Package 'gcdnet' reference manual

Title:	The (Adaptive) LASSO and Elastic Net Penalized Least Squares, Logistic Regression, Hybrid Huberized Support Vector Machines, Squared Hinge Loss Support Vector Machines and Expectile Regression using a Fast Generalized Coordinate Descent Algorithm
Description:	Implements a generalized coordinate descent (GCD) algorithm for computing the solution paths of the hybrid Huberized support vector machine (HHSVM) and its generalizations. Supported models include the (adaptive) LASSO and elastic net penalized least squares, logistic regression, HHSVM, squared hinge loss SVM and expectile regression.
Authors:	Yi Yang <[email protected]>, Yuwen Gu <[email protected]>, Hui Zou <[email protected]>
Maintainer:	Yi Yang <[email protected]>
License:	GPL (>= 2)
Version:	1.0.6
Built:	2024-10-07 06:30:13 UTC
Source:	CRAN

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, ...)
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.

Get coefficients or make coefficient predictions from a "cv.gcdnet" object.

Description

This function gets coefficients or makes coefficient predictions from a cross-validated gcdnet model, using the stored "gcdnet.fit" object, and the optimal value chosen for lambda.

Usage

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

Arguments

`object`	fitted `cv.gcdnet` 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 gcdnet objects.

Author(s)

Yi Yang, Yuwen Gu and Hui Zou

Maintainer: Yi Yang <[email protected]>

References

Yang, Y. and Zou, H. (2012). "An Efficient Algorithm for Computing The HHSVM and Its Generalizations." Journal of Computational and Graphical Statistics, 22, 396-415.
BugReport: https://github.com/emeryyi/gcdnet

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.

Friedman, J., Hastie, T., and Tibshirani, R. (2010). "Regularization paths for generalized linear models via coordinate descent." Journal of Statistical Software, 33, 1.
https://www.jstatsoft.org/v33/i01/

Examples


data(FHT)
set.seed(2011)
cv <- cv.gcdnet(FHT$x, FHT$y, lambda2 = 1, nfolds = 5)
coef(cv, s = "lambda.min")

data(FHT)
set.seed(2011)
cv <- cv.gcdnet(FHT$x, FHT$y, lambda2 = 1, nfolds = 5)
coef(cv, s = "lambda.min")

Get coefficients or make coefficient predictions from a "gcdnet" 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 gcdnet object.

Usage

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

Arguments

`object`	fitted `gcdnet` model object.
`s`	value(s) of the penalty parameter `lambda` at which predictions are required. Default is the entire sequence used to create the model.
`type`	type `"coefficients"` computes the coefficients at the requested values for `s`. Type `"nonzero"` returns a list of the indices of the 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)

Yi Yang, Yuwen Gu and Hui Zou

Maintainer: Yi Yang <[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.

Examples


data(FHT)
fit1 <- gcdnet(x = FHT$x,y = FHT$y)
coef(fit1, type = "coef", s = c(0.1,0.005))
coef(fit1, type = "nonzero")

data(FHT)
fit1 <- gcdnet(x = FHT$x,y = FHT$y)
coef(fit1, type = "coef", s = c(0.1,0.005))
coef(fit1, type = "nonzero")

Cross-validation for gcdnet

Description

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

Usage

cv.gcdnet(
  x,
  y,
  lambda = NULL,
  pred.loss = c("misclass", "loss"),
  nfolds = 5,
  foldid,
  delta = 2,
  omega = 0.5,
  ...
)
cv.gcdnet(
  x,
  y,
  lambda = NULL,
  pred.loss = c("misclass", "loss"),
  nfolds = 5,
  foldid,
  delta = 2,
  omega = 0.5,
  ...
)

Arguments

`x`	`x` matrix as in `gcdnet`.
`y`	response variable or class label `y` as in `gcdnet`.
`lambda`	optional user-supplied lambda sequence; default is `NULL`, and `gcdnet` chooses its own sequence.
`pred.loss`	loss function to use for cross-validation error. Valid options are: `"loss"` Margin based loss function. When use least square loss `"ls"`, it gives mean square error (MSE). When use expectile regression loss `"er"`, it gives asymmetric mean square error (AMSE). `"misclass"` only available for classification: it gives misclassification error. Default is `"loss"`.
`nfolds`	number of folds - default 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 allowable is `nfolds=3`.
`foldid`	an optional vector of values between 1 and `nfold` identifying what fold each observation is in. If supplied, `nfold` can be missing.
`delta`	parameter $\delta$ only used in HHSVM for computing margin based loss function, only available for `pred.loss = "loss"`.
`omega`	parameter $\omega$ only used in expectile regression. Only available for `pred.loss = "loss"`.
`...`	other arguments that can be passed to gcdnet.

