Package 'sdwd' reference manual

Title:	Sparse Distance Weighted Discrimination
Description:	Formulates a sparse distance weighted discrimination (SDWD) for high-dimensional classification and implements a very fast algorithm for computing its solution path with the L1, the elastic-net, and the adaptive elastic-net penalties. More details about the methodology SDWD is seen on Wang and Zou (2016) (<doi:10.1080/10618600.2015.1049700>).
Authors:	Boxiang Wang and Hui Zou
Maintainer:	Boxiang Wang <[email protected]>
License:	GPL-2
Version:	1.0.6
Built:	2024-10-14 04:01:16 UTC
Source:	https://github.com/boxiang-wang/sdwd

Sparse Distance Weighted Discrimination

Description

This package implements the generalized coordinate descent (GCD) algorithm to efficiently compute the solution path of the sparse distance weighted discrimination (DWD) at a given fine grid of regularization parameters. Sparse distance weighted discrimination is a high-dimensional margin-based classifier.

Details

Package:	sdwd
Type:	Package
Version:	1.0.3
Date:	2020-02-16
License:	GPL-2

Suppose x is the predictors and y is the binary response. With a fixed value lambda2, the package produces the solution path of the sparse DWD over a grid of lambda values. The value of lambda2 can be further tuned by cross-validation.

The package sdwd contains five main functions:
sdwd
cv.sdwd
coef.sdwd
plot.sdwd
plot.cv.sdwd

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Marron, J.S., Todd, M.J., Ahn, J. (2007) “Distance-Weighted Discrimination"", Journal of the American Statistical Association, 102(408), 1267–1271.
https://www.tandfonline.com/doi/abs/10.1198/016214507000001120

Tibshirani, Robert., Bien, J., Friedman, J.,Hastie, T.,Simon, N.,Taylor, J., and Tibshirani, Ryan. (2012) Strong Rules for Discarding Predictors in Lasso-type Problems, Journal of the Royal Statistical Society, Series B, 74(2), 245–266.
https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9868.2011.01004.x

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

compute coefficients from a "cv.sdwd" object

Description

Computes coefficients at chosen values of lambda from the cv.sdwd object.

Usage

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

Arguments

`object`	A fitted `cv.sdwd` object, obtained by conducting the cross-validation to the sparse DWD model.
`s`	Value(s) of the L1 tuning parameter `lambda` for computing coefficients. Default value is `"lambda.1se"`, which represents the largest `lambda` value achieving the cross-validation error within one standard error of the minimum. An alternative value is `"lambda.min"`, which is the `lambda` incurring the least cross-validation error. `s` can also be numeric, being taken as the value(s) to be used.
`...`	Other arguments that can be passed to `sdwd`.

Details

This function computes the coefficients at the values of lambda suggested by the cross-validation. This function is modified based on the coef.cv function from the glmnet and the gcdnet packages.

Value

The returned object depends on the choice of s and the ... argument passed on to the sdwd method.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
set.seed(1)
cv = cv.sdwd(colon$x, colon$y, lambda2=1, nfolds=5)
c1 = coef(cv, s="lambda.1se")
data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
set.seed(1)
cv = cv.sdwd(colon$x, colon$y, lambda2=1, nfolds=5)
c1 = coef(cv, s="lambda.1se")

compute coefficients for the sparse DWD

Description

Computes the coefficients or returns the indices of nonzero coefficients at chosen values of lambda from a fitted sdwd object.

Usage

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

Arguments

`object`	A fitted `sdwd` object.
`s`	Value(s) of the L1 tuning parameter `lambda` for computing coefficients. Default is the entire `lambda` sequence obtained by `sdwd`.
`type`	`"coefficients"` or `"nonzero"`? `"coefficients"` computes the coefficients at given values for `s`; `"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. This function is modified based on the coef function from the gcdnet and the glmnet packages.

Value

Either the coefficients at the requested values of lambda, or a list of the indices of the nonzero coefficients for each lambda.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
fit = sdwd(colon$x, colon$y, lambda2=1)
c1 = coef(fit, type="coef",s=c(0.1, 0.005))
c2 = coef(fit, type="nonzero")
data(colon)
fit = sdwd(colon$x, colon$y, lambda2=1)
c1 = coef(fit, type="coef",s=c(0.1, 0.005))
c2 = coef(fit, type="nonzero")

simplified gene expression data from Alon et al. (1999)

Description

Gene expression data (2000 genes for 62 samples) from a DNA microarray experiments of colon tissue samples (Alon et al., 1999).

