is "coefficients".
...

not used. Other arguments to predict.

Details

s is the new vector at which predictions are requested. If s is not in the lambda sequence used for fitting the model, the coef function will use linear interpolation to make predictions. The new values are interpolated using a fraction of coefficients from both left and right lambda indices.

Value

The object returned depends on type.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

ernet, predict.ernet, print.ernet, plot.ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1 <- ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
            pf2 = pf2, standardize = FALSE, intercept = FALSE,
            lambda2 = lambda2)
as.vector(coef(m1, s = m1$lambda[5]))

Regularization paths for the coupled sparse asymmetric least squares (COSALES) regression (or the coupled sparse expectile regression)

Description

Fits regularization paths for coupled sparse asymmetric least squares regression at a sequence of regularization parameters.

Usage

cpernet(
  x,
  y,
  w = 1,
  nlambda = 100L,
  method = "cper",
  lambda.factor = ifelse(2 * nobs < nvars, 0.01, 1e-04),
  lambda = NULL,
  lambda2 = 0,
  pf.mean = rep(1, nvars),
  pf2.mean = rep(1, nvars),
  pf.scale = rep(1, nvars),
  pf2.scale = rep(1, nvars),
  exclude,
  dfmax = nvars + 1,
  pmax = min(dfmax * 1.2, nvars),
  standardize = TRUE,
  intercept = TRUE,
  eps = 1e-08,
  maxit = 1000000L,
  tau = 0.8
)

Arguments

x

matrix of predictors, of dimension (nobs * nvars); each row is an observation.
y

response variable.
w

weight applied to the asymmetric squared error loss of the mean part. See details. Default is 1.0.
nlambda

the number of lambda values (default is 100).
method

a character string specifying the loss function to use. Only cper is available now.
lambda.factor

The factor for getting the minimal lambda in the lambda sequence, where we set min(lambda) = lambda.factor * max(lambda) with max(lambda) being the smallest value of lambda that penalizes all coefficients to zero. The default value depends on the relationship between NN (the number of observations) and pp (the number of predictors). If N<pN < p, the default is 0.01. If N>pN > p, the default is 0.0001, closer to zero. A very small value of lambda.factor will lead to a saturated fit. The argument takes no effect if there is a user-supplied lambda sequence.
lambda

a user-supplied lambda sequence. Typically, by leaving this option unspecified users can have the program compute its own lambda sequence based on nlambda and lambda.factor. It is better to supply, if necessary, a decreasing sequence of lambda values than a single (small) value. The program will ensure that the user-supplied lambda sequence is sorted in decreasing order.
lambda2

regularization parameter lambda2 for the quadratic penalty of the coefficients. Default is 0, meaning no L2 penalization.
pf.mean, pf.scale

L1 penalty factor of length pp used for adaptive LASSO or adaptive elastic net. Separate L1 penalty weights can be applied to each mean or scale coefficient to allow different L1 shrinkage. Can be 0 for some variables, which imposes no shrinkage and results in that variable being always included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude).
pf2.mean, pf2.scale

L2 penalty factor of length pp used for adaptive elastic net. Separate L2 penalty weights can be applied to each mean or scale coefficient to allow different L2 shrinkage. Can be 0 for some variables, which imposes no shrinkage. Default is 1 for all variables.
exclude

indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor.
dfmax

limit the maximum number of variables in the model. Useful for very large pp, if a partial path is desired. Default is p+1p+1.
pmax

limit the maximum number of variables ever to be nonzero. For example once β\beta enters the model, no matter how many times it exits or re-enters the model through the path, it will be counted only once. Default is min(dfmax*1.2, p).
standardize

logical flag for variable standardization, prior to fitting the model sequence. The coefficients are always returned to the original scale. Default is TRUE.
intercept

Should intercept(s) be fitted (default=TRUE) or set to zero (FALSE).
eps

convergence threshold for coordinate descent. Each inner coordinate descent loop continues until the maximum change in any coefficient is less than eps. Defaults value is 1e-8.
maxit

maximum number of outer-loop iterations allowed at fixed lambda values. Default is 1e7. If the algorithm does not converge, consider increasing maxit.
tau

the parameter tau in the coupled ALS regression model. The value must be in (0,1) and cannot be 0.5. Default is 0.8.

