Cross-validation for a sparsegl object. — cv.sparsegl • sparsegl

Performs k-fold cross-validation for sparsegl(). This function is largely similar glmnet::cv.glmnet().

Usage

cv.sparsegl(
  x,
  y,
  group = NULL,
  family = c("gaussian", "binomial"),
  lambda = NULL,
  pred.loss = c("default", "mse", "deviance", "mae", "misclass", "auc"),
  nfolds = 10,
  foldid = NULL,
  weights = NULL,
  offset = NULL,
  ...
)

Arguments

x

Double. A matrix of predictors, of dimension \(n \times p\); each row is a vector of measurements and each column is a feature. Objects of class Matrix::sparseMatrix are supported.

y

Double/Integer/Factor. The response variable. Quantitative for family="gaussian" and for other exponential families. If family="binomial" should be either a factor with two levels or a vector of integers taking 2 unique values. For a factor, the last level in alphabetical order is the target class.

group

Integer. A vector of consecutive integers describing the grouping of the coefficients (see example below).

family

Character or function. Specifies the generalized linear model to use. Valid options are:

"gaussian" - least squares loss (regression, the default),
"binomial" - logistic loss (classification)

For any other type, a valid stats::family() object may be passed. Note that these will generally be much slower to estimate than the built-in options passed as strings. So for example, family = "gaussian" and family = gaussian() will produce the same results, but the first will be much faster.

lambda

A user supplied lambda sequence. The default, NULL results in an automatic computation based on nlambda, the smallest value of lambda that would give the null model (all coefficient estimates equal to zero), and lambda.factor. Supplying a value of lambda overrides this behaviour. It is likely better to supply a decreasing sequence of lambda values than a single (small) value. If supplied, the user-defined lambda sequence is automatically sorted in decreasing order.

pred.loss

Loss to use for cross-validation error. Valid options are:

"default" the same as deviance (mse for regression and deviance otherwise)
"mse" mean square error
"deviance" the default (mse for Gaussian regression, and negative log-likelihood otherwise)
"mae" mean absolute error, can apply to any family
"misclass" for classification only, misclassification error.
"auc" for classification only, area under the ROC curve

nfolds

Number of folds - default is 10. 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 nfolds identifying which fold each observation is in. If supplied, nfolds can be missing.

weights

Double vector. Optional observation weights. These can only be used with a stats::family() object. Internally coerced to sum to the number of observations.

offset

Double vector. Optional offset (constant predictor without a corresponding coefficient). These can only be used with a stats::family() object.

...

Additional arguments to sparsegl().

Value

An object of class cv.sparsegl() is returned, which is a list with the components describing the cross-validation error.

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.
name: A text string indicating type of measure (for plotting purposes).
nnzero: The number of non-zero coefficients for each lambda
active_grps: The number of active groups for each lambda
sparsegl.fit: A fitted sparsegl() 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.
i.min: The index of lambda.min in the lambda sequence.
i.1se: The index of lambda.1se in the lambda sequence.
call: The function call.

Details

The function runs sparsegl() 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 error over the folds are computed.

References

Liang, X., Cohen, A., Sólon Heinsfeld, A., Pestilli, F., and McDonald, D.J. 2024. sparsegl: An R Package for Estimating Sparse Group Lasso. Journal of Statistical Software, Vol. 110(6): 1–23. doi:10.18637/jss.v110.i06 .

Examples

n <- 100
p <- 20
X <- matrix(rnorm(n * p), nrow = n)
eps <- rnorm(n)
beta_star <- c(rep(5, 5), c(5, -5, 2, 0, 0), rep(-5, 5), rep(0, (p - 15)))
y <- X %*% beta_star + eps
groups <- rep(1:(p / 5), each = 5)
cv_fit <- cv.sparsegl(X, y, groups)

Cross-validation for a `sparsegl` object.