Fit regression with network cohesion with cross-validation wrapper

This function fits a regression model with network cohesion regularization with a cross-validation wrapper. This code has been adapted from the netcoh R package with minor tweaks for increased speed and flexibility. Currently, it can handle linear and logistic regression only.

Usage

rnc_cv(
  x,
  y,
  A,
  nodeids = NULL,
  lambdas_netcoh,
  lambdas_x = 0,
  lambdas_l = 0.05,
  lambda_grid = NULL,
  family = c("linear", "logistic"),
  cv = 5,
  cv_foldids = NULL,
  refit = TRUE,
  newton_maxit = 50,
  newton_tol = 1e-04,
  verbose = FALSE
)

Arguments

x: A numeric matrix or data frame of predictors (features); size n x p. Should be centered so that each column has mean 0.
y: A numeric vector of responses of length n. Should be centered so that the mean is 0.
A: An adjacency matrix representing the network structure.
nodeids: (Optional) vector of node IDs of length n. If provided, node IDs indicate the rows of A, corresponding to each sample. If not provided, the rows of A are assumed to be in the same order as the rows of x and y.
lambdas_netcoh: Vector or list of regularization parameters for the network cohesion term.
lambdas_x: Vector or list of regularization parameters for the (linear) covariates. Default is 0 (i.e., no regularization).
lambdas_l: (Optional) Vector or list of regularization parameters for the graph Laplacian.
lambda_grid: (Optional) A data frame with columns lambda_netcoh, lambda_x, and lambda_l, where each row specifies a different set of regularization parameters to try. If NULL, a grid of regularization parameters will be generated based upon all possible combination of the provided lambdas_netcoh, lambdas_x, and lambdas_l.
family: A character string indicating the type of model to fit. Currently, only "linear" and "logistic" are supported.
cv: Number of cross-validation folds. Default is 5.
cv_foldids: (Optional) List of length cv, where each component in the list is a vector of sample indices in that fold. If NULL (default), cross-validation folds will be created randomly.
refit: Logical indicating whether or not to refit tuned model on full training set after cross-validation. Default is TRUE.
newton_maxit: Maximum number of Newton iterations when fitting logistic regression. Default is 50. Ignored for linear regression.
newton_tol: Tolerance for convergence of Newton iterations when fitting logistic regression. Default is 1e-4. Ignored for linear regression.
verbose: Logical indicating whether to print progress messages.

Value

A list with the following components:

lambda_grid: A data frame with the regularization parameters used in the cross-validation.
best_params: A data frame with the best regularization parameters found during cross-validation.
cv_errs: A matrix of cross-validation errors, where each row corresponds to a set of regularization parameters and each column corresponds to a fold. If regression, the RMSE is returned. If classification, the AUROC is returned.
cv_means: A vector of mean cross-validation errors for each set of regularization parameters.
cv_sds: A vector of standard deviations of cross-validation errors for each set of regularization parameters.
Other components from the fitted model if refit = TRUE (see output of rnc()).

Examples

data(example_data)

# fit RNC with CV
cv_fit <- rnc_cv(
  x = example_data$x, y = example_data$y, A = example_data$A,
  lambdas_netcoh = c(0, 0.1, 1),
  lambdas_x = c(0.1, 0.5)
)

# fit RNC with CV, specifying lambda grid manually (equivalent to above)
lambda_grid <- expand.grid(
  lambda_netcoh = c(0, 0.1, 1),
  lambda_x = c(0.1, 0.5),
  lambda_l = 0.05
)
cv_fit <- rnc_cv(
  x = example_data$x, y = example_data$y, A = example_data$A,
  lambda_grid = lambda_grid
)