Details

Note that the objective function in cpernet is

w∗1′Ψ(y−Xβ,0.5)/N+1′Ψ(y−Xβ−Xθ,τ)/N+λ1∗∥β∥1+0.5λ2∥β∥22+μ1∗∥θ∥+0.5μ2∥θ∥22,w*1'\Psi(y-X\beta,0.5)/N + 1'\Psi(y-X\beta-X\theta,\tau)/N + \lambda_1*\Vert\beta\Vert_1 + 0.5\lambda_2\Vert\beta\Vert_2^2 + \mu_1*\Vert\theta\Vert + 0.5\mu_2\Vert\theta\Vert_2^2,

where Ψ(u,τ)=∣τ−I(u<0)∣∗u2\Psi(u,\tau)=|\tau-I(u<0)|*u^2 denotes the asymmetric squared error loss and the penalty is a combination of L1 and L2 terms for both the mean and scale coefficients.

For faster computation, if the algorithm is not converging or running slow, consider increasing eps, decreasing nlambda, or increasing lambda.factor before increasing maxit.

Value

An object with S3 class cpernet.

call

the call that produced this object.
b0, t0

intercept sequences both of length length(lambda) for the mean and scale respectively.
beta, theta

p*length(lambda) matrices of coefficients for the mean and scale respectively, stored as sparse matrices (dgCMatrix class, the standard class for sparse numeric matrices in the Matrix package). To convert them into normal R matrices, use as.matrix().
lambda

the actual sequence of lambda values used
df.beta, df.theta

the number of nonzero mean and scale coefficients respectively for each value of lambda.
dim

dimensions of coefficient matrices.
npasses

total number of iterations summed over all lambda values.
jerr

error flag, for warnings and errors, 0 if no error.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

References

Gu, Y., and Zou, H. (2016). "High-dimensional generalizations of asymmetric least squares regression and their applications." The Annals of Statistics, 44(6), 2661–2694.

See Also

plot.cpernet, coef.cpernet, predict.cpernet, print.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2 <- cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
              pf.mean = pf, pf.scale = pf2,
              standardize = FALSE, lambda2 = lambda2)

Cross-validation for cpernet

Description

Does k-fold cross-validation for cpernet, produces a plot, and returns a value for lambda. This function is based on the cv function from the glmnet package.

Usage

cv.cpernet(
  x,
  y,
  w = 1,
  lambda = NULL,
  pred.loss = "loss",
  nfolds = 5,
  foldid,
  tau = 0.8,
  ...
)

Arguments

x

x matrix as in cpernet.
y

response variable y as in cpernet.
w

weight applied to the asymmetric squared error loss of the mean part. Default is 1.0.
lambda

optional user-supplied lambda sequence; default is NULL, and cpernet chooses its own sequence.
pred.loss

loss function used to calculate cross-validation error. The only option now is "loss", which is the asymmetric squared error loss (ASEL).
nfolds

number of folds. Default value is 5. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowed is 3.
foldid

an optional vector of values between 1 and nfolds, identifying what fold each observation is in. If supplied, nfolds will be supressed.
tau

the asymmetry coefficient τ\tau used in the asymmetric squared error loss.
...

other arguments that can be passed to cpernet.

Details

The function runs cpernet nfolds+1 times. The first gets the lambda sequence, and the remainder fits the model with each of the folds removed. The average error and standard deviation over the folds are computed.

Value

an object of class cv.cpernet is returned, which is a list with the ingredients of the cross-validation fit.

lambda

the values of lambda used in the fits.
cvm

the mean cross-validated error - a vector of length length(lambda).
cvsd

estimate of standard error of cvm.
cvupper

upper curve = cvm+cvsd.
cvlower

lower curve = cvm-cvsd.
nzero

a list of two components, each representing the number of non-zero coefficients at each lambda in the mean and scale part.
name

a text string indicating type of measure (for plotting purposes).
cpernet.fit

a fitted cpernet object for the full data.
lambda.min

The optimal value of lambda that gives minimum cross validation error cvm.
lambda.1se

The largest value of lambda such that error is within 1 standard error of the minimum.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2.cv <- cv.cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
                    pf.mean = pf, pf.scale = pf2,
                    standardize = FALSE, lambda2 = lambda2)

Cross-validation for ernet

Description

Does k-fold cross-validation for ernet, produces a plot, and returns a value for lambda. This function is based on the cv function from the glmnet package.

