wip: proper package implementation
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# Generated by roxygen2: do not edit by hand
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S3method(plot,cve)
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export(cve)
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export(cve_cpp)
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export(cve.call)
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export(dataset)
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export(estimateBandwidth)
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export(rStiefel)
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import(Rcpp)
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import(stats)
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importFrom(Rcpp,evalCpp)
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importFrom(graphics,lines)
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importFrom(graphics,plot)
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importFrom(graphics,points)
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importFrom(stats,model.frame)
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importFrom(stats,rbinom)
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importFrom(stats,rnorm)
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useDynLib(CVE)
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167
CVE/R/CVE.R
167
CVE/R/CVE.R
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@ -1,44 +1,145 @@
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#' Conditional Variance Estimator
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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 for regressions satisfying E(Y|X) = E(Y|B'X),
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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 X A matrix of type numeric of dimensions N times dim where N is the number
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#' of entries with dim as data dimension.
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#' @param Y A vector of type numeric of length N (coresponds to \code{x}).
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#' @param k Guess for rank(B).
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#' @param nObs As describet in the paper.
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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 "linesearch" determines stepsize with backtracking linesearch
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#' using Armijo-Wolf conditions.
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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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#' TODO: See ...
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#' @examples
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#' library(CVE)
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#' ds <- dataset("M5")
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#' X <- ds$X
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#' Y <- ds$Y
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#' dr <- cve(Y ~ X, k = 1)
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#'
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#' @param tol Tolerance for optimization stopping creteria.
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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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#' @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", ...) {
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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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#' @rdname cve
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#' @export
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cve.call <- function(X, Y, method = "simple", nObs = nrow(X)^.5, k, ...) {
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# TODO: replace default value of `k` by `max.dim` when fast enough
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if (missing(k)) {
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stop("TODO: parameter `k` (rank(B)) is required, replace by `max.dim`.")
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}
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# parameter checking
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if (!(is.matrix(X) && is.matrix(Y))) {
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stop('X and Y should be matrices.')
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}
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if (nrow(X) != nrow(Y)) {
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stop('Rows of X and Y 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 (ncol(Y) > 1) {
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stop('Only one dimensional responces Y are supported.')
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}
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# call C++ CVE implementation
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# dr ... Dimension Reduction
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dr <- cve_cpp(X, Y, tolower(method), k = k, nObs = nObs, ...)
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# augment result information
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dr$method <- method
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dr$call <- match.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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#' @seealso TODO: \code{vignette("CVE_paper", package="CVE")}.
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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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#' @references Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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cve <- function(X, Y, k,
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nObs = sqrt(nrow(X)),
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tauInitial = 1.0,
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tol = 1e-3,
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slack = -1e-10,
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maxIter = 50L,
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attempts = 10L
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) {
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# check data parameter types
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stopifnot(
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is.matrix(X),
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is.vector(Y),
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typeof(X) == 'double',
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typeof(Y) == 'double'
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#' @seealso see \code{\link{par}} for graphical parameters to pass through.
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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[H[, 1] > 0, 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 CVE C++ implementation
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return(cve_cpp(X, Y, k,
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nObs,
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tauInitial,
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tol,
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slack,
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maxIter,
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attempts
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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[h > 0]) })
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y.ends <- apply(H, 2, function(h) { min(h[h > 0]) })
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points(x.ends, y.ends)
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}
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@ -1,6 +1,18 @@
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# Generated by using Rcpp::compileAttributes() -> do not edit by hand
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# Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393
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#' Gradient computation of the loss `L_n(V)`.
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#'
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#' The loss is defined as
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#' \deqn{L_n(V) := \frac{1}{n}\sum_{j=1}^n y_2(V, X_j) - y_1(V, X_j)^2}{L_n(V) := 1/n sum_j( (y_2(V, X_j) - y_1(V, X_j)^2 )}
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#' with
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#' \deqn{y_l(s_0) := \sum_{i=1}^n w_i(V, s_0)Y_i^l}{y_l(s_0) := sum_i(w_i(V, s_0) Y_i^l)}
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#'
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#' @rdname optStiefel
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#' @keywords internal
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#' @name gradient
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NULL
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#' Stiefel Optimization.
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#'
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#' Stiefel Optimization for \code{V} given a dataset \code{X} and responces
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@ -24,8 +36,13 @@
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#' orthogonal space spaned by \code{V}.
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#'
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#' @rdname optStiefel
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#' @name optStiefel
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#' @keywords internal
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#' @name optStiefel_simple
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NULL
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#' @rdname optStiefel
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#' @keywords internal
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#' @name optStiefel_linesearch
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NULL
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#' Estimated bandwidth for CVE.