Details

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

Value

an object of class cv.gcdnet 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).
`gcdnet.fit`	a fitted `gcdnet` 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)

Yi Yang, Yuwen Gu and Hui Zou
Maintainer: Yi Yang <[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.

Examples


# fit an elastic net penalized HHSVM with lambda2 = 0.1 for the L2 penalty.
# Use the misclassification rate as the cross validation prediction loss.
# Use five-fold CV to choose the optimal lambda for the L1 penalty.

data(FHT)
set.seed(2011)
cv <- cv.gcdnet(FHT$x, FHT$y, method = "hhsvm",
                lambda2 = 0.1, pred.loss = "misclass",
                nfolds = 5, delta = 1.5)
plot(cv)

# fit an elastic net penalized least squares
# with lambda2 = 0.1 for the L2 penalty. Use the
# least square loss as the cross validation
# prediction loss. Use five-fold CV to choose
# the optimal lambda for the L1 penalty.

set.seed(2011)
cv1 <- cv.gcdnet(FHT$x, FHT$y_reg, method ="ls",
                 lambda2 = 0.1, pred.loss = "loss",
                 nfolds = 5)
plot(cv1)

# To fit a LASSO penalized logistic regression
# we set lambda2 = 0 to disable the L2 penalty. Use the
# logistic loss as the cross validation
# prediction loss. Use five-fold CV to choose
# the optimal lambda for the L1 penalty.

set.seed(2011)
cv2 <- cv.gcdnet(FHT$x, FHT$y, method ="logit",
                 lambda2 = 0, pred.loss="loss",
                 nfolds=5)
plot(cv2)

# fit an elastic net penalized HHSVM with lambda2 = 0.1 for the L2 penalty.
# Use the misclassification rate as the cross validation prediction loss.
# Use five-fold CV to choose the optimal lambda for the L1 penalty.

data(FHT)
set.seed(2011)
cv <- cv.gcdnet(FHT$x, FHT$y, method = "hhsvm",
                lambda2 = 0.1, pred.loss = "misclass",
                nfolds = 5, delta = 1.5)
plot(cv)

# fit an elastic net penalized least squares
# with lambda2 = 0.1 for the L2 penalty. Use the
# least square loss as the cross validation
# prediction loss. Use five-fold CV to choose
# the optimal lambda for the L1 penalty.

set.seed(2011)
cv1 <- cv.gcdnet(FHT$x, FHT$y_reg, method ="ls",
                 lambda2 = 0.1, pred.loss = "loss",
                 nfolds = 5)
plot(cv1)

# To fit a LASSO penalized logistic regression
# we set lambda2 = 0 to disable the L2 penalty. Use the
# logistic loss as the cross validation
# prediction loss. Use five-fold CV to choose
# the optimal lambda for the L1 penalty.

set.seed(2011)
cv2 <- cv.gcdnet(FHT$x, FHT$y, method ="logit",
                 lambda2 = 0, pred.loss="loss",
                 nfolds=5)
plot(cv2)

FHT data introduced in Friedman et al. (2010).

Description

The FHT data set has n = 50 observations and p = 100 predictors. The covariance between predictors Xj and Xj' has the same correlation 0.5. See details in Friedman et al. (2010).

Format

This data frame contains the following columns:

x: a matrix with 100 rows and 5000 columns
y: class labels
y_reg: response variable for regression

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.

Examples


data(FHT)

data(FHT)

Fits the regularization paths for large margin classifiers

Description

Fits a regularization path for large margin classifiers at a sequence of regularization parameters lambda.