Usage

cv.ernet(
  x,
  y,
  lambda = NULL,
  pred.loss = "loss",
  nfolds = 5,
  foldid,
  tau = 0.5,
  ...
)

Arguments

x

x matrix as in ernet.
y

response variable y as in ernet.
lambda

optional user-supplied lambda sequence; default is NULL, and ernet chooses its own sequence.
pred.loss

loss function used to calculate cross-validation error. The only option now is "loss", which is the asymmetric squared error loss (ASEL).
nfolds

number of folds. Default value is 5. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowed is 3.
foldid

an optional vector of values between 1 and nfolds, identifying what fold each observation is in. If supplied, nfolds will be supressed.
tau

the asymmetry coefficient τ\tau used in the asymmetric squared error loss.
...

other arguments that can be passed to ernet.

Details

The function runs ernet nfolds+1 times; the first to get the lambda sequence, and the remainder to compute the fit with each of the folds removed. The average error and standard deviation over the folds are computed.

Value

an object of class cv.ernet is returned, which is a list with the ingredients of the cross-validation fit.

lambda

the values of lambda used in the fits.
cvm

the mean cross-validated error - a vector of length length(lambda).
cvsd

estimate of standard error of cvm.
cvupper

upper curve = cvm+cvsd.
cvlower

lower curve = cvm-cvsd.
nzero

number of non-zero coefficients at each lambda.
name

a text string indicating type of measure (for plotting purposes).
ernet.fit

a fitted ernet object for the full data.
lambda.min

The optimal value of lambda that gives minimum cross validation error cvm.
lambda.1se

The largest value of lambda such that error is within 1 standard error of the minimum.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1.cv <- cv.ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
                  pf2 = pf2, standardize = FALSE, intercept = FALSE,
                  lambda2 = lambda2)

Regularization paths for the sparse asymmetric least squares (SALES) regression (or the sparse expectile regression)

Description

Fits regularization paths for the Lasso or elastic net penalized asymmetric least squares regression at a sequence of regularization parameters.

Usage

ernet(
  x,
  y,
  nlambda = 100L,
  method = "er",
  lambda.factor = ifelse(nobs < nvars, 0.01, 1e-04),
  lambda = NULL,
  lambda2 = 0,
  pf = rep(1, nvars),
  pf2 = rep(1, nvars),
  exclude,
  dfmax = nvars + 1,
  pmax = min(dfmax * 1.2, nvars),
  standardize = TRUE,
  intercept = TRUE,
  eps = 1e-08,
  maxit = 1000000L,
  tau = 0.5
)

Arguments

x

matrix of predictors, of dimension (nobs * nvars); each row is an observation.
y

response variable.
nlambda

the number of lambda values (default is 100).
method

a character string specifying the loss function to use. only er is available now.
lambda.factor

The factor for getting the minimal lambda in the lambda sequence, where we set min(lambda) = lambda.factor * max(lambda) with max(lambda) being the smallest value of lambda that penalizes all coefficients to zero. The default depends on the relationship between NN (the number of rows in the matrix of predictors) and pp (the number of predictors). If N<pN < p, the default is 0.01. If N>pN > p, the default is 0.0001, closer to zero. A very small value of lambda.factor will lead to a saturated fit. It takes no effect if there is a user-supplied lambda sequence.
lambda

a user-supplied lambda sequence. Typically, by leaving this option unspecified users can have the program compute its own lambda sequence based on nlambda and lambda.factor. It is better to supply, if necessary, a decreasing sequence of lambda values than a single (small) value. The program will ensure that the user-supplied lambda sequence is sorted in decreasing order before fitting the model.
lambda2

regularization parameter lambda2 for the quadratic penalty of the coefficients.
pf

L1 penalty factor of length pp used for the adaptive LASSO or adaptive elastic net. Separate L1 penalty weights can be applied to each coefficient to allow different L1 shrinkage. Can be 0 for some variables, which imposes no shrinkage, and results in that variable always be included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude).
pf2