Usage

data(colon)
data(colon)

Details

This data set contains 62 colon tissue samples with 2000 gene expression levels. Among 62 samples, 40 are tumor tissues (coded 1) and 22 are normal tissues (coded -1).

Value

A list with the following elements:

`x`	A matrix of 2000 columns and 62 rows standing for 2000 gene expression levels and 62 colon tissue samples. Each row corresponds to a patient.
`y`	A numeric vector of length 62 representing the tissue type (1 for tumor; -1 for normal).

Source

The data were introduced in Alon et al. (1999).

References

Alon, U., Barkai, N., Notterman, D.A., Gish, K., Ybarra, S., Mack, D., and Levine, A.J. (1999). “Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays”, Proceedings of the National Academy of Sciences, 96(12), 6745–6750.

Examples

# load sdwd library
library(sdwd)

# load data set
data(colon)

# how many samples and how many predictors?
dim(colon$x)

# how many samples of class -1 and 1 respectively?
sum(colon$y == -1)
sum(colon$y == 1)
# load sdwd library
library(sdwd)

# load data set
data(colon)

# how many samples and how many predictors?
dim(colon$x)

# how many samples of class -1 and 1 respectively?
sum(colon$y == -1)
sum(colon$y == 1)

cross-validation for the sparse DWD

Description

Conducts a k-fold cross-validation for sdwd and returns the suggested values of the L1 parameter lambda.

Usage

cv.sdwd(x, y, lambda = NULL, pred.loss = c("misclass", "loss"), nfolds = 5, foldid, ...)
cv.sdwd(x, y, lambda = NULL, pred.loss = c("misclass", "loss"), nfolds = 5, foldid, ...)

Arguments

`x`	A matrix of predictors, i.e., the `x` matrix used in `sdwd`.
`y`	A vector of binary class labels, i.e., the `y` used in `sdwd`.
`lambda`	Default is `NULL`, and the sequence generated by `sdwd` is used. User can also provide a new `lambda` sequence to use in cross-validation.
`pred.loss`	`misclass` for classification error, `loss` for DWD loss.
`nfolds`	The number of folds. Default value is 5. The allowable range is from 3 to the sample size. Larger `nfolds` needs more timing.
`foldid`	An optional vector with values between 1 and `nfold`, representing the folder indices for each observation. If supplied, `nfold` can be missing.
`...`	Other arguments that can be passed to `sdwd`.

Details

This function runs sdwd to the sparse DWD by excluding every fold alternatively, and then computes the mean cross-validation error and the standard deviation. This function is modified based on the cv function from the gcdnet and the glmnet packages.

Value

A cv.sdwd object is returned, which includes the cross-validation fit.

`lambda`	The `lambda` sequence used in `sdwd`.
`cvm`	A vector of length `length(lambda)` for the mean cross-validated error.
`cvsd`	A vector of length `length(lambda)` for estimates of standard error of `cvm`.
`cvupper`	The upper curve: `cvm + cvsd`.
`cvlower`	The lower curve: `cvm - cvsd`.
`nzero`	Numbers of non-zero coefficients at each `lambda`.
`name`	“Mis-classification error", for plotting purposes.
`sdwd.fit`	A fitted `sdwd` object using the full data.
`lambda.min`	The `lambda` incurring the minimum cross validation error `cvm`.
`lambda.1se`	The largest value of `lambda` such that error is within one standard error of the minimum.
`cv.min`	The minimum cross-validation error.
`cv.1se`	The cross-validation error associated with `lambda.1se`.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
n = nrow(colon$x)
set.seed(1)
id = sample(n, trunc(n/3))
cvfit = cv.sdwd(colon$x[-id, ], colon$y[-id], lambda2=1, nfolds=5)
plot(cvfit)
predict(cvfit, newx=colon$x[id, ], s="lambda.min")
data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
n = nrow(colon$x)
set.seed(1)
id = sample(n, trunc(n/3))
cvfit = cv.sdwd(colon$x[-id, ], colon$y[-id], lambda2=1, nfolds=5)
plot(cvfit)
predict(cvfit, newx=colon$x[id, ], s="lambda.min")

plot the cross-validation curve of the sparse DWD

Description

Plots the cross-validation curve against a function of lambda values. The function also provides the upper and lower standard deviation curves.

