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add: CVE,

add: R document files,
add: CVE_paper,
add: package-doc,
fix: doc typo
This commit is contained in:
Daniel Kapla 2019-08-10 00:08:17 +02:00
parent 4bc9ca2f58
commit 095e463463
17 changed files with 756 additions and 19 deletions

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export(cve) export(cve)
export(cve_cpp) export(cve_cpp)
export(dataset) export(dataset)
export(estimate.bandwidth) export(estimateBandwidth)
export(index_test)
export(kron_test)
export(rStiefel) export(rStiefel)
export(test1)
export(test2)
export(test3)
export(test4)
import(Rcpp) import(Rcpp)
importFrom(Rcpp,evalCpp) importFrom(Rcpp,evalCpp)
useDynLib(CVE) useDynLib(CVE)

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#' Conditional Variance Estimator
#'
#' Conditional Variance Estimator (CVE) is a novel sufficient dimension
#' reduction (SDR) method for regressions satisfying E(Y|X) = E(Y|B'X),
#' where B'X is a lower dimensional projection of the predictors.
#'
#' @param X A matrix of type numeric of dimensions N times dim where N is the number
#' of entries with dim as data dimension.
#' @param Y A vector of type numeric of length N (coresponds to \code{x}).
#' @param k Guess for rank(B).
#' @param nObs As describet in the paper.
#'
#' @param tol Tolerance for optimization stopping creteria.
#' @export
#'
#' @seealso TODO: \code{vignette("CVE_paper", package="CVE")}.
#'
#' @references Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
cve <- function(X, Y, k,
nObs = sqrt(nrow(X)),
tauInitial = 1.0,
tol = 1e-3,
slack = -1e-10,
maxIter = 50L,
attempts = 10L
) {
# check data parameter types
stopifnot(
is.matrix(X),
is.vector(Y),
typeof(X) == 'double',
typeof(Y) == 'double'
)
# call CVE C++ implementation
return(cve_cpp(X, Y, k,
nObs,
tauInitial,
tol,
slack,
maxIter,
attempts
))
}

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# Generated by using Rcpp::compileAttributes() -> do not edit by hand
# Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393
#' Stiefel Optimization.
#'
#' 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}}{%
#' span(B) = orth(span(B))}.
#'
#' @param X data points
#' @param Y response
#' @param k assumed \eqn{rank(B)}
#' @param nObs parameter for bandwidth estimation, typical value
#' \code{nObs = nrow(X)^lambda} with \code{lambda} in the range [0.3, 0.8].
#' @param tau Initial step size
#' @param tol Tolerance for update error used for stopping criterion
#' \eqn{|| V(j) V(j)' - V(j+1) V(j+1)' ||_2 < tol}{%
#' \| V_j V_j' - V_{j+1} V_{j+1}' \|_2 < tol}.
#' @param maxIter Upper bound of optimization iterations
#'
#' @return List containing the bandwidth \code{h}, optimization objective \code{V}
#' and the matrix \code{B} estimated for the model as a orthogonal basis of the
#' orthogonal space spaned by \code{V}.
#'
#' @rdname optStiefel
#' @name optStiefel
#' @keywords internal
NULL
#' Estimated bandwidth for CVE.
#'
#' Estimates a propper bandwidth \code{h} according
#' \deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
#' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
#'
#' @param X data matrix of dimension (n x p) with n data points X_i of dimension
#' q. Therefor each row represents a datapoint of dimension p.
#' @param k Guess for rank(B).
#' @param nObs Ether numeric of a function. If specified as numeric value
#' its used in the computation of the bandwidth directly. If its a function
#' `nObs` is evaluated as \code{nObs(nrow(x))}. The default behaviou if not
#' supplied at all is to use \code{nObs <- nrow(x)^0.5}.
#'
#' @seealso [qchisq()]
#'
#' @export
estimateBandwidth <- function(X, k, nObs) {
.Call('_CVE_estimateBandwidth', PACKAGE = 'CVE', X, k, nObs)
}
#' Random element from Stiefel Manifold `S(p, q)`.
#'
#' Draws an element of \eqn{S(p, q)} which is the Stiefel Manifold.
#' This is done by taking the Q-component of the QR decomposition
#' from a `(p, q)` Matrix with independent standart normal entries.
#' As a semi-orthogonal Matrix the result `V` satisfies \eqn{V'V = I_q}.
#'
#' @param p Row dimension
#' @param q Column dimension
#'
#' @return Matrix of dim `(p, q)`.
#'
#' @seealso <https://en.wikipedia.org/wiki/Stiefel_manifold>
#'
#' @export
rStiefel <- function(p, q) {
.Call('_CVE_rStiefel', PACKAGE = 'CVE', p, q)
}
#' Conditional Variance Estimation (CVE) method.
#'
#' This version uses a "simple" stiefel optimization schema.
#'
#' @param X data points
#' @param Y response
#' @param k assumed \eqn{rank(B)}
#' @param nObs parameter for bandwidth estimation, typical value
#' \code{nObs = nrow(X)^lambda} with \code{lambda} in the range [0.3, 0.8].
#' @param tau Initial step size (default 1)
#' @param tol Tolerance for update error used for stopping criterion (default 1e-5)
#' @param slack Ratio of small negative error allowed in loss optimization (default -1e-10)
#' @param maxIter Upper bound of optimization iterations (default 50)
#' @param attempts Number of tryes with new random optimization starting points (default 10)
#'
#' @return List containing the bandwidth \code{h}, optimization objective \code{V}
#' 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
cve_cpp <- function(X, Y, k, nObs, tauInitial = 1., tol = 1e-5, slack = -1e-10, maxIter = 50L, attempts = 10L) {
.Call('_CVE_cve_cpp', PACKAGE = 'CVE', X, Y, k, nObs, tauInitial, tol, slack, maxIter, attempts)
}

