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#
# Description of this R script:
# R interface for linear multiple output sparse group lasso routines.
#
# Intended for use with R.
# Copyright (C) 2014 Martin Vincent
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>
#
#' @title Fit a linear multiple output model using sparse group lasso
#'
#' @description
#' For a linear multiple output model with \eqn{p} features (covariates) dived into \eqn{m} groups using sparse group lasso.
#'
#' @details
#' This function computes a sequence of minimizers (one for each lambda given in the \code{lambda} argument) of
#' \deqn{\frac{1}{N}\|Y-X\beta\|_F^2 + \lambda \left( (1-\alpha) \sum_{J=1}^m \gamma_J \|\beta^{(J)}\|_2 + \alpha \sum_{i=1}^{n} \xi_i |\beta_i| \right)}
#' where \eqn{\|\cdot\|_F} is the frobenius norm.
#' The vector \eqn{\beta^{(J)}} denotes the parameters associated with the \eqn{J}'th group of features.
#' The group weights are denoted by \eqn{\gamma \in [0,\infty)^m} and the parameter weights by \eqn{\xi \in [0,\infty)^n}.
#'
#' @param x design matrix, matrix of size \eqn{N \times p}.
#' @param y response matrix, matrix of size \eqn{N \times K}.
#' @param intercept should the model include intercept parameters.
#' @param weights sample weights, vector of size \eqn{N \times K}.
#' @param grouping grouping of features, a factor or vector of length \eqn{p}.
#' Each element of the factor/vector specifying the group of the feature.
#' @param groupWeights the group weights, a vector of length \eqn{m} (the number of groups).
#' @param parameterWeights a matrix of size \eqn{K \times p}.
#' @param alpha the \eqn{\alpha} value 0 for group lasso, 1 for lasso, between 0 and 1 gives a sparse group lasso penalty.
#' @param lambda lambda.min relative to lambda.max or the lambda sequence for the regularization path.
#' @param d length of lambda sequence (ignored if \code{length(lambda) > 1})
#' @param algorithm.config the algorithm configuration to be used.
#'
#' @return
#' \item{beta}{the fitted parameters -- the list \eqn{\hat\beta(\lambda(1)), \dots, \hat\beta(\lambda(d))} of length \code{length(return)}.
#' With each entry of list holding the fitted parameters, that is matrices of size \eqn{K\times p} (if \code{intercept = TRUE} matrices of size \eqn{K\times (p+1)})}
#' \item{loss}{the values of the loss function.}
#' \item{objective}{the values of the objective function (i.e. loss + penalty).}
#' \item{lambda}{the lambda values used.}
#' @author Martin Vincent
#' @examples
#'
#' set.seed(100) # This may be removed, ensures consistency of tests
#'
#' # Simulate from Y = XB + E,
#' # the dimension of Y is N x K, X is N x p, B is p x K
#'
#' N <- 50 # number of samples
#' p <- 50 # number of features
#' K <- 25 # number of groups
#'
#' B <- matrix(
#' sample(c(rep(1,p*K*0.1), rep(0, p*K-as.integer(p*K*0.1)))),
#' nrow = p,ncol = K)
#'
#' X <- matrix(rnorm(N*p,1,1), nrow=N, ncol=p)
#' Y <- X %*% B + matrix(rnorm(N*K,0,1), N, K)
#'
#' fit <-lsgl::fit(X,Y, alpha=1, lambda = 0.1, intercept=FALSE)
#'
#' ## ||B - \beta||_F
#' sapply(fit$beta, function(beta) sum((B - beta)^2))
#'
#' ## Plot
#' par(mfrow = c(3,1))
#' image(B, main = "True B")
#' image(
#' x = as.matrix(fit$beta[[100]]),
#' main = paste("Lasso estimate (lambda =", round(fit$lambda[100], 2), ")")
#' )
#' image(solve(t(X)%*%X)%*%t(X)%*%Y, main = "Least squares estimate")
#'
#' # The training error of the models
#' Err(fit, X, loss="OVE")
#' # This is simply the loss function
#' sqrt(N*fit$loss)
#'
#' @import Matrix
#' @importFrom utils packageVersion
#' @importFrom methods is
#' @importFrom sglOptim sgl_fit
#' @importFrom sglOptim print_with_metric_prefix
#' @export
fit <- function(x, y,
intercept = TRUE,
weights = NULL,
grouping = NULL,
groupWeights = NULL,
parameterWeights = NULL,
alpha = 1,
lambda,
d = 100,
algorithm.config = lsgl.standard.config)
{
# Get call
cl <- match.call()
setup <- .process_args(x, y,
weights = weights,
intercept = intercept,
grouping = grouping,
groupWeights = groupWeights,
parameterWeights = parameterWeights)
data <- setup$data
# Print info
if(algorithm.config$verbose) {
cat("\nRunning lsgl ")
if(data$sparseX & data$sparseY) {
cat("(sparse design and response matrices)")
}
if(data$sparseX & !data$sparseY) {
cat("(sparse design matrix)")
}
if(!data$sparseX & data$sparseY) {
cat("(sparse response matrix)")
}
cat("\n\n")
print(data.frame(
'Samples: ' = print_with_metric_prefix(data$n_samples),
'Features: ' = print_with_metric_prefix(data$n_covariate),
'Models: ' = print_with_metric_prefix(ncol(data$data$Y)),
'Groups: ' = print_with_metric_prefix(length(unique(setup$grouping))),
'Parameters: ' = print_with_metric_prefix(length(setup$parameterWeights)),
check.names = FALSE),
row.names = FALSE, digits = 2, right = TRUE
)
cat("\n")
}
# Call sglOptim
res <- sgl_fit(
module_name = setup$callsym,
PACKAGE = "lsgl",
data = data,
parameterGrouping = setup$grouping,
groupWeights = setup$groupWeights,
parameterWeights = setup$parameterWeights,
alpha = alpha,
lambda = lambda,
d = d,
algorithm.config = algorithm.config
)
# Add weights
res$weights <- weights
# Transpose all beta matrices
res$beta <- lapply(res$beta, t)
res$intercept <- intercept
res$lsgl_version <- packageVersion("lsgl")
res$call <- cl
class(res) <- "lsgl"
return(res)
}
#' Deprecated fit function
#'
#' @keywords internal
#' @export
lsgl <- function(
x,
y,
intercept = TRUE,
weights = NULL,
grouping = NULL,
groupWeights = NULL,
parameterWeights = NULL,
alpha = 1,
lambda,
d = 100,
algorithm.config = lsgl.standard.config) {
warning("lsgl is deprecated, use lsgl::fit")
lsgl::fit(
x = x,
y = y,
intercept = intercept,
weights = weights,
grouping = grouping,
groupWeights = groupWeights,
parameterWeights = parameterWeights,
alpha = alpha,
lambda = lambda,
d = d,
algorithm.config = algorithm.config
)
}
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