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CVE/CVE_R/R/CVE.R

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#' Implementation of the CVE method.
#'
#' Conditional Variance Estimator (CVE) is a novel sufficient dimension
#' reduction (SDR) method assuming a model
#' \deqn{Y \sim g(B'X) + \epsilon}{Y ~ g(B'X) + epsilon}
#' where B'X is a lower dimensional projection of the predictors.
#'
#' @param formula Formel for the regression model defining `X`, `Y`.
#' See: \code{\link{formula}}.
#' @param data data.frame holding data for formula.
#' @param method The different only differe in the used optimization.
#' All of them are Gradient based optimization on a Stiefel manifold.
#' \itemize{
#' \item "simple" Simple reduction of stepsize.
#' \item "sgd" stocastic gradient decent.
#' \item TODO: further
#' }
#' @param ... Further parameters depending on the used method.
#' @examples
#' library(CVE)
#'
#' # sample dataset
#' ds <- dataset("M5")
#'
#' # call ´cve´ with default method (aka "simple")
#' dr.simple <- cve(ds$Y ~ ds$X, k = ncol(ds$B))
#' # plot optimization history (loss via iteration)
#' plot(dr.simple, main = "CVE M5 simple")
#'
#' # call ´cve´ with method "linesearch" using ´data.frame´ as data.
#' data <- data.frame(Y = ds$Y, X = ds$X)
#' # Note: ´Y, X´ are NOT defined, they are extracted from ´data´.
#' dr.linesearch <- cve(Y ~ ., data, method = "linesearch", k = ncol(ds$B))
#' plot(dr.linesearch, main = "CVE M5 linesearch")
#'
#' @references Fertl L., Bura E. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
#'
#' @seealso \code{\link{formula}}. For a complete parameters list (dependent on
#' the method) see \code{\link{cve_simple}}, \code{\link{cve_sgd}}
#' @import stats
#' @importFrom stats model.frame
#' @export
cve <- function(formula, data, method = "simple", ...) {
# check for type of `data` if supplied and set default
if (missing(data)) {
data <- environment(formula)
} else if (!is.data.frame(data)) {
stop('Parameter `data` must be a `data.frame` or missing.')
}
# extract `X`, `Y` from `formula` with `data`
model <- stats::model.frame(formula, data)
X <- as.matrix(model[,-1, drop = FALSE])
Y <- as.matrix(model[, 1, drop = FALSE])
# pass extracted data on to [cve.call()]
dr <- cve.call(X, Y, method = method, ...)
# overwrite `call` property from [cve.call()]
dr$call <- match.call()
return(dr)
}
#' @param nObs as describet in the Paper.
#' @param X Data
#' @param Y Responces
#' @param nObs Like in the paper.
#' @param k guess for SDR dimension.
#' @param ... Method specific parameters.
#' @rdname cve
#' @export
cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5, k, ...) {
# TODO: replace default value of `k` by `max.dim` when fast enough
if (missing(k)) {
stop("TODO: parameter `k` (rank(B)) is required, replace by `max.dim`.")
}
# parameter checking
if (!is.matrix(X)) {
stop('X should be a matrices.')
}
if (is.matrix(Y)) {
Y <- as.vector(Y)
}
if (nrow(X) != length(Y)) {
stop('Rows of X and number of Y elements are not compatible.')
}
if (ncol(X) < 2) {
stop('X is one dimensional, no need for dimension reduction.')
}
# Call specified method.
method <- tolower(method)
if (method == 'simple') {
dr <- cve_simple(X, Y, k, nObs = nObs, ...)
} else if (method == 'linesearch') {
dr <- cve_linesearch(X, Y, k, nObs = nObs, ...)
} else if (method == 'sgd') {
dr <- cve_sgd(X, Y, k, nObs = nObs, ...)
} else {
stop('Got unknown method.')
}
# augment result information
dr$method <- method
dr$call <- match.call()
class(dr) <- "cve"
return(dr)
}
# TODO: write summary
# summary.cve <- function() {
# # code #
# }
#' Ploting helper for objects of class \code{cve}.
#'
#' @param x Object of class \code{cve} (result of [cve()]).
#' @param content Specifies what to plot:
#' \itemize{
#' \item "history" Plots the loss history from stiefel optimization
#' (default).
#' \item ... TODO: add (if there are any)
#' }
#' @param ... Pass through parameters to [plot()] and [lines()]
#'
#' @usage ## S3 method for class 'cve'
#' plot(x, content = "history", ...)
#' @seealso see \code{\link{par}} for graphical parameters to pass through
#' as well as \code{\link{plot}} for standard plot utility.
#' @importFrom graphics plot lines points
#' @method plot cve
#' @export
plot.cve <- function(x, ...) {
H <- x$history
H_1 <- H[!is.na(H[, 1]), 1]
defaults <- list(
main = "History",
xlab = "Iterations i",
ylab = expression(loss == L[n](V^{(i)})),
xlim = c(1, nrow(H)),
ylim = c(0, max(H)),
type = "l"
)
call.plot <- match.call()
keys <- names(defaults)
keys <- keys[match(keys, names(call.plot)[-1], nomatch = 0) == 0]
for (key in keys) {
call.plot[[key]] <- defaults[[key]]
}
call.plot[[1L]] <- quote(plot)
call.plot$x <- quote(1:length(H_1))
call.plot$y <- quote(H_1)
eval(call.plot)
if (ncol(H) > 1) {
for (i in 2:ncol(H)) {
H_i <- H[H[, i] > 0, i]
lines(1:length(H_i), H_i)
}
}
x.ends <- apply(H, 2, function(h) { length(h[!is.na(h)]) })
y.ends <- apply(H, 2, function(h) { tail(h[!is.na(h)], n=1) })
points(x.ends, y.ends)
}
#' Prints a summary of a \code{cve} result.
#' @param object Instance of 'cve' as return of \code{cve}.
#' @method summary cve
#' @export
summary.cve <- function(object, ...) {
cat('Summary of CVE result - Method: "', object$method, '"\n',
'\n',
'Dataset size: ', nrow(object$X), '\n',
'Data Dimension: ', ncol(object$X), '\n',
'SDR Dimension: ', object$k, '\n',
'loss: ', object$loss, '\n',
'\n',
'Called via:\n',
' ',
sep='')
print(object$call)
}