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Fit regression with network cohesion

rnc.Rd

This function fits a regression model with network cohesion regularization. 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(
  x,
  y,
  A,
  nodedegrees = NULL,
  nodeids = NULL,
  lambda_netcoh,
  lambda_x = 0,
  lambda_l = 0.05,
  family = c("linear", "logistic"),
  low_dim = NULL,
  init = NULL,
  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.

nodedegrees

(Optional) A vector of node degrees. If provided, it is used to compute the graph Laplacian. If not provided, it is computed from the adjacency matrix A.

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.

lambda_netcoh

Regularization parameter for the network cohesion term.

lambda_x

(Optional) Regularization parameter for the (linear) covariates. Default is 0 (i.e., no regularization).

lambda_l

(Optional) Regularization parameter for the graph Laplacian. Default is 0.05.

family

A character string indicating the type of model to fit. Currently, only "linear" and "logistic" are supported.

low_dim

(Optional) If TRUE, the algorithm will use a naive solver for low-dimensional problems. Default is NULL, which will use the navie low-dimensional solver if the number of covariates is <= 1/5 * the number of samples. Only used if family = "linear".

init

(Optional) initial values for the optimization algorithm to fit logistic regression. Ignored for linear regression.

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:

  • alpha: n x 1 matrix of coefficients corresponding to the individual node effects

  • beta: p x 1 matrix of coefficients corresponding to the covariates

  • lambda_netcoh: Regularization parameter for the network cohesion term.

  • lambda_x: Regularization parameter for the covariates.

  • lambda_l: Regularization parameter for the graph Laplacian.

  • nalpha_train: Number of distinct nodes in the training set (i.e., number of rows in A).

  • family: The type of model fitted, either "linear" or "logistic".

Examples

data(example_data)
rnc_fit <- rnc(
  x = example_data$x, y = example_data$y, A = example_data$A,
  lambda_netcoh = 1, lambda_x = 0.5
)