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@ -87,9 +104,8 @@ rStiefel <- function(p, q) {
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#' and the matrix \code{B} estimated for the model as a orthogonal basis of the
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#' orthogonal space spaned by \code{V}.
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#'
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#' @rdname cve_cpp_V1
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#' @export
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cve_cpp <- function(X, Y, k, nObs, tauInitial = 1., tol = 1e-5, slack = -1e-10, maxIter = 50L, attempts = 10L) {
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.Call('_CVE_cve_cpp', PACKAGE = 'CVE', X, Y, k, nObs, tauInitial, tol, slack, maxIter, attempts)
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#' @keywords internal
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cve_cpp <- function(X, Y, method, k, nObs, tauInitial = 1., rho1 = 0.1, rho2 = 0.9, tol = 1e-5, maxIter = 50L, maxLineSearchIter = 10L, attempts = 10L) {
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.Call('_CVE_cve_cpp', PACKAGE = 'CVE', X, Y, method, k, nObs, tauInitial, rho1, rho2, tol, maxIter, maxLineSearchIter, attempts)
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}
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#' @param lambda Only for \code{"M4"}, see: below.
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#'
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#' @return List with elements
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#' \itemize{
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#' \item{X}{data}
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#' \item{Y}{response}
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#' \item{B}{Used dim-reduction matrix}
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#' \item{name}{Name of the dataset (name parameter)}
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#' }
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#'
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#' @section M1:
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#' The data follows \eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} for a subspace
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#' @section M5:
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#' TODO:
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#'
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#' @import stats
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#' @importFrom stats rnorm rbinom
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#' @export
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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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dataset <- function(name = "M1", n, B, p.mix = 0.3, lambda = 1.0) {
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# validate parameters
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stopifnot(name %in% c("M1", "M2", "M3", "M4", "M5"))
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@ -5,6 +5,9 @@
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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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#' @import Rcpp
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@ -12,6 +12,9 @@ Conditional Variance Estimator for Sufficient Dimension
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\details{
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TODO: And some details
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}
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\references{
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Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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}
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\author{
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Loki
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}
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% Please edit documentation in R/CVE.R
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\name{cve}
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\alias{cve}
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\title{Conditional Variance Estimator}
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\alias{cve.call}
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\title{Implementation of the CVE method.}
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\usage{
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cve(X, Y, k, nObs = sqrt(nrow(X)), tauInitial = 1, tol = 0.001,
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slack = -1e-10, maxIter = 50L, attempts = 10L)
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cve(formula, data, method = "simple", ...)
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cve.call(X, Y, method = "simple", nObs = nrow(X)^0.5, k, ...)
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}
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\arguments{
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\item{X}{A matrix of type numeric of dimensions N times dim where N is the number
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of entries with dim as data dimension.}
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\item{formula}{Formel for the regression model defining `X`, `Y`.
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See: \code{\link{formula}}.}
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\item{Y}{A vector of type numeric of length N (coresponds to \code{x}).}
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\item{data}{data.frame holding data for formula.}
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\item{k}{Guess for rank(B).}
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\item{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 "linesearch" determines stepsize with backtracking linesearch
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using Armijo-Wolf conditions.
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\item TODO: further
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}}
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\item{nObs}{As describet in the paper.}
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\item{tol}{Tolerance for optimization stopping creteria.}
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\item{...}{Further parameters depending on the used method.
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TODO: See ...}
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}
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\description{
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Conditional Variance Estimator (CVE) is a novel sufficient dimension
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reduction (SDR) method for regressions satisfying E(Y|X) = E(Y|B'X),
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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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\examples{
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library(CVE)
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ds <- dataset("M5")
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X <- ds$X
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Y <- ds$Y
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dr <- cve(Y ~ X, k = 1)
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}
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\references{
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Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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}
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\seealso{
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TODO: \code{vignette("CVE_paper", package="CVE")}.
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Fertl L, Bura E. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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}
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\alias{cve_cpp}
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\title{Conditional Variance Estimation (CVE) method.}
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\usage{
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cve_cpp(X, Y, k, nObs, tauInitial = 1, tol = 1e-05, slack = -1e-10,
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maxIter = 50L, attempts = 10L)
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cve_cpp(X, Y, method, k, nObs, tauInitial = 1, rho1 = 0.1,
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rho2 = 0.9, tol = 1e-05, maxIter = 50L, maxLineSearchIter = 10L,
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attempts = 10L)
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}
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\arguments{
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\item{X}{data points}
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\item{tol}{Tolerance for update error used for stopping criterion (default 1e-5)}
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\item{slack}{Ratio of small negative error allowed in loss optimization (default -1e-10)}
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\item{maxIter}{Upper bound of optimization iterations (default 50)}
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\item{attempts}{Number of tryes with new random optimization starting points (default 10)}
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\item{tau}{Initial step size (default 1)}
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\item{slack}{Ratio of small negative error allowed in loss optimization (default -1e-10)}
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}
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\value{
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List containing the bandwidth \code{h}, optimization objective \code{V}
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@ -35,3 +36,4 @@ List containing the bandwidth \code{h}, optimization objective \code{V}
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\description{
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This version uses a "simple" stiefel optimization schema.