Usage

## S3 method for class 'cv.sdwd'
plot(x, sign.lambda, ...)
## S3 method for class 'cv.sdwd'
plot(x, sign.lambda, ...)

Arguments

`x`	A fitted `cv.sdwd` object.
`sign.lambda`	Whether to plot against `log(lambda)` (default) or its negative if `sign.lambda=-1`.
`...`	Other graphical parameters to `plot`.

Details

This function depicts the cross-validation curves. This function is modified based on the plot.cv function from the glmnet and the gcdnet packages.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
set.seed(1)
cv = cv.sdwd(colon$x, colon$y, lambda2=1, nfolds=5)
plot(cv)
data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
set.seed(1)
cv = cv.sdwd(colon$x, colon$y, lambda2=1, nfolds=5)
plot(cv)

plot coefficients for the sparse DWD

Description

Plots the solution paths for a fitted sdwd object.

Usage

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

Arguments

`x`	A fitted `sdwd` model.
`xvar`	Specifies the X-axis. If `xvar == "norm"`, plots against the L1-norm of the coefficients; if `xvar == "lambda"` against the log-lambda sequence.
`color`	If `TRUE`, plots the curves with rainbow colors; otherwise, with gray colors (default).
`label`	If `TRUE`, labels the curves with variable sequence numbers. Default is `FALSE`.
`...`	Other graphical parameters to `plot`.

Details

Plots the solution paths as a coefficient profile plot. This function is modified based on the plot function from the gcdnet and the glmnet packages.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
fit = sdwd(colon$x, colon$y)
par(mfrow=c(1,3))
# plots against the L1-norm of the coefficients
plot(fit) 
# plots against the log-lambda sequence
plot(fit, xvar="lambda", label=TRUE)
# plots with colors
plot(fit, color=TRUE)
data(colon)
fit = sdwd(colon$x, colon$y)
par(mfrow=c(1,3))
# plots against the L1-norm of the coefficients
plot(fit) 
# plots against the log-lambda sequence
plot(fit, xvar="lambda", label=TRUE)
# plots with colors
plot(fit, color=TRUE)

make predictions from a "cv.sdwd" object

Description

This function predicts the class labels of new observations by the sparse DWD at the lambda values suggested by cv.sdwd.

Usage

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

Arguments

`object`	A fitted `cv.sdwd` object.
`newx`	A matrix of new values for `x` at which predictions are to be made. Must be a matrix. See documentation for `predict.sdwd`.
`s`	Value(s) of the L1 tuning parameter `lambda` for making predictions. Default is the `s="lambda.1se"` saved on the `cv.sdwd` object. An alternative choice is `s="lambda.min"`. `s` can also be numeric, being taken as the value(s) to be used.
`...`	Not used. Other arguments to `predict`.

Details

This function uses the cross-validation results to making predictions. This function is modified based on the predict.cv function from the glmnet and the gcdnet packages.

Value

Predicted class labels or fitted values, depending on the choice of s and the ... argument passed on to the sdwd method.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
set.seed(1)
cv = cv.sdwd(colon$x, colon$y, lambda2=1, nfolds=5)
predict(cv$sdwd.fit, newx=colon$x[2:5, ], 
  s=cv$lambda.1se, type="class")
data(colon)
colon$x = colon$x[ , 1:100] # this example only uses the first 100 columns 
set.seed(1)
cv = cv.sdwd(colon$x, colon$y, lambda2=1, nfolds=5)
predict(cv$sdwd.fit, newx=colon$x[2:5, ], 
  s=cv$lambda.1se, type="class")

make predictions for the sparse DWD

Description

This function predicts the binary class labels or the fitted values of an sdwd object.

Usage

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

Arguments

`object`	A fitted `sdwd` object.
`newx`	A matrix of new values for `x` at which predictions are to be made. We note that `newx` must be a matrix, `predict` function does not accept a vector or other formats of `newx`.
`s`	Value(s) of the L1 tuning parameter `lambda` for computing coefficients. Default is the entire `lambda` sequence obtained by `sdwd`.
`type`	`"class"` or `"link"`? `"class"` produces the predicted binary class labels.`"link"` returns the fitted values. Default is `"class"`.
`...`	Not used. Other arguments to `predict`.

Details

s stands for the new lambda values for making predictions. If s is not in the original lambda sequence generated by sdwd, the predict.sdwd function will use linear interpolation by using a fraction of predicted values from the lambda values in the original sequence adjacent to the s to make predictions. The predict.sdwd function is modified based on the predict function from the glmnet and the gcdnet packages.