Usage

gcdnet(
  x,
  y,
  nlambda = 100,
  method = c("hhsvm", "logit", "sqsvm", "ls", "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 = FALSE,
  intercept = TRUE,
  eps = 1e-08,
  maxit = 1e+06,
  delta = 2,
  omega = 0.5
)
gcdnet(
  x,
  y,
  nlambda = 100,
  method = c("hhsvm", "logit", "sqsvm", "ls", "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 = FALSE,
  intercept = TRUE,
  eps = 1e-08,
  maxit = 1e+06,
  delta = 2,
  omega = 0.5
)

Arguments

`x`	matrix of predictors, of dimension $N \times p$ ; each row is an observation vector.
`y`	response variable. This argument should be a two-level factor for classification.
`nlambda`	the number of `lambda` values - default is 100.
`method`	a character string specifying the loss function to use, valid options are: `"hhsvm"` Huberized squared hinge loss, `"sqsvm"` Squared hinge loss, `"logit"` logistic loss, `"ls"` least square loss. `"er"` expectile regression loss. Default is `"hhsvm"`.
`lambda.factor`	The factor for getting the minimal lambda in `lambda` sequence, where `min(lambda)` = `lambda.factor` * `max(lambda)`, where `max(lambda)` is the smallest value of `lambda` for which all coefficients are zero. The default depends on the relationship between $N$ (the number of rows in the matrix of predictors) and $p$ (the number of predictors). If $N > p$ , the default is `0.0001`, close to zero. If $N<p$ , the default is `0.01`. A very small value of `lambda.factor` will lead to a saturated fit. It takes no effect if there is user-defined `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`. Supplying a value of `lambda` overrides this. It is better to supply a decreasing sequence of `lambda` values than a single (small) value, if not, the program will sort user-defined `lambda` sequence in decreasing order automatically.
`lambda2`	regularization parameter $\lambda_2$ for the quadratic penalty of the coefficients.
`pf`	L1 penalty factor of length $p$ used for adaptive LASSO or adaptive elastic net. Separate L1 penalty weights can be applied to each coefficient of $\beta$ to allow differential L1 shrinkage. Can be 0 for some variables, which implies no L1 shrinkage, and results in that variable always being included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in `exclude`).
`pf2`	L2 penalty factor of length $p$ used for adaptive LASSO or adaptive elastic net. Separate L2 penalty weights can be applied to each coefficient of $\beta$ to allow differential L2 shrinkage. Can be 0 for some variables, which implies no L2 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 $p$ , if a partial path is desired. Default is $p+1$ .
`pmax`	limit the maximum number of variables ever to be nonzero. For example once $\beta$ enters the model, no matter how many times it exits or re-enters 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. If `TRUE`, `x` matrix is normalized such that `x` is centered (i.e. $\sum^N_{i=1}x_{ij}=0$ ), and sum squares of each column $\sum^N_{i=1}x_{ij}^2/N=1$ . If `x` matrix is standardized, the ending coefficients will be transformed back to the original scale. Default is `FALSE`.
`intercept`	logical flag to indicate whether to include or exclude the intercept in the model.
`eps`	convergence threshold for coordinate majorization descent. Each inner coordinate majorization descent loop continues until the relative change in any coefficient (i.e., $\max_j(\beta_j^{new} -\beta_j^{old})^2$ ) is less than `eps`. For HHSVM, i.e., `method="hhsvm"`, it is $\frac{2}{\delta}\max_j(\beta_j^{new}-\beta_j^{old})^2$ . For expectile regression, i.e., `method="er"`, it is $2\max(1-\omega,\omega) \max_j(\beta_j^{new}-\beta_j^{old})^2$ . Defaults value is `1e-8`.
`maxit`	maximum number of outer-loop iterations allowed at fixed lambda value. Default is 1e6. If models do not converge, consider increasing `maxit`.
`delta`	the parameter $\delta$ in the HHSVM model. The value must be greater than 0. Default is 2.
`omega`	the parameter $\omega$ in the expectile regression model. The value must be in (0,1). Default is 0.5.

Details

Note that the objective function in gcdnet is

$Loss(y, X, \beta)/N + \lambda_1\Vert\beta\Vert_1 + 0.5\lambda_2\Vert\beta\Vert_2^2$

where the penalty is a combination of L1 and L2 term. Users can specify the loss function to use, options include Huberized squared hinge loss, Squared hinge loss, least square loss, logistic regression and expectile regression loss. Users can also tweak the penalty by choosing different $lambda2$ and penalty factor.

For computing speed reason, if models are not converging or running slow, consider increasing eps, decreasing nlambda, or increasing lambda.factor before increasing maxit.

FAQ:

Question: “I couldn't get an idea how to specify an option to get adaptive LASSO, how to specify an option to get elastic net and adaptive elastic net? Could you please give me a quick hint?”

Answer: lambda2 is the regularize parameter for L2 penalty part. To use LASSO, set lambda2=0. To use elastic net, set lambda2 as nonzero.

pf is the L1 penalty factor of length $p$ ( $p$ is the number of predictors). Separate L1 penalty weights can be applied to each coefficient to allow differential L1 shrinkage. Similiarly pf2 is the L2 penalty factor of length $p$ .