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}
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\keyword{internal}
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@ -19,11 +19,13 @@ dataset(name = "M1", n, B, p.mix = 0.3, lambda = 1)
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}
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\value{
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List with elements
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\itemize{
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\item{X}{data}
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\item{Y}{response}
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\item{B}{Used dim-reduction matrix}
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\item{name}{Name of the dataset (name parameter)}
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}
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}
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\description{
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Provides sample datasets. There are 5 different datasets named
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M1, M2, M3, M4 and M5 describet in the paper references below.
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@ -60,6 +62,3 @@ TODO:
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TODO:
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}
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\references{
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Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
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}
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@ -1,8 +1,10 @@
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% Generated by roxygen2: do not edit by hand
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% Please edit documentation in R/RcppExports.R
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\name{optStiefel}
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\alias{optStiefel}
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\title{Stiefel Optimization.}
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\name{gradient}
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\alias{gradient}
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\alias{optStiefel_simple}
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\alias{optStiefel_linesearch}
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\title{Gradient computation of the loss `L_n(V)`.}
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\arguments{
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\item{X}{data points}
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@ -27,6 +29,11 @@ List containing the bandwidth \code{h}, optimization objective \code{V}
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orthogonal space spaned by \code{V}.
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}
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\description{
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The loss is defined as
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\deqn{L_n(V) := \frac{1}{n}\sum_{j=1}^n y_2(V, X_j) - y_1(V, X_j)^2}{L_n(V) := 1/n sum_j( (y_2(V, X_j) - y_1(V, X_j)^2 )}
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with
|
||||
\deqn{y_l(s_0) := \sum_{i=1}^n w_i(V, s_0)Y_i^l}{y_l(s_0) := sum_i(w_i(V, s_0) Y_i^l)}
|
||||
|
||||
Stiefel Optimization for \code{V} given a dataset \code{X} and responces
|
||||
\code{Y} for the model \deqn{Y\sim g(B'X) + \epsilon}{Y ~ g(B'X) + epsilon}
|
||||
to compute the matrix `B` such that \eqn{span{B} = span(V)^{\bot}}{%
|
||||
|
|
|
|||
|
|
@ -0,0 +1,25 @@
|
|||
% Generated by roxygen2: do not edit by hand
|
||||
% Please edit documentation in R/CVE.R
|
||||
\name{plot.cve}
|
||||
\alias{plot.cve}
|
||||
\title{Ploting helper for objects of class \code{"cve"}.}
|
||||
\usage{
|
||||
\method{plot}{cve}(x, ...)
|
||||
}
|
||||
\arguments{
|
||||
\item{x}{Object of class \code{"cve"} (result of [cve()]).}
|
||||
|
||||
\item{...}{Pass through parameters to [plot()] and [lines()]}
|
||||
|
||||
\item{content}{Specifies what to plot:
|
||||
\itemize{
|
||||
\item "history" Plots the loss history from stiefel optimization.
|
||||
\item ... TODO: add (if there are any)
|
||||
}}
|
||||
}
|
||||
\description{
|
||||
Ploting helper for objects of class \code{"cve"}.
|
||||
}
|
||||
\seealso{
|
||||
see \code{\link{par}} for graphical parameters to pass through.
|
||||
}
|
||||
179
CVE/src/CVE.cpp
179
CVE/src/CVE.cpp
|
|
@ -1,8 +1,3 @@
|
|||
//
|
||||
// Usage:
|
||||
// ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V1.cpp')"
|
||||
//
|
||||
|
||||
// only `RcppArmadillo.h` which includes `Rcpp.h`
|
||||
#include <RcppArmadillo.h>
|
||||
|
||||
|
|
@ -14,6 +9,9 @@
|
|||
// required for `R::qchisq()` used in `estimateBandwidth()`
|
||||
#include <Rmath.h>
|
||||
|
||||
// for proper error handling
|
||||
#include <stdexcept>
|
||||
|
||||
//' Estimated bandwidth for CVE.
|
||||
//'
|
||||
//' Estimates a propper bandwidth \code{h} according
|
||||
|
|
@ -72,18 +70,27 @@ arma::mat rStiefel(arma::uword p, arma::uword q) {
|
|||
return Q;
|
||||
}
|
||||
|
||||
//' Gradient computation of the loss `L_n(V)`.
