% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{cve}
\alias{cve}
\alias{cve.call}
\title{Conditional Variance Estimator (CVE).}
\usage{
cve(formula, data, method = "simple", max.dim = 10L, ...)

cve.call(X, Y, method = "simple", nObs = sqrt(nrow(X)), h = NULL,
  min.dim = 1L, max.dim = 10L, k = NULL, momentum = 0, tau = 1,
  tol = 0.001, slack = 0, gamma = 0.5, V.init = NULL,
  max.iter = 50L, attempts = 10L, logger = NULL)
}
\arguments{
\item{formula}{an object of class \code{"formula"} which is a symbolic
description of the model to be fitted.}

\item{data}{an optional data frame, containing the data for the formula if
supplied.}

\item{method}{specifies the CVE method variation as one of
\itemize{
     \item "simple" exact implementation as described in the paper listed 
         below.
     \item "weighted" variation with addaptive weighting of slices.
}}

\item{max.dim}{upper bounds for \code{k}, (ignored if \code{k} is supplied).}

\item{...}{Parameters passed on to \code{cve.call}.}

\item{X}{data matrix with samples in its rows.}

\item{Y}{Responses (1 dimensional).}

\item{nObs}{parameter for choosing bandwidth \code{h} using
\code{\link{estimate.bandwidth}} (ignored if \code{h} is supplied).}

\item{h}{bandwidth or function to estimate bandwidth, defaults to internaly
estimated bandwidth.}

\item{min.dim}{lower bounds for \code{k}, (ignored if \code{k} is supplied).}

\item{k}{Dimension of lower dimensional projection, if \code{k} is given
only the specified dimension \code{B} matrix is estimated.}

\item{momentum}{number of [0, 1) giving the ration of momentum for eucledian
gradient update with a momentum term.}

\item{tau}{Initial step-size.}

\item{tol}{Tolerance for break condition.}

\item{slack}{Positive scaling to allow small increases of the loss while
optimizing.}

\item{gamma}{step-size reduction multiple.}

\item{V.init}{Semi-orthogonal matrix of dimensions `(ncol(X), ncol(X) - k)` #'      as optimization starting value. (If supplied, \code{attempts} is
set to 1 and \code{k} to match dimension)}

\item{max.iter}{maximum number of optimization steps.}

\item{attempts}{number of arbitrary different starting points.}

\item{logger}{a logger function (only for advanced user, significantly slows
down the computation).}
}
\value{
dr is a S3 object of class \code{cve} with named properties:
\itemize{
   \item X: Original training data,
   \item Y: Responce of original training data,
   \item method: Name of used method,
   \item call: The method call
}
as well as indexed entries \code{dr$res[[k]]} storing the k-dimensional SDR
projection matrices.

dr is a list which contains:
\itemize{
\item dir: dir[[d]] is the central space with d-dimension
        d = 1, 2, ..., p reduced direction of different dimensions
\item y: the value of response
\item idx: the index of variables which survives after screening
\item max.dim: the largest dimensions of CS or CMS which have been calculated in mave function
\item ky: parameter used for DIM for selection
\item x: the original training data
}
}
\description{
TODO: reuse of package description and details!!!!
}
\examples{
# create dataset
x <- matrix(rnorm(400), 100, 4)
y <- x[, 1] + x[, 2] + as.matrix(rnorm(100))

# Call CVE using momentum.
dr.momentum <- cve(y ~ x, momentum = 0.2)
# Call weighted CVE.
dr.weighted <- cve(y ~ x, method = "weighted")

}
\seealso{
For a detailed description of \code{formula} see
     \code{\link{formula}}.
}