L2 penalty factor of length pp used for adaptive elastic net. Separate L2 penalty weights can be applied to each coefficient to allow different L2 shrinkage. Can be 0 for some variables, which imposes no shrinkage. Default is 1 for all variables.
exclude

indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor.
dfmax

the maximum number of variables allowed in the model. Useful for very large pp when a partial path is desired. Default is p+1p+1.
pmax

the maximum number of coefficients allowed ever to be nonzero. For example once β\beta enters the model, no matter how many times it exits or re-enters the model through the path, it will be counted only once. Default is min(dfmax*1.2, p).
standardize

logical flag for variable standardization, prior to fitting the model sequence. The coefficients are always returned to the original scale. Default is TRUE.
intercept

Should intercept(s) be fitted (default is TRUE) or set to zero (FALSE)?
eps

convergence threshold for coordinate descent. Each inner coordinate descent loop continues until the maximum change in any coefficient is less than eps. Defaults value is 1e-8.
maxit

maximum number of outer-loop iterations allowed at fixed lambda values. Default is 1e7. If the algorithm does not converge, consider increasing maxit.
tau

the parameter τ\tau in the ALS regression model. The value must be in (0,1). Default is 0.5.

Details

Note that the objective function in ernet is

1′Ψτ(y−Xβ)/N+λ1∗∥β∥1+0.5λ2∗∥β∥22,1'\Psi_{\tau}(y-X\beta)/N + \lambda_{1}*\Vert\beta\Vert_1 + 0.5\lambda_{2}*\Vert\beta\Vert_2^2,

where Ψτ\Psi_{\tau} denotes the asymmetric squared error loss and the penalty is a combination of weighted L1 and L2 terms.

For faster computation, if the algorithm is not converging or running slow, consider increasing eps, decreasing nlambda, or increasing lambda.factor before increasing maxit.

Value

An object with S3 class ernet.

call

the call that produced this object
b0

intercept sequence of length length(lambda)
beta

a p*length(lambda) matrix of coefficients, stored as a sparse matrix (dgCMatrix class, the standard class for sparse numeric matrices in the Matrix package.). To convert it into normal type matrix use as.matrix().
lambda

the actual sequence of lambda values used
df

the number of nonzero coefficients for each value of lambda.
dim

dimension of coefficient matrix
npasses

total number of iterations summed over all lambda values
jerr

error flag, for warnings and errors, 0 if no error.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

References

Gu, Y., and Zou, H. (2016). "High-dimensional generalizations of asymmetric least squares regression and their applications." The Annals of Statistics, 44(6), 2661–2694.

See Also

plot.ernet, coef.ernet, predict.ernet, print.ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1 <- ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
            pf2 = pf2, standardize = FALSE, intercept = FALSE,
            lambda2 = lambda2)

Plot coefficients from a cpernet object

Description

Produces a coefficient profile plot of the coefficient paths for a fitted cpernet object. This function is modified based on the plot method in the glmnet package.

Usage

## S3 method for class 'cpernet'
plot(x, xvar = c("norm", "lambda"), color = FALSE, label = FALSE, ...)

Arguments

x

fitted cpernet model
xvar

what is on the x-axis. "norm" plots against the L1-norm of the coefficients, "lambda" against the log-lambda sequence.
color

if TRUE, plot the curves with rainbow colors. Otherwise, plot the curves with gray colors. Default is FALSE.
label

if TRUE, label the curves with variable sequence numbers. Otherwise, do not put labels. Default is FALSE.
...

other graphical parameters to plot.

Details

Two coefficient profile plots are produced, one for the mean coefficients and the other for the scale coefficients.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

plot.cv.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2 <- cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
              pf.mean = pf, pf.scale = pf2, intercept = TRUE,
              standardize = FALSE, lambda2 = lambda2)
plot(m2)

Plot the cross-validated curve produced by cv.cpernet

Description

Plots the cross-validated curve, and upper and lower standard deviation curves, as a function of the lambda values used. This function is modified based on the plot.cv.glmnet function from the glmnet package.