|
||||
//'
|
||||
//' The loss is defined as
|
||||
//' \deqn{L_n(V) := \frac{1}{n}\sum_{j=1}^n y_2(V, X_j) - y_1(V, X_j)^2}{L_n(V) := 1/n sum_j( (y_2(V, X_j) - y_1(V, X_j)^2 )}
|
||||
//' with
|
||||
//' \deqn{y_l(s_0) := \sum_{i=1}^n w_i(V, s_0)Y_i^l}{y_l(s_0) := sum_i(w_i(V, s_0) Y_i^l)}
|
||||
//'
|
||||
//' @rdname optStiefel
|
||||
//' @keywords internal
|
||||
//' @name gradient
|
||||
double gradient(const arma::mat& X,
|
||||
const arma::mat& X_diff,
|
||||
const arma::mat& Y,
|
||||
const arma::mat& Y_rep,
|
||||
const arma::mat& V,
|
||||
const double h,
|
||||
arma::mat* G = 0
|
||||
arma::mat* G = 0 // out
|
||||
) {
|
||||
using namespace arma;
|
||||
|
||||
uword n = X.n_rows;
|
||||
uword p = X.n_cols;
|
||||
|
||||
// orthogonal projection matrix `Q = I - VV'` for dist computation
|
||||
mat Q = -(V * V.t());
|
||||
|
|
@ -138,16 +145,15 @@ double gradient(const arma::mat& X,
|
|||
//' orthogonal space spaned by \code{V}.
|
||||
//'
|
||||
//' @rdname optStiefel
|
||||
//' @name optStiefel
|
||||
//' @keywords internal
|
||||
double optStiefel(
|
||||
//' @name optStiefel_simple
|
||||
double optStiefel_simple(
|
||||
const arma::mat& X,
|
||||
const arma::vec& Y,
|
||||
const int k,
|
||||
const double h,
|
||||
const double tauInitial,
|
||||
const double tol,
|
||||
const double slack,
|
||||
const int maxIter,
|
||||
arma::mat& V, // out
|
||||
arma::vec& history // out
|
||||
|
|
@ -177,9 +183,9 @@ double optStiefel(
|
|||
double loss;
|
||||
double error = datum::inf;
|
||||
double tau = tauInitial;
|
||||
int count;
|
||||
int iter;
|
||||
// main optimization loop
|
||||
for (count = 0; count < maxIter && error > tol; ++count) {
|
||||
for (iter = 0; iter < maxIter && error > tol; ++iter) {
|
||||
// calc gradient `G = grad_V(L)(V)`
|
||||
mat G;
|
||||
loss = gradient(X, X_diff, Y, Y_rep, V, h, &G);
|
||||
|
|
@ -190,11 +196,11 @@ double optStiefel(
|
|||
// loss after step `L(V(tau))`
|
||||
double loss_tau = gradient(X, X_diff, Y, Y_rep, V_tau, h);
|
||||
|
||||
// store `loss` in `history` and increase `count`
|
||||
history(count) = loss;
|
||||
// store `loss` in `history` and increase `iter`
|
||||
history(iter) = loss;
|
||||
|
||||
// validate if loss decreased
|
||||
if ((loss_tau - loss) > slack * loss) {
|
||||
if ((loss_tau - loss) > 0.0) {
|
||||
// ignore step, retry with half the step size
|
||||
tau = tau / 2.;
|
||||
error = datum::inf;
|
||||
|
|
@ -208,7 +214,121 @@ double optStiefel(
|
|||
}
|
||||
|
||||
// store final `loss`
|
||||
history(count) = loss;
|
||||
history(iter) = loss;
|
||||
|
||||
return loss;
|
||||
}
|
||||
|
||||
//' @rdname optStiefel
|
||||
//' @keywords internal
|
||||
//' @name optStiefel_linesearch
|
||||
double optStiefel_linesearch(
|
||||
const arma::mat& X,
|
||||
const arma::vec& Y,
|
||||
const int k,
|
||||
const double h,
|
||||
const double tauInitial,
|
||||
const double tol,
|
||||
const int maxIter,
|
||||
const double rho1,
|
||||
const double rho2,
|
||||
const int maxLineSearchIter,
|
||||
arma::mat& V, // out
|
||||
arma::vec& history // out
|
||||
) {
|
||||
using namespace arma;
|
||||
|
||||
// get dimensions
|
||||
const uword n = X.n_rows; // nr samples
|
||||
const uword p = X.n_cols; // dim of random variable `X`
|
||||
const uword q = p - k; // rank(V) e.g. dim of ortho space of span{B}
|
||||
|
||||
// all `X_i - X_j` differences, `X_diff.row(i * n + j) = X_i - X_j`
|
||||
mat X_diff(n * n, p);
|
||||
for (uword i = 0, k = 0; i < n; ++i) {
|
||||
for (uword j = 0; j < n; ++j) {
|
||||
X_diff.row(k++) = X.row(i) - X.row(j);
|
||||
}
|
||||
}
|
||||
const vec Y_rep = repmat(Y, n, 1);
|
||||
const mat I_p = eye<mat>(p, p);
|
||||
const mat I_2q = eye<mat>(2 * q, 2 * q);
|
||||
|
||||
// initial start value for `V`
|
||||
V = rStiefel(p, q);
|
||||
|
||||
// first gradient initialization
|
||||
mat G;
|
||||
double loss = gradient(X, X_diff, Y, Y_rep, V, h, &G);
|
||||
|
||||
// set first `loss` in history
|
||||
history(0) = loss;
|
||||
|
||||
// main curvilinear optimization loop
|
||||
double error = datum::inf;
|
||||
int iter = 0;
|
||||
while (iter++ < maxIter && error > tol) {
|
||||
// helper matrices `lU` (linesearch U), `lV` (linesearch V)
|
||||
// as describet in [Wen, Yin] Lemma 4.
