223 lines
6.6 KiB
R
223 lines
6.6 KiB
R
#' Conditional Variance Estimator (CVE)
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#'
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#' Conditional Variance Estimator for Sufficient Dimension
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#' Reduction
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#'
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#' TODO: And some details
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#'
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#'
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#' @references Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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#'
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#' @docType package
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#' @author Loki
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"_PACKAGE"
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#' Implementation of the CVE method.
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#'
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#' Conditional Variance Estimator (CVE) is a novel sufficient dimension
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#' reduction (SDR) method assuming a model
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#' \deqn{Y \sim g(B'X) + \epsilon}{Y ~ g(B'X) + epsilon}
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#' where B'X is a lower dimensional projection of the predictors.
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#'
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#' @param formula Formel for the regression model defining `X`, `Y`.
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#' See: \code{\link{formula}}.
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#' @param data data.frame holding data for formula.
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#' @param method The different only differe in the used optimization.
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#' All of them are Gradient based optimization on a Stiefel manifold.
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#' \itemize{
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#' \item "simple" Simple reduction of stepsize.
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#' \item "sgd" stocastic gradient decent.
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#' \item TODO: further
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#' }
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#' @param ... Further parameters depending on the used method.
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#' @examples
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#' library(CVE)
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#'
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#' # sample dataset
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#' ds <- dataset("M5")
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#'
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#' # call ´cve´ with default method (aka "simple")
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#' dr.simple <- cve(ds$Y ~ ds$X, k = ncol(ds$B))
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#' # plot optimization history (loss via iteration)
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#' plot(dr.simple, main = "CVE M5 simple")
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#'
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#' # call ´cve´ with method "linesearch" using ´data.frame´ as data.
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#' data <- data.frame(Y = ds$Y, X = ds$X)
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#' # Note: ´Y, X´ are NOT defined, they are extracted from ´data´.
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#' dr.linesearch <- cve(Y ~ ., data, method = "linesearch", k = ncol(ds$B))
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#' plot(dr.linesearch, main = "CVE M5 linesearch")
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#'
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#' @references Fertl L., Bura E. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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#'
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#' @seealso \code{\link{formula}}. For a complete parameters list (dependent on
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#' the method) see \code{\link{cve_simple}}, \code{\link{cve_sgd}}
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#' @import stats
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#' @importFrom stats model.frame
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#' @export
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cve <- function(formula, data, method = "simple", max.dim = 10, ...) {
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# check for type of `data` if supplied and set default
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if (missing(data)) {
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data <- environment(formula)
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} else if (!is.data.frame(data)) {
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stop('Parameter `data` must be a `data.frame` or missing.')
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}
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# extract `X`, `Y` from `formula` with `data`
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model <- stats::model.frame(formula, data)
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X <- as.matrix(model[,-1, drop = FALSE])
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Y <- as.matrix(model[, 1, drop = FALSE])
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# pass extracted data on to [cve.call()]
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dr <- cve.call(X, Y, method = method, ...)
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# overwrite `call` property from [cve.call()]
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dr$call <- match.call()
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return(dr)
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}
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#' @param nObs as describet in the Paper.
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#' @param X Data
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#' @param Y Responces
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#' @param nObs Like in the paper.
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#' @param k guess for SDR dimension.
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#' @param ... Method specific parameters.
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#' @rdname cve
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#' @export
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cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5,
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min.dim = 1, max.dim = 10, k, ...) {
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# parameter checking
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if (!is.matrix(X)) {
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stop('X should be a matrices.')
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}
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if (is.matrix(Y)) {
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Y <- as.vector(Y)
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}
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if (nrow(X) != length(Y)) {
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stop('Rows of X and number of Y elements are not compatible.')
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}
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if (ncol(X) < 2) {
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stop('X is one dimensional, no need for dimension reduction.')