Usage

## S3 method for class 'cv.cpernet'
plot(x, sign.lambda = 1, ...)

Arguments

x

fitted cv.cpernet object
sign.lambda

either plot against log(lambda) (default) or its negative if sign.lambda=-1.
...

other graphical parameters to plot

Details

A plot is produced.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

plot.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2.cv <- cv.cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
                    pf.mean = pf, pf.scale = pf2,
                    standardize = FALSE, lambda2 = lambda2)
plot(m2.cv)

Plot the cross-validated curve produced by cv.ernet

Description

Plots the cross-validated curve, and upper and lower standard deviation curves, as a function of the lambda values used. This function is modified based on the plot.cv.glmnet function from the glmnet package.

Usage

## S3 method for class 'cv.ernet'
plot(x, sign.lambda = 1, ...)

Arguments

x

fitted cv.ernet object
sign.lambda

either plot against log(lambda) (default) or its negative if sign.lambda=-1.
...

other graphical parameters to plot

Details

A plot is produced.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

plot.ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1.cv <- cv.ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
                  pf2 = pf2, standardize = FALSE, intercept = FALSE,
                  lambda2 = lambda2)
plot(m1.cv)

Plot coefficients from an ernet object

Description

Produces a coefficient profile plot of the coefficient paths for a fitted ernet object. This function is modified based on the plot method in the glmnet package.

Usage

## S3 method for class 'ernet'
plot(x, xvar = c("norm", "lambda"), color = FALSE, label = FALSE, ...)

Arguments

x

fitted ernet model
xvar

what is on the x-axis. "norm" plots against the L1-norm of the coefficients, "lambda" against the log-lambda sequence.
color

if TRUE, plot the curves with rainbow colors. Otherwise, plot the curves with gray colors. Default is FALSE.
label

if TRUE, label the curves with variable sequence numbers. Otherwise, do not put labels. Default is FALSE.
...

other graphical parameters to plot.

Details

A coefficient profile plot is produced.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

plot.cv.ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1 <- ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
            pf2 = pf2, standardize = FALSE, intercept = FALSE,
            lambda2 = lambda2)
plot(m1)

Model predictions

Description

predict is a generic function for predictions from the results of various model fitting functions. The function invokes particular methods which depend on the class of the first argument.

Usage

predict(object, ...)

Arguments

object

a model object for which prediction is desired.
...

additional arguments affecting the predictions produced.

Value

The form of the value returned by predict depends on the class of its argument. See the documentation of the particular methods for details of what is produced by that method.

See Also

predict.ernet, predict.cpernet.

Make predictions from a cpernet object

Description

Similar to other predict methods, this function predicts fitted values from a cpernet object.

Usage

## S3 method for class 'cpernet'
predict(object, newx, s = NULL, type = "response", ...)

Arguments

object

fitted cpernet model object.
newx

matrix of new values for x at which predictions are to be made. NOTE: newx must be a matrix, predict function does not accept a vector or other formats of newx.
s

value(s) of the penalty parameter lambda at which predictions are to be made. Default is the entire sequence used to create the model.
type

type of prediction required. Only response is available. Gives predicted response for regression problems.
...

Not used. Other arguments to predict.

Details

s is the new vector at which predictions are to be made. If s is not in the lambda sequence used for fitting the model, the predict function will use linear interpolation to make predictions. The new values are interpolated using a fraction of predicted values from both left and right lambda indices.

Value

The object returned depends on type.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cpernet, coef.cpernet, plot.cpernet, print.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2 <- cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
              pf.mean = pf, pf.scale = pf2,
              standardize = FALSE, lambda2 = lambda2)
predict(m2, newx = x, s = m2$lambda[50])

Make predictions from a cv.cpernet object

Description

This function makes predictions from a cross-validated cpernet model, using the fitted cv.cpernet object, and the optimal value chosen for lambda.

Usage

## S3 method for class 'cv.cpernet'
predict(object, newx, s = c("lambda.1se", "lambda.min"), ...)

Arguments

object

fitted cv.cpernet object.
newx

matrix of new values for x at which predictions are to be made. Must be a matrix. See documentation for predict.cpernet.
s

value(s) of the penalty parameter lambda at which predictions are to be made. Default is the value s = "lambda.1se" stored on the CV object. Alternatively s = "lambda.min" can be used. If s is numeric, it is taken as the value(s) of lambda to be used.
...

not used. Other arguments to predict.

Details

This function makes it easier to use the results of cross-validation to make a prediction.