|
||||
mat lU = join_rows(G, V); // linesearch "U"
|
||||
mat lV = join_rows(V, -1.0 * G); // linesearch "V"
|
||||
// `A = G V' - V G'`
|
||||
mat A = lU * lV.t();
|
||||
|
||||
// set initial step size for curvilinear line search
|
||||
double tau = tauInitial, lower = 0., upper = datum::inf;
|
||||
|
||||
// TODO: check if `tau` is valid for inverting
|
||||
|
||||
// set line search internal gradient and loss to cycle for next iteration
|
||||
mat V_tau; // next position after a step of size `tau`, a.k.a. `V(tau)`
|
||||
mat G_tau; // gradient of `V` at `V(tau) = V_tau`
|
||||
double loss_tau; // loss (objective) at position `V(tau)`
|
||||
int lsIter = 0; // linesearch iter
|
||||
// start line search
|
||||
do {
|
||||
mat HV = inv(I_2q + (tau/2.) * lV.t() * lU) * lV.t();
|
||||
// next step `V`
|
||||
V_tau = V - tau * (lU * (HV * V));
|
||||
|
||||
double LprimeV = -trace(G.t() * A * V);
|
||||
|
||||
mat lB = I_p - (tau / 2.) * lU * HV;
|
||||
|
||||
loss_tau = gradient(X, X_diff, Y, Y_rep, V_tau, h, &G_tau);
|
||||
|
||||
double LprimeV_tau = -2. * trace(G_tau.t() * lB * A * (V + V_tau));
|
||||
|
||||
// Armijo condition
|
||||
if (loss_tau > loss + (rho1 * tau * LprimeV)) {
|
||||
upper = tau;
|
||||
tau = (lower + upper) / 2.;
|
||||
// Wolfe condition
|
||||
} else if (LprimeV_tau < rho2 * LprimeV) {
|
||||
lower = tau;
|
||||
if (upper == datum::inf) {
|
||||
tau = 2. * lower;
|
||||
} else {
|
||||
tau = (lower + upper) / 2.;
|
||||
}
|
||||
} else {
|
||||
break;
|
||||
}
|
||||
} while (++lsIter < maxLineSearchIter);
|
||||
|
||||
// compute error (break condition)
|
||||
// Note: `error` is the decrease of the objective `L_n(V)` and not the
|
||||
// norm of the gradient as proposed in [Wen, Yin] Algorithm 1.
|
||||
error = loss - loss_tau;
|
||||
|
||||
// cycle `V`, `G` and `loss` for next iteration
|
||||
V = V_tau;
|
||||
loss = loss_tau;
|
||||
G = G_tau;
|
||||
|
||||
// store final `loss`
|
||||
history(iter) = loss;
|
||||
}
|
||||
|
||||
return loss;
|
||||
}
|
||||
|
|
@ -232,18 +352,20 @@ double optStiefel(
|
|||
//' and the matrix \code{B} estimated for the model as a orthogonal basis of the
|
||||
//' orthogonal space spaned by \code{V}.
