Package 'combss'

Extract the subset of selected feature indices.

Description

Extract the subset of selected feature indices.

Usage

## S3 method for class 'combss'
coef(object, k = NULL, ...)

Arguments

object	A combss object.
k	Subset size to return. Defaults to the best k if validation data was used, else the largest k evaluated.
...	Unused.

Value

Integer vector of selected column indices (1-indexed).

Examples

set.seed(1)
x <- matrix(rnorm(100 * 20), 100, 20)
y <- as.numeric(x[, 1] + x[, 2] + rnorm(100) * 0.1)
fit <- combss(x, y, family = "gaussian", q = 5)
coef(fit, k = 2)

---

Best subset selection for generalised linear models via continuous optimisation (COMBSS).

Description

Reformulates the NP-hard discrete subset selection problem as a continuous optimisation over the hypercube ⁠[0, 1]^p⁠, solved via a Frank-Wolfe homotopy algorithm. The inner ridge problem is solved with glmnet. For each subset size ⁠k = 1, ..., q⁠, COMBSS returns the selected feature set; if validation data is supplied, the best k is chosen by validation MSE (Gaussian) or accuracy (binomial / multinomial).

Usage

combss(
  x,
  y,
  family = c("gaussian", "binomial", "multinomial"),
  q = NULL,
  x_val = NULL,
  y_val = NULL,
  lam_ridge = 0,
  Niter = 25,
  alpha = 0.01,
  scale = TRUE,
  mandatory = NULL,
  verbose = FALSE
)

Arguments

x	Numeric design matrix ⁠(n, p)⁠ without an intercept column.
y	Response. Numeric for family = "gaussian"; ⁠{0, 1}⁠ (or two-level factor) for family = "binomial"; factor or integer in ⁠{1, ..., C}⁠ for family = "multinomial".
family	One of "gaussian" (alias: "linear"), "binomial", "multinomial".
q	Maximum subset size. Defaults to min(n, p).
x_val, y_val	Optional validation data. When provided, the best k is selected by validation metric and coef_ is returned for the best subset.
lam_ridge	Ridge penalty for the inner solver. Default 0.
Niter	Number of homotopy iterations. Default 25.
alpha	Frank-Wolfe step size. Default 0.01.
scale	Column-normalise x before the algorithm. Default TRUE.
mandatory	Optional integer vector of 1-indexed columns of x that must be included in every model.
verbose	Print progress. Default FALSE.

Value

An object of class "combss", a list with elements:

• family: one of "gaussian", "binomial", "multinomial"

• subset_list: list of length up to q; element k is an integer vector of selected column indices (1-indexed) for subset size k

• subset: best subset (requires validation data; otherwise NULL)

• mse / accuracy: validation metric for the best subset (requires validation data)

• lam_ridge: ridge penalty used

• q: maximum subset size evaluated

References

Moka, S., Liquet, B., Zhu, H. and Muller, S. (2024). COMBSS: best subset selection via continuous optimization. Statistics and Computing. doi:10.1007/s11222-024-10387-8

Mathur, A., Liquet, B., Muller, S. and Moka, S. (2026). Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications. arXiv:2603.21952.

Examples

set.seed(1)
n <- 200; p <- 30
beta <- c(3, 2, 1.5, 1, 0.5, rep(0, p - 5))
x <- matrix(rnorm(n * p), n, p)
y <- as.numeric(x %*% beta + rnorm(n) * 0.5)
fit <- combss(x, y, family = "gaussian", q = 10)
fit$subset_list[1:5]

---

Select the ridge penalty for COMBSS by leave-one-out cross-validation.

Description

Mirrors combss.cv.select_lambda in the Python combss package. For each candidate lambda and each subset size ⁠k = 1, ..., q⁠, runs COMBSS to obtain a subset and evaluates LOOCV error of a refit. Returns the best lambda overall and the best lambda per k.

Usage

combss_cv(
  x,
  y,
  family = c("gaussian", "binomial", "multinomial"),
  q,
  lambda_grid = NULL,
  Niter = 25,
  verbose = FALSE
)

Arguments

x	Numeric design matrix ⁠(n, p)⁠.
y	Response (numeric / binary / factor depending on family).
family	One of "gaussian" (alias "linear"), "binomial", "multinomial".
q	Maximum subset size.
lambda_grid	Candidate ridge penalties. Defaults to c(0, 10^seq(-3, 1, length.out = 10)).
Niter	Number of homotopy iterations passed to combss().
verbose	Print progress.

Value

List with:

• best_lambda: ridge penalty with best mean LOOCV metric across k

• best_lambda_per_k: numeric vector, length q

• results: data frame ⁠(lambda, k, loocv_metric)⁠

---

Predict from a combss fit.

Description

Refits the chosen subset on the original training data via OLS or ridge (Gaussian / binomial / multinomial as appropriate) and predicts on newx. Note: the training data is not stored on the fit object, so newx must be supplied along with x_train and y_train.

Usage

## S3 method for class 'combss'
predict(object, newx, x_train, y_train, k = NULL, ...)

Arguments

object	A combss object.
newx	Numeric matrix of new observations.
x_train, y_train	Original training data used to refit on the chosen subset.
k	Subset size to use. Defaults to the best k if validation data was used, else the largest k evaluated.
...	Unused.

Value

Numeric vector of predictions for newx.

Examples

set.seed(1)
x <- matrix(rnorm(100 * 20), 100, 20)
y <- as.numeric(x[, 1] + x[, 2] + rnorm(100) * 0.1)
fit <- combss(x, y, family = "gaussian", q = 5)
newx <- matrix(rnorm(5 * 20), 5, 20)
predict(fit, newx = newx, x_train = x, y_train = y, k = 2)

---