122 lines
4.1 KiB
R
122 lines
4.1 KiB
R
% Generated by roxygen2: do not edit by hand
|
|
% Please edit documentation in R/CVE.R
|
|
\name{cve.call}
|
|
\alias{cve.call}
|
|
\title{Conditional Variance Estimator (CVE).}
|
|
\usage{
|
|
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{X}{Design predictor matrix.}
|
|
|
|
\item{Y}{\eqn{n}-dimensional vector of responces.}
|
|
|
|
\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{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{max.dim}{upper 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 \eqn{[0, 1)} giving the ration of momentum for
|
|
eucledian gradient update with a momentum term. \code{momentum = 0}
|
|
corresponds to normal gradient descend.}
|
|
|
|
\item{tau}{Initial step-size.}
|
|
|
|
\item{tol}{Tolerance for break condition.}
|
|
|
|
\item{slack}{Positive scaling to allow small increases of the loss while
|
|
optimizing, i.e. \code{slack = 0.1} allows the target function to
|
|
increase up to \eqn{10 \%} in one optimization step.}
|
|
|
|
\item{gamma}{step-size reduction multiple. If gradient step with step size
|
|
\code{tau} is not accepted \code{gamma * tau} is set to the next step
|
|
size.}
|
|
|
|
\item{V.init}{Semi-orthogonal matrix of dimensions `(ncol(X), ncol(X) - k)
|
|
used as starting value in the optimization. (If supplied,
|
|
\code{attempts} is set to 0 and \code{k} to match dimension).}
|
|
|
|
\item{max.iter}{maximum number of optimization steps.}
|
|
|
|
\item{attempts}{If \code{V.init} not supplied, the optimization is carried
|
|
out \code{attempts} times with starting values drawn from the invariant
|
|
measure on the Stiefel manifold (see \code{\link{rStiefel}}).}
|
|
|
|
\item{logger}{a logger function (only for advanced users, slows down the
|
|
computation).}
|
|
}
|
|
\value{
|
|
an S3 object of class \code{cve} with components:
|
|
\describe{
|
|
\item{X}{design matrix of predictor vector used for calculating
|
|
cve-estimate,}
|
|
\item{Y}{\eqn{n}-dimensional vector of responses used for calculating
|
|
cve-estimate,}
|
|
\item{method}{Name of used method,}
|
|
\item{call}{the matched call,}
|
|
\item{res}{list of components \code{V, L, B, loss, h} for
|
|
each \code{k = min.dim, ..., max.dim}. If \code{k} was supplied in the
|
|
call \code{min.dim = max.dim = k}.
|
|
\itemize{
|
|
\item \code{B} is the cve-estimate with dimension
|
|
\eqn{p\times k}{p x k}.
|
|
\item \code{V} is the orthogonal complement of \eqn{B}.
|
|
\item \code{L} is the loss for each sample seperatels such that
|
|
it's mean is \code{loss}.
|
|
\item \code{loss} is the value of the target function that is
|
|
minimized, evaluated at \eqn{V}.
|
|
\item \code{h} bandwidth parameter used to calculate
|
|
\code{B, V, loss, L}.
|
|
}
|
|
}
|
|
}
|
|
}
|
|
\description{
|
|
This is the main function in the \code{CVE} package. It creates objects of
|
|
class \code{"cve"} to estimate the mean subspace. Helper functions that
|
|
require a \code{"cve"} object can then be applied to the output from this
|
|
function.
|
|
}
|
|
\examples{
|
|
# create B for simulation (k = 1)
|
|
B <- rep(1, 5) / sqrt(5)
|
|
|
|
set.seed(21)
|
|
# creat predictor data X ~ N(0, I_p)
|
|
X <- matrix(rnorm(500), 100, 5)
|
|
# simulate response variable
|
|
# Y = f(B'X) + err
|
|
# with f(x1) = x1 and err ~ N(0, 0.25^2)
|
|
Y <- X \%*\% B + 0.25 * rnorm(100)
|
|
|
|
# calculate cve with method 'simple' for k = 1
|
|
set.seed(21)
|
|
cve.obj.simple1 <- cve(Y ~ X, k = 1)
|
|
|
|
# same as
|
|
set.seed(21)
|
|
cve.obj.simple2 <- cve.call(X, Y, k = 1)
|
|
|
|
# extract estimated B's.
|
|
coef(cve.obj.simple1, k = 1)
|
|
coef(cve.obj.simple2, k = 1)
|
|
}
|