|
||||
//'
|
||||
//' @rdname cve_cpp_V1
|
||||
//' @export
|
||||
//' @keywords internal
|
||||
// [[Rcpp::export]]
|
||||
Rcpp::List cve_cpp(
|
||||
const arma::mat& X,
|
||||
const arma::vec& Y,
|
||||
const std::string method,
|
||||
const int k,
|
||||
const double nObs,
|
||||
const double tauInitial = 1.,
|
||||
const double rho1 = 0.1,
|
||||
const double rho2 = 0.9,
|
||||
const double tol = 1e-5,
|
||||
const double slack = -1e-10,
|
||||
const int maxIter = 50,
|
||||
const int maxLineSearchIter = 10,
|
||||
const int attempts = 10
|
||||
) {
|
||||
using namespace arma;
|
||||
|
|
@ -263,12 +385,27 @@ Rcpp::List cve_cpp(
|
|||
// declare output variables
|
||||
mat V; // estimated `V` space
|
||||
vec hist = vec(history.n_rows, fill::zeros); // optimization history
|
||||
double loss = optStiefel(X, Y, k, h, tauInitial, tol, slack, maxIter, V, hist);
|
||||
double loss;
|
||||
if (method == "simple") {
|
||||
loss = optStiefel_simple(
|
||||
X, Y, k, h,
|
||||
tauInitial, tol, maxIter,
|
||||
V, hist
|
||||
);
|
||||
} else if (method == "linesearch") {
|
||||
loss = optStiefel_linesearch(
|
||||
X, Y, k, h,
|
||||
tauInitial, tol, maxIter, rho1, rho2, maxLineSearchIter,
|
||||
V, hist
|
||||
);
|
||||
} else {
|
||||
throw std::invalid_argument("Unknown method.");
|
||||
}
|
||||
if (loss < loss_best) {
|
||||
loss_best = loss;
|
||||
V_best = V;
|
||||
}
|
||||
// write history to history collection
|
||||
// add history to history collection
|
||||
history.col(i) = hist;
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -32,21 +32,24 @@ BEGIN_RCPP
|
|||
END_RCPP
|
||||
}
|
||||
// cve_cpp
|
||||
Rcpp::List cve_cpp(const arma::mat& X, const arma::vec& Y, const int k, const double nObs, const double tauInitial, const double tol, const double slack, const int maxIter, const int attempts);
|
||||
RcppExport SEXP _CVE_cve_cpp(SEXP XSEXP, SEXP YSEXP, SEXP kSEXP, SEXP nObsSEXP, SEXP tauInitialSEXP, SEXP tolSEXP, SEXP slackSEXP, SEXP maxIterSEXP, SEXP attemptsSEXP) {
|
||||
Rcpp::List cve_cpp(const arma::mat& X, const arma::vec& Y, const std::string method, const int k, const double nObs, const double tauInitial, const double rho1, const double rho2, const double tol, const int maxIter, const int maxLineSearchIter, const int attempts);
|
||||
RcppExport SEXP _CVE_cve_cpp(SEXP XSEXP, SEXP YSEXP, SEXP methodSEXP, SEXP kSEXP, SEXP nObsSEXP, SEXP tauInitialSEXP, SEXP rho1SEXP, SEXP rho2SEXP, SEXP tolSEXP, SEXP maxIterSEXP, SEXP maxLineSearchIterSEXP, SEXP attemptsSEXP) {
|
||||
BEGIN_RCPP
|
||||
Rcpp::RObject rcpp_result_gen;
|
||||
Rcpp::RNGScope rcpp_rngScope_gen;
|
||||
Rcpp::traits::input_parameter< const arma::mat& >::type X(XSEXP);
|
||||
Rcpp::traits::input_parameter< const arma::vec& >::type Y(YSEXP);
|
||||
Rcpp::traits::input_parameter< const std::string >::type method(methodSEXP);
|
||||
Rcpp::traits::input_parameter< const int >::type k(kSEXP);
|
||||
Rcpp::traits::input_parameter< const double >::type nObs(nObsSEXP);
|
||||
Rcpp::traits::input_parameter< const double >::type tauInitial(tauInitialSEXP);
|
||||
Rcpp::traits::input_parameter< const double >::type rho1(rho1SEXP);
|
||||
Rcpp::traits::input_parameter< const double >::type rho2(rho2SEXP);
|
||||
Rcpp::traits::input_parameter< const double >::type tol(tolSEXP);
|
||||
Rcpp::traits::input_parameter< const double >::type slack(slackSEXP);
|
||||
Rcpp::traits::input_parameter< const int >::type maxIter(maxIterSEXP);
|
||||
Rcpp::traits::input_parameter< const int >::type maxLineSearchIter(maxLineSearchIterSEXP);
|
||||
Rcpp::traits::input_parameter< const int >::type attempts(attemptsSEXP);
|
||||
rcpp_result_gen = Rcpp::wrap(cve_cpp(X, Y, k, nObs, tauInitial, tol, slack, maxIter, attempts));
|
||||
rcpp_result_gen = Rcpp::wrap(cve_cpp(X, Y, method, k, nObs, tauInitial, rho1, rho2, tol, maxIter, maxLineSearchIter, attempts));
|
||||
return rcpp_result_gen;
|
||||
END_RCPP
|
||||
}
|
||||
|
|
@ -54,7 +57,7 @@ END_RCPP
|
|||
static const R_CallMethodDef CallEntries[] = {
|
||||
{"_CVE_estimateBandwidth", (DL_FUNC) &_CVE_estimateBandwidth, 3},
|
||||
{"_CVE_rStiefel", (DL_FUNC) &_CVE_rStiefel, 2},
|
||||
{"_CVE_cve_cpp", (DL_FUNC) &_CVE_cve_cpp, 9},
|
||||
{"_CVE_cve_cpp", (DL_FUNC) &_CVE_cve_cpp, 12},
|
||||
{NULL, NULL, 0}
|
||||
};
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,7 @@
|
|||
|
||||
# Overview
|
||||
- **CVE/**: Contains actual `R` package.