Value

Returns either the predicted class labels or the fitted values, depending on the choice of type.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
fit = sdwd(colon$x, colon$y, lambda2=1)
print(predict(fit ,type="class",newx=colon$x[2:5,]))
data(colon)
fit = sdwd(colon$x, colon$y, lambda2=1)
print(predict(fit ,type="class",newx=colon$x[2:5,]))

print an sdwd object

Description

Print a summary of the sdwd solution paths.

Usage

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

Arguments

`x`	A fitted `sdwd` object.
`digits`	Specify the significant digits.
`...`	Additional print arguments.

Details

This function prints a two-column matrix with columns Df and Lambda, where the Df column exhibits the number of nonzero coefficients and the Lambda column displays the corresponding lambda value. This function is modified based on the print function from the gcdnet and the glmnet packages.

Value

A two-column matrix with one column of the number of nonzero coefficients and a second column of lambda values.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Examples

data(colon)
fit = sdwd(colon$x, colon$y)
print(fit)
data(colon)
fit = sdwd(colon$x, colon$y)
print(fit)

fit the sparse DWD

Description

Fits the sparse distance weighted discrimination (SDWD) model with imposing L1, elastic-net, or adaptive elastic-net penalties. The solution path is computed at a grid of values of tuning parameter lambda. This function is modified based on the glmnet and the gcdnet packages.

Usage

sdwd(x, y, nlambda=100, 
     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, 
     eps=1e-8, maxit=1e6, strong=TRUE)
sdwd(x, y, nlambda=100, 
     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, 
     eps=1e-8, maxit=1e6, strong=TRUE)

Arguments

`x`	A matrix with $N$ rows and $p$ columns for predictors.
`y`	A vector of length $p$ for binary responses. The element of `y` is either -1 or 1.
`nlambda`	The number of `lambda` values, i.e., length of the `lambda` sequence. Default is 100.
`lambda.factor`	The ratio of the smallest to the largest `lambda` in the sequence: `lambda.factor` = `min(lambda)` / `max(lambda)`. `max(lambda)` is the least `lambda` to make all coefficients to be zero. The default value of `lambda.factor` is 0.0001 if $N >= p$ or 0.01 if $N < p$ . Takes no effect when user specifies a `lambda` sequence.
`lambda`	An optional user-supplied `lambda` sequence. If `lambda = NULL` (default), the program computes its own `lambda` sequence based on `nlambda` and `lambda.factor`; otherwise, the program uses the user-specified one. Since the program will automatically sort user-defined `lambda` sequence in decreasing order, it is better to supply a decreasing sequence.
`lambda2`	The L2 tuning parameter $\lambda_2$ .
`pf`	A vector of length $p$ representing the L1 penalty weights to each coefficient of $\beta$ for adaptive L1 or adaptive elastic net. `pf` can be 0 for some predictor(s), leading to including the predictor(s) all the time. One suggested choice of `pf` is ${(\beta + 1/n)}^{-1}$ , where $n$ is the sample size and $\beta$ is the coefficents obtained by L1 DWD or enet DWD. Default is 1 for all predictors (and infinity if some predictors are listed in `exclude`).
`pf2`	A vector of length $p$ for L2 penalty factor for adaptive L1 or adaptive elastic net. To allow different L2 shrinkage, user can set `pf2` to be different L2 penalty weights for each coefficient of $\beta$ . `pf2` can be 0 for some variables, indicating no L2 shrinkage. Default is 1 for all predictors.
`exclude`	Whether to exclude some predictors from the model. This is equivalent to adopting an infinite penalty factor when excluding some predictor. Default is none.
`dfmax`	Restricts at most how many predictors can be incorporated in the model. Default is $p+1$ . This restriction is helpful when $p$ is large, provided that a partial path is acceptable.
`pmax`	Restricts the maximum number of variables ever to be nonzero; e.g, once some $\beta$ enters the model, it counts once. The count will not change when the $\beta$ exits or re-enters the model. Default is `min(dfmax*1.2,p)`.
`standardize`	Whether to standardize the data. If `TRUE`, `sdwd` normalizes the predictors such that each column has sum squares $\sum^N_{i=1}x_{ij}^2/N=1$ of one. Note that x is always centered (i.e. $\sum^N_{i=1}x_{ij}=0$ ) no matter `standardize` is `TRUE` or `FALSE`. `sdwd` always returns coefficient `beta` on the original scale. Default value is `TRUE`.
`eps`	The algorithm stops when (i.e. $4\max_j(\beta_j^{new}-\beta_j^{old})^2$ is less than `eps`, where $j=0,\ldots, p$ . Defaults value is `1e-8`.
`maxit`	Restricts how many outer-loop iterations are allowed. Default is 1e6. Consider increasing `maxit` when the algorithm does not converge.
`strong`	If `TRUE`, adopts the strong rule to accelerate the algorithm.

