regress {multivarious}

Multi-output linear regression

Description

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)