|
||||
- **CVE_legacy/**: Contains original (first) `R` implementatin of the CVE method.
|
||||
The `*.R` and `*.cpp` files in the root directory are _development_ and _test_ files.
|
||||
|
||||
## TODO: README.md
|
||||
23
cve_V1.cpp
23
cve_V1.cpp
|
|
@ -1,5 +1,5 @@
|
|||
//
|
||||
// Standalone implementation for development.
|
||||
// Development file.
|
||||
//
|
||||
// Usage:
|
||||
// ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V1.cpp')"
|
||||
|
|
@ -74,6 +74,15 @@ arma::mat rStiefel(arma::uword p, arma::uword q) {
|
|||
return Q;
|
||||
}
|
||||
|
||||
//' Gradient computation of the loss `L_n(V)`.
|
||||
//'
|
||||
//' The loss is defined as
|
||||
//' \deqn{L_n(V) := \frac{1}{n}\sum_{j=1}^n (y_2(V, X_j) - y_1(V, X_j)^2)}
|
||||
//' with
|
||||
//' \deqn{y_l(s_0) := \sum_{i=1}^n w_i(V, s_0)Y_i^l}{y_l(s_0) := sum_i(w_i(V, s_0) Y_i^l)}
|
||||
//'
|
||||
//' @rdname optStiefel
|
||||
//' @keywords internal
|
||||
double gradient(const arma::mat& X,
|
||||
const arma::mat& X_diff,
|
||||
const arma::mat& Y,
|
||||
|
|
@ -178,9 +187,9 @@ double optStiefel(
|
|||
double loss;
|
||||
double error = datum::inf;
|
||||
double tau = tauInitial;
|
||||
int count;
|
||||
int iter;
|
||||
// main optimization loop
|
||||
for (count = 0; count < maxIter && error > tol; ++count) {
|
||||
for (iter = 0; iter < maxIter && error > tol; ++iter) {
|
||||
// calc gradient `G = grad_V(L)(V)`
|
||||
mat G;
|
||||
loss = gradient(X, X_diff, Y, Y_rep, V, h, &G);
|
||||
|
|
@ -191,8 +200,8 @@ double optStiefel(
|
|||
// loss after step `L(V(tau))`
|
||||
double loss_tau = gradient(X, X_diff, Y, Y_rep, V_tau, h);
|
||||
|
||||
// store `loss` in `history` and increase `count`
|
||||
history(count) = loss;
|
||||
// store `loss` in `history` and increase `iter`
|
||||
history(iter) = loss;
|
||||
|
||||
// validate if loss decreased
|
||||
if ((loss_tau - loss) > slack * loss) {
|
||||
|
|
@ -209,7 +218,7 @@ double optStiefel(
|
|||
}
|
||||
|
||||
// store final `loss`
|
||||
history(count) = loss;
|
||||
history(iter) = loss;
|
||||
|
||||
return loss;
|
||||
}
|
||||
|
|
@ -233,7 +242,7 @@ double optStiefel(
|
|||
//' and the matrix \code{B} estimated for the model as a orthogonal basis of the
|
||||
//' orthogonal space spaned by \code{V}.
|
||||
//'
|
||||
//' @rdname cve_cpp_V1
|
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//' @rdname cve_cpp
|
||||
//' @export
|
||||
// [[Rcpp::export]]
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Rcpp::List cve_cpp(
|
||||
|
|
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|||
|
|
@ -1,5 +1,5 @@
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|||
//
|
||||
// Standalone implementation for development.