To use adaptive LASSO, you should set lambda2=0 and also specify pf and pf2. To use adaptive elastic net, you should set lambda2 as nonzero and specify pf and pf2,

For example:

    library('gcdnet')
    # Dataset N = 100, p = 10
    x_log <- matrix(rnorm(100*10),100,10)
    y_log <- sample(c(-1,1),100,replace=TRUE)

    # LASSO
    m <- gcdnet(x=x_log,y=y_log,lambda2=0,method="log")
    plot(m)

    # elastic net with lambda2 = 1
    m <- gcdnet(x=x_log,y=y_log,lambda2=1,method="log")
    plot(m)

    # adaptive lasso with penalty factor
    # pf = 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0
    m <- gcdnet(x=x_log,y=y_log,lambda2=0,method="log",
                pf=c(rep(0.5,5),rep(1,5)))
    plot(m)

    # adaptive elastic net with lambda2 = 1 and penalty factor pf =
    # c(rep(0.5,5),rep(1,5)) pf2 = 3 3 3 3 3 1 1 1 1 1
    m <- gcdnet(x=x_log,y=y_log,lambda2=1,method="log",
                pf=c(rep(0.5,5),rep(1,5)),
                pf2 = c(rep(3,5),rep(1,5)))
    plot(m)

Question: “what is the meaning of the parameter pf? On the package documentation, it said pf is the penalty weight applied to each coefficient of beta?”

Answer: Yes, pf and pf2 are L1 and L2 penalty factor of length $p$ used for adaptive LASSO or adaptive elastic net. 0 means that the feature (variable) is always excluded, 1 means that the feature (variable) is included with weight 1.

Question: “Does gcdnet deal with both continuous and categorical response variables?”

Answer: Yes, both are supported, you can use a continuous type response variable with the least squares regression loss, or a categorical type response with losses for classification problem.

Question: “Why does predict function not work? predict should return the predicted probability of the positive class. Instead I get:”

    Error in as.matrix(as.matrix(cbind2(1, newx)) %*% nbeta):
    error in evaluating the argument 'x' in selecting a method for function 'as.matrix':
    Error in t(.Call(Csparse_dense_crossprod, y, t(x))):
    error in evaluating the argument 'x' in selecting a method for function 't':
    Error: Cholmod error 'X and/or Y have wrong dimensions' at
      file ../MatrixOps/cholmod_sdmult.c, line 90?

“Using the Arcene dataset and executing the following code will give the above error:”

    library(gcdnet)
    arc <- read.csv("arcene.csv", header=FALSE)
    fit <- gcdnet(arc[,-10001], arc[,10001], standardize=FALSE,
                  method="logit")
    pred <- rnorm(10000)
    predict(fit, pred, type="link")

Answer: It is actually NOT a bug of gcdnet. When make prediction using a new matrix x, each observation of x should be arranged as a row of a matrix. In your code, because "pred" is a vector, you need to convert "pred" into a matrix, try the following code:

     pred <- rnorm(10000)
     pred <- matrix(pred,1,10000)
     predict(fit, pred, type="link")

Value

An object with S3 class gcdnet.

`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 (ices)
`npasses`	total number of iterations (the most inner loop) summed over all lambda values
`jerr`	error flag, for warnings and errors, 0 if no error.

Author(s)

Yi Yang, Yuwen Gu and Hui Zou
Maintainer: Yi Yang <[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.

Examples


data(FHT)
# 1. solution paths for the LASSO penalized least squares.
# To use LASSO set lambda2 = 0.

m1 <- gcdnet(x = FHT$x, y = FHT$y_reg, lambda2 = 0, method = "ls")
plot(m1)

# 2. solution paths for the elastic net penalized HHSVM.
# lambda2 is the parameter controlling the L2 penalty.
m2 <- gcdnet(x = FHT$x, y = FHT$y, delta = 1, lambda2 = 1, method = "hhsvm")
plot(m2)

# 3. solution paths for the adaptive LASSO penalized SVM
# with the squared hinge loss. To use the adaptive LASSO,
# set lambda2 = 0 and meanwhile specify the L1 penalty weights.
p <- ncol(FHT$x)
# set the first three L1 penalty weights as 0.1 and the rest are 1
pf = c(0.1, 0.1, 0.1, rep(1, p-3))
m3 <- gcdnet(x = FHT$x, y = FHT$y, pf = pf, lambda2 = 0, method = "sqsvm")
plot(m3)

# 4. solution paths for the adaptive elastic net penalized
# logistic regression.

p <- ncol(FHT$x)
# set the first three L1 penalty weights as 10 and the rest are 1.
pf <- c(10, 10, 10, rep(1, p-3))
# set the last three L2 penalty weights as 0.1 and the rest are 1.
pf2 <- c(rep(1, p-3), 0.1, 0.1, 0.1)
# set the L2 penalty parameter lambda2=0.01.
m4 <- gcdnet(x = FHT$x, y = FHT$y, pf = pf, pf2 = pf2,
             lambda2 = 0.01, method = "logit")
plot(m4)

# 5. solution paths for the LASSO penalized expectile regression
# with the asymmetric least square parameter omega=0.9.

m5 <- gcdnet(x = FHT$x, y = FHT$y_reg, omega = 0.9,
             lambda2 = 0, method = "er")
plot(m5)

data(FHT)
# 1. solution paths for the LASSO penalized least squares.
# To use LASSO set lambda2 = 0.

m1 <- gcdnet(x = FHT$x, y = FHT$y_reg, lambda2 = 0, method = "ls")
plot(m1)

# 2. solution paths for the elastic net penalized HHSVM.
# lambda2 is the parameter controlling the L2 penalty.
m2 <- gcdnet(x = FHT$x, y = FHT$y, delta = 1, lambda2 = 1, method = "hhsvm")
plot(m2)

# 3. solution paths for the adaptive LASSO penalized SVM
# with the squared hinge loss. To use the adaptive LASSO,
# set lambda2 = 0 and meanwhile specify the L1 penalty weights.
p <- ncol(FHT$x)
# set the first three L1 penalty weights as 0.1 and the rest are 1
pf = c(0.1, 0.1, 0.1, rep(1, p-3))
m3 <- gcdnet(x = FHT$x, y = FHT$y, pf = pf, lambda2 = 0, method = "sqsvm")
plot(m3)

# 4. solution paths for the adaptive elastic net penalized
# logistic regression.

p <- ncol(FHT$x)
# set the first three L1 penalty weights as 10 and the rest are 1.
pf <- c(10, 10, 10, rep(1, p-3))
# set the last three L2 penalty weights as 0.1 and the rest are 1.
pf2 <- c(rep(1, p-3), 0.1, 0.1, 0.1)
# set the L2 penalty parameter lambda2=0.01.
m4 <- gcdnet(x = FHT$x, y = FHT$y, pf = pf, pf2 = pf2,
             lambda2 = 0.01, method = "logit")
plot(m4)

# 5. solution paths for the LASSO penalized expectile regression
# with the asymmetric least square parameter omega=0.9.

m5 <- gcdnet(x = FHT$x, y = FHT$y_reg, omega = 0.9,
             lambda2 = 0, method = "er")
plot(m5)

Plot the cross-validation curve produced by cv.gcdnet

Description

Plots the cross-validation 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 function from the glmnet package.

Usage

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

Arguments

`x`	fitted `cv.gcdnet` 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)

Yi Yang, Yuwen Gu and Hui Zou

Maintainer: Yi Yang <[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.

Examples


# fit an elastic net penalized logistic regression with lambda2 = 1 for the
# L2 penalty. Use the logistic loss as the cross validation prediction loss.
# Use five-fold CV to choose the optimal lambda for the L1 penalty.
data(FHT)
set.seed(2011)
cv=cv.gcdnet(FHT$x, FHT$y, method ="logit", lambda2 = 1,
             pred.loss="loss", nfolds=5)
plot(cv)

# fit an elastic net penalized logistic regression with lambda2 = 1 for the
# L2 penalty. Use the logistic loss as the cross validation prediction loss.
# Use five-fold CV to choose the optimal lambda for the L1 penalty.
data(FHT)
set.seed(2011)
cv=cv.gcdnet(FHT$x, FHT$y, method ="logit", lambda2 = 1,
             pred.loss="loss", nfolds=5)
plot(cv)

Plot coefficients from a "gcdnet" object

Description

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

Usage

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

Arguments

`x`	fitted `gcdnet` 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. `FALSE` is gray colors. Default is `FALSE`
`label`	if `TRUE`, label the curves with variable sequence numbers. Default is `FALSE`
`...`	other graphical parameters to plot

Details

A coefficient profile plot is produced.