Details

The sdwd minimizes the sparse penalized DWD loss function,

$L(y, X, \beta)/N + \lambda_1||\beta||_1 + 0.5\lambda_2||\beta||_2^2,$

where $L(u)=1-u$ if $u \le 1/2$ , $1/(4u)$ if $u > 1/2$ is the DWD loss. The value of lambda2 is user-specified.

To use the L1 penalty (lasso), set lambda2=0. To use the elastic net, set lambda2 as nonzero. To use the adaptive L1, set lambda2=0 and specify pf and pf2. To use the adaptive elastic net, set lambda2 as nonzero and specify pf and pf2 as well.

When the algorithm do not converge or run slow, consider increasing eps, decreasing nlambda, or increasing lambda.factor before increasing maxit.

Value

An object with S3 class sdwd.

`b0`	A vector of length `length(lambda)` representing the intercept at each `lambda` value.
`beta`	A matrix of dimension `p*length(lambda)` representing the coefficients at each `lambda` value. The matrix is stored as a sparse matrix (`Matrix` package). To convert it into normal type matrix use `as.matrix()`.
`df`	The number of nonzero coefficients at each `lambda`.
`dim`	The dimension of coefficient matrix, i.e., `p*length(lambda)`.
`lambda`	The `lambda` sequence that was actually used.
`npasses`	Total number of iterations for all lambda values.
`jerr`	Warnings and errors; 0 if no error.
`call`	The call that produced this object.

Author(s)

Boxiang Wang and Hui Zou
Maintainer: Boxiang Wang [email protected]

References

Wang, B. and Zou, H. (2016) “Sparse Distance Weighted Discrimination", Journal of Computational and Graphical Statistics, 25(3), 826–838.
https://www.tandfonline.com/doi/full/10.1080/10618600.2015.1049700

Friedman, J., Hastie, T., and Tibshirani, R. (2010), "Regularization paths for generalized linear models via coordinate descent", Journal of Statistical Software, 33(1), 1–22.
https://www.jstatsoft.org/v33/i01/paper

Marron, J.S., Todd, M.J., and Ahn, J. (2007) “Distance-Weighted Discrimination", Journal of the American Statistical Association, 102(408), 1267–1271.
https://www.tandfonline.com/doi/abs/10.1198/016214507000001120

Tibshirani, Robert., Bien, J., Friedman, J.,Hastie, T.,Simon, N.,Taylor, J., and Tibshirani, Ryan. (2012) Strong Rules for Discarding Predictors in Lasso-type Problems, Journal of the Royal Statistical Society, Series B, 74(2), 245–266.
https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9868.2011.01004.x

Yang, Y. and Zou, H. (2013) “An Efficient Algorithm for Computing the HHSVM and Its Generalizations", Journal of Computational and Graphical Statistics, 22(2), 396–415.
https://www.tandfonline.com/doi/full/10.1080/10618600.2012.680324

Examples

# load the data
data(colon)
# fit the elastic-net penalized DWD with lambda2=1
fit = sdwd(colon$x, colon$y, lambda2=1)
print(fit)
# coefficients at some lambda value
c1 = coef(fit, s=0.005)
# make predictions
predict(fit, newx=colon$x[1:10, ], s=c(0.01, 0.005))

# load the data
data(colon)
# fit the elastic-net penalized DWD with lambda2=1
fit = sdwd(colon$x, colon$y, lambda2=1)
print(fit)
# coefficients at some lambda value
c1 = coef(fit, s=0.005)
# make predictions
predict(fit, newx=colon$x[1:10, ], s=c(0.01, 0.005))

Package 'sdwd'

Help Index

Sparse Distance Weighted Discrimination

Description

Details

Author(s)

References

compute coefficients from a "cv.sdwd" object

Description

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Arguments

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Value

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Examples

compute coefficients for the sparse DWD

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simplified gene expression data from Alon et al. (1999)

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Examples

cross-validation for the sparse DWD

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plot the cross-validation curve of the sparse DWD

Description

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plot coefficients for the sparse DWD

Description

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make predictions from a "cv.sdwd" object

Description

Usage

Arguments

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Value

Author(s)

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Examples

make predictions for the sparse DWD

Description

Usage

Arguments

Details

Value

Author(s)