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||||
// Development file.
|
||||
//
|
||||
// Usage:
|
||||
// ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V2.cpp')"
|
||||
|
|
@ -149,10 +149,10 @@ double optStiefel(
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const int k,
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const double h,
|
||||
const double tauInitial,
|
||||
const double rho1,
|
||||
const double rho2,
|
||||
const double tol,
|
||||
const int maxIter,
|
||||
const double rho1,
|
||||
const double rho2,
|
||||
const int maxLineSeachIter,
|
||||
arma::mat& V, // out
|
||||
arma::vec& history // out
|
||||
|
|
@ -309,7 +309,7 @@ Rcpp::List cve_cpp(
|
|||
mat V; // estimated `V` space
|
||||
vec hist = vec(history.n_rows, fill::zeros); // optimization history
|
||||
double loss = optStiefel(X, Y, k, h,
|
||||
tauInitial, rho1, rho2, tol, maxIter, maxLineSeachIter, V, hist
|
||||
tauInitial, tol, maxIter, rho1, rho2, maxLineSeachIter, V, hist
|
||||
);
|
||||
if (loss < loss_best) {
|
||||
loss_best = loss;
|
||||
|
|
|
|||
|
|
@ -252,26 +252,48 @@ arma::mat grad_p(const arma::mat& X_ref,
|
|||
loss /= n;
|
||||
|
||||
// scaling for gradient summation
|
||||
for (uword k = 0; k < n; ++k) {
|
||||
// this scaling matrix is the lower triangular matrix defined as
|
||||
//
|
||||
// S_kl := (s_{kl} + s_{lk}) D_{kl}
|
||||
// s_ij := (L_n(V, X_j) - (Y_i - y1(V, X_j))^2) W_ij
|
||||
double factor;
|
||||
for (uword l = 0; l < n; ++l) {
|
||||
for (uword k = l + 1; k < n; ++k) {
|
||||
tmp = Y[k] - y1[l];
|
||||
S[l * n + k] = (L[l] - (tmp * tmp)) * W[l * n + k] * D[l * n + k];
|
||||
factor = (L[l] - (tmp * tmp)) * W[l * n + k]; // \tile{S}_{kl}
|
||||
tmp = Y[l] - y1[k];
|
||||
factor += (L[k] - (tmp * tmp)) * W[k * n + l]; // \tile{S}_{lk}
|
||||
S[l * n + k] = factor * D[l * n + k]; // (s_kl + s_lk) * D_kl
|
||||
}
|
||||
}
|
||||
|
||||
// gradient
|
||||
double factor = -2. / (n * h * h);
|
||||
for (uword j = 0; j < q; ++j) {
|
||||
// reuse memory area of `Q`
|
||||
// no longer needed and provides enough space (`q < p`)
|
||||
double* GD = Q;
|
||||
const double* X_l;
|
||||
const double* X_k;
|
||||
for (uword j = 0; j < p; ++j) {
|
||||
for (uword i = 0; i < p; ++i) {
|
||||
sum = 0.0;
|
||||
for (uword k = 0; k < n; ++k) {
|
||||
for (uword l = 0; l < n; ++l) {
|
||||
mvm = 0.0;
|
||||
for (uword m = 0; m < p; ++m) {
|
||||
mvm += (X[l * p + m] - X[k * p + m]) * V[j * p + m];
|
||||
X_l = X + (l * p);
|
||||
for (uword k = l + 1; k < n; ++k) {
|
||||
X_k = X + (k * p);
|
||||
sum += S[l * n + k] * (X_l[i] - X_k[i]) * (X_l[j] - X_k[j]);
|
||||
}
|
||||
sum += S[l * n + k] * (X[l * p + i] - X[k * p + i]) * mvm;
|
||||
}
|
||||
GD[j * p + i] = sum;
|
||||
}
|
||||
}
|
||||
|
||||
// distance gradient `DG` to gradient by multiplying with `V`
|
||||
factor = -2. / (n * h * h);
|
||||
for (uword i = 0; i < p; ++i) {
|
||||
for (uword j = 0; j < q; ++j) {
|
||||
sum = 0.0;
|
||||
for (uword k = 0; k < p; ++k) {
|
||||
sum += GD[k * p + i] * V[j * p + k];
|
||||
}
|
||||
G[j * p + i] = factor * sum;
|
||||
}
|
||||
|
|
@ -352,16 +374,17 @@ setup.tests <- function () {
|
|||
}
|
||||
counter <<- counter + 1
|
||||
}
|
||||
(mbm <- microbenchmark(
|
||||
mbm <- microbenchmark(
|
||||
arma = arma_grad(X, X_diff, Y, Y_rep, V, h),
|
||||
grad = grad(Xt, Y, V, h),
|
||||
grad_p = grad_p(Xt, Y, V, h),
|
||||
check = comp.all,
|
||||
setup = setup.tests(),
|
||||
times = 100L
|
||||
))
|
||||
|
||||
cat("Total time:", format(Sys.time() - time.start), '\n')
|
||||
)
|
||||
cat("\033[1m\033[92mTotal time:", format(Sys.time() - time.start), '\n')
|
||||
print(mbm)
|
||||
cat("\033[0m")
|
||||
|
||||
boxplot(mbm, las = 2, xlab = NULL)
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue