283 lines
9.6 KiB
R
283 lines
9.6 KiB
R
#' Conditional Variance Estimator (CVE) Package.
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#'
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#' Conditional Variance Estimation (CVE) is a novel sufficient dimension
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#' reduction (SDR) method for regressions satisfying \eqn{E(Y|X) = E(Y|B'X)},
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#' where \eqn{B'X} is a lower dimensional projection of the predictors. CVE,
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#' similarly to its main competitor, the mean average variance estimation
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#' (MAVE), is not based on inverse regression, and does not require the
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#' restrictive linearity and constant variance conditions of moment based SDR
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#' methods. CVE is data-driven and applies to additive error regressions with
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#' continuous predictors and link function. The effectiveness and accuracy of
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#' CVE compared to MAVE and other SDR techniques is demonstrated in simulation
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#' studies. CVE is shown to outperform MAVE in some model set-ups, while it
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#' remains largely on par under most others.
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#'
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#' Let \eqn{Y} be real denotes a univariate response and \eqn{X} a real
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#' \eqn{p}-dimensional covariate vector. We assume that the dependence of
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#' \eqn{Y} and \eqn{X} is modelled by
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#' \deqn{Y = g(B'X) + \epsilon}
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#' where \eqn{X} is independent of \eqn{\epsilon} with positive definite
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#' variance-covariance matrix \eqn{Var(X) = \Sigma_X}. \eqn{\epsilon} is a mean
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#' zero random variable with finite \eqn{Var(\epsilon) = E(\epsilon^2)}, \eqn{g}
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#' is an unknown, continuous non-constant function,
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#' and \eqn{B = (b_1, ..., b_k)} is
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#' a real \eqn{p \times k}{p x k} of rank \eqn{k <= p}{k \leq p}.
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#' Without loss of generality \eqn{B} is assumed to be orthonormal.
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#'
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#' @author Daniel Kapla, Lukas Fertl, Bura Efstathia
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#' @references Fertl Lukas, Bura Efstathia. Conditional Variance Estimation for
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#' Sufficient Dimension Reduction, 2019
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#'
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#' @importFrom stats model.frame
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#' @docType package
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#' @useDynLib CVE, .registration = TRUE
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"_PACKAGE"
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#' Conditional Variance Estimator (CVE).
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#'
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#' TODO: reuse of package description and details!!!!
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#'
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#' @param formula an object of class \code{"formula"} which is a symbolic
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#' description of the model to be fitted.
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#' @param data an optional data frame, containing the data for the formula if
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#' supplied.
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#' @param method specifies the CVE method variation as one of
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#' \itemize{
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#' \item "simple" exact implementation as describet in the paper listed
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#' below.
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#' \item "weighted" variation with addaptive weighting of slices.
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#' }
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#' @param ... Parameters passed on to \code{cve.call}.
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#' @examples
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#' library(CVE)
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#'
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#' # create dataset
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#' n <- 200
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#' p <- 12
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#' X <- matrix(rnorm(n * p), n, p)
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#' B <- cbind(c(1, rep(0, p - 1)), c(0, 1, rep(0, p - 2)))
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#' Y <- X %*% B
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#' Y <- Y[, 1L]^2 + Y[, 2L]^2 + rnorm(n, 0, 0.3)
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#'
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#' # Call the CVE method.
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#' dr <- cve(Y ~ X)
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#' round(dr[[2]]$B, 1)
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#'
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#' @seealso For a detailed description of the formula parameter see
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#' [\code{\link{formula}}].
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#' @export
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cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
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# check for type of `data` if supplied and set default
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if (missing(data)) {
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data <- environment(formula)
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} else if (!is.data.frame(data)) {
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stop("Parameter 'data' must be a 'data.frame' or missing.")
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}
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# extract `X`, `Y` from `formula` with `data`
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model <- stats::model.frame(formula, data)
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X <- as.matrix(model[ ,-1L, drop = FALSE])
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Y <- as.double(model[ , 1L])
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# pass extracted data on to [cve.call()]
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dr <- cve.call(X, Y, method = method, max.dim = max.dim, ...)
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# overwrite `call` property from [cve.call()]
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dr$call <- match.call()
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return(dr)
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}
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#' @param nObs parameter for choosing bandwidth \code{h} using
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#' \code{\link{estimate.bandwidth}} (ignored if \code{h} is supplied).
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#' @param X data matrix with samples in its rows.
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#' @param Y Responces (1 dimensional).
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#' @param k Dimension of lower dimensional projection, if given only the
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#' specified dimension is estimated.
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#' @param min.dim lower bounds for \code{k}, (ignored if \code{k} is supplied).
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#' @param max.dim upper bounds for \code{k}, (ignored if \code{k} is supplied).
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#' @param tau Initial step-size.
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#' @param tol Tolerance for break condition.
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#' @param epochs maximum number of optimization steps.
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#' @param attempts number of arbitrary different starting points.
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#' @param logger a logger function (only for addvanced user).
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#' @rdname cve
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#' @export
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cve.call <- function(X, Y, method = "simple",
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nObs = sqrt(nrow(X)), h = NULL,
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min.dim = 1L, max.dim = 10L, k = NULL,
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tau = 1.0, tol = 1e-3,
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epochs = 50L, attempts = 10L,
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logger = NULL) {
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# parameter checking
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if (!(is.matrix(X) && is.numeric(X))) {
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stop("Parameter 'X' should be a numeric matrices.")
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}
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if (!is.numeric(Y)) {
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stop("Parameter 'Y' must be numeric.")
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}
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if (is.matrix(Y) || !is.double(Y)) {
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Y <- as.double(Y)
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}
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if (nrow(X) != length(Y)) {
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stop("Rows of 'X' and '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) || is.null(k)) {
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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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} else {
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min.dim <- as.integer(k)
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max.dim <- as.integer(k)
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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' (or 'k') must be smaller than 'ncol(X)'.")
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}
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if (missing(h) || is.null(h)) {
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estimate <- TRUE
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} else if (is.function(h)) {
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estimate <- TRUE
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estimate.bandwidth <- h
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} else if (is.numeric(h) && h > 0.0) {
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estimate <- FALSE
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h <- as.double(h)
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} else {
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stop("Bandwidth 'h' must be positive numeric.")
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}
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if (!is.numeric(tau) || length(tau) > 1L || tau <= 0.0) {
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stop("Initial step-width 'tau' must be positive number.")
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} else {
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tau <- as.double(tau)
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}
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if (!is.numeric(tol) || length(tol) > 1L || tol < 0.0) {
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stop("Break condition tolerance 'tol' must be not negative number.")
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} else {
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tol <- as.double(tol)
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}
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if (!is.numeric(epochs) || length(epochs) > 1L) {
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stop("Parameter 'epochs' must be positive integer.")
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} else if (!is.integer(epochs)) {
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epochs <- as.integer(epochs)
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}
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if (epochs < 1L) {
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stop("Parameter 'epochs' must be at least 1L.")
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}
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if (!is.numeric(attempts) || length(attempts) > 1L) {
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stop("Parameter 'attempts' must be positive integer.")
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} else if (!is.integer(attempts)) {
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attempts <- as.integer(attempts)
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}
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if (attempts < 1L) {
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stop("Parameter 'attempts' must be at least 1L.")
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}
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if (is.function(logger)) {
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loggerEnv <- environment(logger)
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} else {
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loggerEnv <- NULL
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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 (estimate) {
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h <- estimate.bandwidth(X, k, nObs)
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}
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if (method == 'simple') {
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dr.k <- .Call('cve_simple', PACKAGE = 'CVE',
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X, Y, k, h,
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tau, tol,
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epochs, attempts,
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logger, loggerEnv)
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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 == 'rcg') {
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# dr.k <- cve_rcg(X, Y, k, nObs = nObs, ...)
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# } else if (method == 'momentum') {
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# dr.k <- cve_momentum(X, Y, k, nObs = nObs, ...)
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# } else if (method == 'rmsprob') {
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# dr.k <- cve_rmsprob(X, Y, k, nObs = nObs, ...)
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# } else if (method == 'sgdrmsprob') {
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# dr.k <- cve_sgdrmsprob(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$B <- null(dr.k$V)
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dr.k$loss <- mean(dr.k$L)
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dr.k$h <- h
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dr.k$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$X <- X
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dr$Y <- Y
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dr$method <- method
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dr$call <- call
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class(dr) <- "cve"
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return(dr)
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}
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#' Loss distribution kink plot.
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#'
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#' @param x Object of class \code{"cve"} (result of [\code{\link{cve}}]).
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#' @param ... Pass through parameters to [\code{\link{plot}}] and
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#' [\code{\link{lines}}]
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#'
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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}}, the 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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L <- c()
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k <- c()
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for (dr.k in x) {
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if (class(dr.k) == 'cve.k') {
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k <- c(k, paste0(dr.k$k))
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L <- c(L, dr.k$L)
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}
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}
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L <- matrix(L, ncol = length(k)) / var(x$Y)
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boxplot(L, main = "Kink plot",
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xlab = "SDR dimension",
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ylab = "Sample loss distribution",
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names = k)
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# lines(apply(L, 2, mean)) # TODO: ?
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}
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#' Prints a summary of a \code{cve} result.
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#' @param object Instance of 'cve' as return of \code{cve}.
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#' @method summary cve
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#' @export
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summary.cve <- function(object, ...) {
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cat('Summary of CVE result - Method: "', object$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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