Author(s)

Yi Yang, Yuwen Gu and Hui Zou
Maintainer: Yi Yang <[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.

Examples


data(FHT)
m1 <- gcdnet(x = FHT$x,y = FHT$y)
par(mfrow = c(1,3))
plot(m1) # plots against the L1-norm of the coefficients
plot(m1,xvar = "lambda",label = TRUE) # plots against the log-lambda sequence
plot(m1,color = TRUE)

data(FHT)
m1 <- gcdnet(x = FHT$x,y = FHT$y)
par(mfrow = c(1,3))
plot(m1) # plots against the L1-norm of the coefficients
plot(m1,xvar = "lambda",label = TRUE) # plots against the log-lambda sequence
plot(m1,color = TRUE)

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, ...)
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.

Make predictions from a "cv.gcdnet" object.

Description

This function makes predictions from a cross-validated gcdnet model, using the stored "gcdnet.fit" object, and the optimal value chosen for lambda.

Usage

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

Arguments

`object`	fitted `cv.gcdnet` object.
`newx`	matrix of new values for `x` at which predictions are to be made. Must be a matrix. See documentation for `predict.gcdnet`.
`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. 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 gcdnet objects.

Author(s)

Yi Yang, Yuwen Gu and Hui Zou

Maintainer: Yi Yang <[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.

Examples


data(FHT)
set.seed(2011)
cv=cv.gcdnet(FHT$x, FHT$y, lambda2 = 1, pred.loss="misclass",
             lambda.factor=0.05, nfolds=5)
pre = predict(cv$gcdnet.fit, newx = FHT$x, s = cv$lambda.1se,
              type = "class")

data(FHT)
set.seed(2011)
cv=cv.gcdnet(FHT$x, FHT$y, lambda2 = 1, pred.loss="misclass",
             lambda.factor=0.05, nfolds=5)
pre = predict(cv$gcdnet.fit, newx = FHT$x, s = cv$lambda.1se,
              type = "class")

Make predictions from a "gcdnet" object

Description

Similar to other predict methods, this functions predicts fitted values and class labels from a fitted gcdnet object.

Usage

## S3 method for class 'gcdnet'
predict(object, newx, s = NULL, type = c("class", "link"), ...)
## S3 method for class 'gcdnet'
predict(object, newx, s = NULL, type = c("class", "link"), ...)

Arguments

`object`	fitted `gcdnet` 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 required. Default is the entire sequence used to create the model.
`type`	type of prediction required. Type `"link"` gives the linear predictors for classification problems and gives predicted response for regression problems. Type `"class"` produces the class label corresponding to the maximum probability. Only available for classification problems.
`...`	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 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)

Yi Yang, Yuwen Gu and Hui Zou

Maintainer: Yi Yang <[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.

Examples


data(FHT)
m1 <- gcdnet(x = FHT$x,y = FHT$y)
print(predict(m1, type = "class",newx = FHT$x[2:5, ]))

data(FHT)
m1 <- gcdnet(x = FHT$x,y = FHT$y)
print(predict(m1, type = "class",newx = FHT$x[2:5, ]))

Print a gcdnet object

Description

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

Usage

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

Arguments

`x`	fitted `gcdnet` object
`digits`	significant digits in printout
`...`	additional print arguments

Details

The call that produced the gcdnet 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)

Yi Yang, Yuwen Gu and Hui Zou

Maintainer: Yi Yang <[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.

Examples


data(FHT)
m1 <- gcdnet(x = FHT$x, y = FHT$y, delta = 1, lambda2 = 0.1)
print(m1)

data(FHT)
m1 <- gcdnet(x = FHT$x, y = FHT$y, delta = 1, lambda2 = 0.1)
print(m1)

Package 'gcdnet'

Help Index

Extract Model Coefficients

Description

Usage

Arguments

Value

See Also

Get coefficients or make coefficient predictions from a "cv.gcdnet" object.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Get coefficients or make coefficient predictions from a "gcdnet" object.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Cross-validation for gcdnet

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

FHT data introduced in Friedman et al. (2010).

Description

Format

References

Examples

Fits the regularization paths for large margin classifiers

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plot the cross-validation curve produced by cv.gcdnet

Description

Usage

Arguments

Details

Author(s)

References

See Also

Examples

Plot coefficients from a "gcdnet" object

Description

Usage

Arguments

Details

Author(s)

References

Examples

Model predictions

Description

Usage

Arguments

Value

See Also

Make predictions from a "cv.gcdnet" object.

Description

Usage

Arguments