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}
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if (!missing(k)) {
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min.dim <- as.integer(k)
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max.dim <- as.integer(k)
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} else {
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min.dim <- as.integer(min.dim)
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max.dim <- as.integer(min(max.dim, ncol(X) - 1L))
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}
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if (min.dim > max.dim) {
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stop('`min.dim` bigger `max.dim`.')
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}
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if (max.dim >= ncol(X)) {
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stop('`max.dim` must be smaller than `ncol(X)`.')
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}
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# Call specified method.
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method <- tolower(method)
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call <- match.call()
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dr <- list()
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for (k in min.dim:max.dim) {
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if (method == 'simple') {
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dr.k <- cve_simple(X, Y, k, nObs = nObs, ...)
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} else if (method == 'linesearch') {
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dr.k <- cve_linesearch(X, Y, k, nObs = nObs, ...)
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} else if (method == 'sgd') {
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dr.k <- cve_sgd(X, Y, k, nObs = nObs, ...)
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} else {
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stop('Got unknown method.')
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}
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dr.k$k <- k
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class(dr.k) <- "cve.k"
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dr[[k]] <- dr.k
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}
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# augment result information
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dr.k$method <- method
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dr.k$call <- call
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class(dr) <- "cve"
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return(dr)
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}
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# TODO: write summary
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# summary.cve <- function() {
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# # code #
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# }
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#' Ploting helper for objects of class \code{cve}.
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#'
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#' @param x Object of class \code{cve} (result of [cve()]).
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#' @param content Specifies what to plot:
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#' \itemize{
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#' \item "history" Plots the loss history from stiefel optimization
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#' (default).
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#' \item ... TODO: add (if there are any)
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#' }
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#' @param ... Pass through parameters to [plot()] and [lines()]
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#'
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#' @usage ## S3 method for class 'cve'
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#' plot(x, content = "history", ...)
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#' @seealso see \code{\link{par}} for graphical parameters to pass through
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#' as well as \code{\link{plot}} for standard plot utility.
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#' @importFrom graphics plot lines points
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#' @method plot cve
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#' @export
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plot.cve <- function(x, ...) {
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# H <- x$history
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# H_1 <- H[!is.na(H[, 1]), 1]
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# defaults <- list(
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# main = "History",
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# xlab = "Iterations i",
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# ylab = expression(loss == L[n](V^{(i)})),
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# xlim = c(1, nrow(H)),
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# ylim = c(0, max(H)),
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# type = "l"
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# )
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# call.plot <- match.call()
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# keys <- names(defaults)
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# keys <- keys[match(keys, names(call.plot)[-1], nomatch = 0) == 0]
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# for (key in keys) {
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# call.plot[[key]] <- defaults[[key]]
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# }
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# call.plot[[1L]] <- quote(plot)
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# call.plot$x <- quote(1:length(H_1))
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# call.plot$y <- quote(H_1)
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# eval(call.plot)
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# if (ncol(H) > 1) {
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# for (i in 2:ncol(H)) {
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# H_i <- H[H[, i] > 0, i]
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# lines(1:length(H_i), H_i)
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# }
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# }
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# x.ends <- apply(H, 2, function(h) { length(h[!is.na(h)]) })
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# y.ends <- apply(H, 2, function(h) { tail(h[!is.na(h)], n=1) })
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# points(x.ends, y.ends)
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}
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#' Prints a summary of a \code{cve} result.
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#' @param object Instance of 'cve' as return of \code{cve}.
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#' @method summary cve
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#' @export
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summary.cve <- function(object, ...) {
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cat('Summary of CVE result - Method: "', object$method, '"\n',
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'\n',
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'Dataset size: ', nrow(object$X), '\n',
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'Data Dimension: ', ncol(object$X), '\n',
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'SDR Dimension: ', object$k, '\n',
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'loss: ', object$loss, '\n',
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'\n',
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'Called via:\n',
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' ',
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sep='')
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print(object$call)
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}
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