Value

The object returned depends the ... argument which is passed on to the predict method for cpernet objects.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cv.cpernet, coef.cv.cpernet, plot.cv.cpernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2.cv <- cv.cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
                    pf.mean = pf, pf.scale = pf2,
                    standardize = FALSE, lambda2 = lambda2)
as.vector(predict(m2.cv, newx = x, s = "lambda.min"))

Make predictions from a cv.ernet object

Description

This function makes predictions from a cross-validated ernet model, using the fitted cv.ernet object, and the optimal value chosen for lambda.

Usage

## S3 method for class 'cv.ernet'
predict(object, newx, s = c("lambda.1se", "lambda.min"), ...)

Arguments

object

fitted cv.ernet object.
newx

matrix of new values for x at which predictions are to be made. Must be a matrix. See documentation for predict.ernet.
s

value(s) of the penalty parameter lambda at which predictions are to be made. Default is the value s = "lambda.1se" stored on the CV object. Alternatively s = "lambda.min" can be used. If s is numeric, it is taken as the value(s) of lambda to be used.
...

not used. Other arguments to predict.

Details

This function makes it easier to use the results of cross-validation to make a prediction.

Value

The object returned depends the ... argument which is passed on to the predict method for ernet objects.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

cv.ernet, coef.cv.ernet, plot.cv.ernet

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1.cv <- cv.ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
                  pf2 = pf2, standardize = FALSE, intercept = FALSE,
                  lambda2 = lambda2)
as.vector(predict(m1.cv, newx = x, s = "lambda.min"))

Make predictions from an ernet object

Description

Similar to other predict methods, this functions predicts fitted values from a fitted ernet object.

Usage

## S3 method for class 'ernet'
predict(object, newx, s = NULL, type = "response", ...)

Arguments

object

fitted ernet model object.
newx

matrix of new values for x at which predictions are to be made. NOTE: newx must be a matrix, predict function does not accept a vector or other formats of newx.
s

value(s) of the penalty parameter lambda at which predictions are to be made. Default is the entire sequence used to create the model.
type

type of prediction required. Only response is available. Gives predicted response for regression problems.
...

Not used. Other arguments to predict.

Details

s is the new vector at which predictions are to be made. If s is not in the lambda sequence used for fitting the model, the predict function will use linear interpolation to make predictions. The new values are interpolated using a fraction of predicted values from both left and right lambda indices.

Value

The object returned depends on type.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

See Also

ernet, coef.ernet, plot.ernet, print.ernet

Print a cpernet object

Description

Print a summary of the cpernet path at each step along the path.

Usage

## S3 method for class 'cpernet'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x

fitted cpernet object.
digits

significant digits in the output.
...

additional print arguments.

Details

The call that produced the cpernet object is printed, followed by a three-column matrix with columns Df1, Df2 and Lambda. The Df1 and Df2 columns are the number of nonzero mean and scale coefficients respectively.

Value

a three-column matrix, the first two columns are the number of nonzero mean and scale coefficients respectively and the third column is Lambda.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.30
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
w <- 2.0
lambda2 <- 1
m2 <- cpernet(y = y, x = x, w = w, tau = tau, eps = 1e-8,
              pf.mean = pf, pf.scale = pf2,
              standardize = FALSE, lambda2 = lambda2)
print(m2)

Print an ernet object

Description

Print a summary of the ernet path at each step along the path.

Usage

## S3 method for class 'ernet'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x

fitted ernet object.
digits

significant digits in the output.
...

additional print arguments.

Details

The call that produced the ernet object is printed, followed by a two-column matrix with columns Df and Lambda. The Df column is the number of nonzero coefficients.

Value

a two-column matrix, the first columns is the number of nonzero coefficients and the second column is Lambda.

Author(s)

Yuwen Gu and Hui Zou

Maintainer: Yuwen Gu <[email protected]>

Examples

set.seed(1)
n <- 100
p <- 400
x <- matrix(rnorm(n * p), n, p)
y <- rnorm(n)
tau <- 0.90
pf <- abs(rnorm(p))
pf2 <- abs(rnorm(p))
lambda2 <- 1
m1 <- ernet(y = y, x = x, tau = tau, eps = 1e-8, pf = pf,
            pf2 = pf2, standardize = FALSE, intercept = FALSE,
            lambda2 = lambda2)
print(m1)