W2L1: 2-Wasserstein distance linear projections with an \(L_1\) penalty

Description

2-Wasserstein distance linear projections with an \(L_1\) penalty

Usage

W2L1(
  X,
  Y = NULL,
  theta = NULL,
  penalty = c("lasso", "ols", "mcp", "elastic.net", "selection.lasso", "scad", "mcp.net",
    "scad.net", "grp.lasso", "grp.lasso.net", "grp.mcp", "grp.scad", "grp.mcp.net",
    "grp.scad.net", "sparse.grp.lasso"),
  method = c("projection", "selection.variable", "location.scale", "scale"),
  transport.method = transport_options(),
  epsilon = 0.05,
  OTmaxit = 100,
  model.size = NULL,
  lambda = numeric(0),
  nlambda = 100L,
  lambda.min.ratio = NULL,
  alpha = 1,
  gamma = 1,
  tau = 0.5,
  groups = numeric(0),
  scale.factor = numeric(0),
  penalty.factor = NULL,
  group.weights = NULL,
  maxit = 500L,
  tol = 1e-07,
  irls.maxit = 100L,
  irls.tol = 0.001,
  infimum.maxit = NULL,
  display.progress = FALSE
)

Value

Object of class WpProj

Arguments

X: An n x p matrix of covariates
Y: An n x s matrix of predictions
theta: optional parameter matrix for selection methods. Should be p x s.
penalty: Form of penalty. One of "lasso", "ols", "mcp", "elastic.net","selection.lasso", "scad", "mcp.net", "scad.net", "grp.lasso", "grp.lasso.net", "grp.mcp","grp.scad", "grp.mcp.net", "grp.scad.net", "sparse.grp.lasso"
method: "selection.variable" or "projection
transport.method: Method for calculating the Wasserstein distance. One of "exact", "sinkhorn", "greenkhorn","hilbert"
epsilon: Penalty parameter for Sinkhorn and Greenkhorn and optimal transport
OTmaxit: Maximum iterations for the optimal transport iterations
model.size: The maximum number of desired covariates. Defaults to the number of covariates.
lambda: Penalty parameter for lasso regression. See oem.
nlambda: Number of lambda values. See oem.
lambda.min.ratio: Minimum lambda ratio for self selected lambda. See oem.
alpha: elastic net mixing. See oem.
gamma: tuning parameters for SCAD and MCP. See oem.
tau: mixing parameter for sparse group lasso. See oem.
groups: A vector of grouping values. See oem.
scale.factor: Value to standardize the covariates by. Typically, is the standard deviation. Should have length 1 or length same as the number of covariates
penalty.factor: Penalty factor for OEM. See oem.
group.weights: Weights for group lasso. See oem.
maxit: Max iteration for OEM. See oem.
tol: Tolerance for OEM. See oem.
irls.maxit: IRLS max iterations for OEM. See oem.
irls.tol: IRLS tolerance for OEM. See oem.
infimum.maxit: Maximum number of iterations alternating optimization and Wasserstein distance calculation. Irrelevant for projection method.
display.progress: Display intermediate progress?