Multi-output linear regression — regress • multivarious

Fit a multivariate regression model for a matrix of basis functions, X, and a response matrix Y. The goal is to find a projection matrix that can be used for mapping and reconstruction.

Usage

regress(
  X,
  Y,
  preproc = NULL,
  method = c("lm", "enet", "mridge", "pls"),
  intercept = FALSE,
  lambda = 0.001,
  alpha = 0,
  ncomp = ceiling(ncol(X)/2),
  ...
)

Arguments

X: the set of independent (basis) variables
Y: the response matrix
preproc: the pre-processor (currently unused)
method: the regression method: lm, enet, mridge, or pls
intercept: whether to include an intercept term
lambda: ridge shrinkage parameter (for methods mridge and enet)
alpha: the elastic net mixing parameter if method is enet
ncomp: number of PLS components if method is pls
...: extra arguments sent to the underlying fitting function

Value

a bi-projector of type regress

Examples

# Generate synthetic data
Y <- matrix(rnorm(100 * 10), 10, 100)
X <- matrix(rnorm(10 * 9), 10, 9)
# Fit regression models and reconstruct the response matrix
r_lm <- regress(X, Y, intercept = FALSE, method = "lm")
recon_lm <- reconstruct(r_lm)
r_mridge <- regress(X, Y, intercept = TRUE, method = "mridge", lambda = 0.001)
recon_mridge <- reconstruct(r_mridge)
r_enet <- regress(X, Y, intercept = TRUE, method = "enet", lambda = 0.001, alpha = 0.5)
recon_enet <- reconstruct(r_enet)
r_pls <- regress(X, Y, intercept = TRUE, method = "pls", ncomp = 5)
recon_pls <- reconstruct(r_pls)