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#' Conditional Variance Estimator (CVE)
#'
#' Conditional Variance Estimator for Sufficient Dimension
#' Reduction
#'
#' TODO: And some details
#'
#' @docType package
#' @author Loki
#' @import Rcpp
#' @importFrom Rcpp evalCpp
#' @useDynLib CVE
"_PACKAGE"

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/package.R
\docType{package}
\name{CVE-package}
\alias{CVE}
\alias{CVE-package}
\title{Conditional Variance Estimator (CVE)}
\description{
Conditional Variance Estimator for Sufficient Dimension
Reduction
}
\details{
TODO: And some details
}
\author{
Loki
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CVE.R
\name{cve}
\alias{cve}
\title{Conditional Variance Estimator}
\usage{
cve(X, Y, k, nObs = sqrt(nrow(X)), tauInitial = 1, tol = 0.001,
slack = -1e-10, maxIter = 50L, attempts = 10L)
}
\arguments{
\item{X}{A matrix of type numeric of dimensions N times dim where N is the number
of entries with dim as data dimension.}
\item{Y}{A vector of type numeric of length N (coresponds to \code{x}).}
\item{k}{Guess for rank(B).}
\item{nObs}{As describet in the paper.}
\item{tol}{Tolerance for optimization stopping creteria.}
}
\description{
Conditional Variance Estimator (CVE) is a novel sufficient dimension
reduction (SDR) method for regressions satisfying E(Y|X) = E(Y|B'X),
where B'X is a lower dimensional projection of the predictors.
}
\references{
Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
}
\seealso{
TODO: \code{vignette("CVE_paper", package="CVE")}.
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/RcppExports.R
\name{cve_cpp}
\alias{cve_cpp}
\title{Conditional Variance Estimation (CVE) method.}
\usage{
cve_cpp(X, Y, k, nObs, tauInitial = 1, tol = 1e-05, slack = -1e-10,
maxIter = 50L, attempts = 10L)
}
\arguments{
\item{X}{data points}
\item{Y}{response}
\item{k}{assumed \eqn{rank(B)}}
\item{nObs}{parameter for bandwidth estimation, typical value
\code{nObs = nrow(X)^lambda} with \code{lambda} in the range [0.3, 0.8].}
\item{tol}{Tolerance for update error used for stopping criterion (default 1e-5)}
\item{slack}{Ratio of small negative error allowed in loss optimization (default -1e-10)}
\item{maxIter}{Upper bound of optimization iterations (default 50)}
\item{attempts}{Number of tryes with new random optimization starting points (default 10)}
\item{tau}{Initial step size (default 1)}
}
\value{
List containing the bandwidth \code{h}, optimization objective \code{V}
and the matrix \code{B} estimated for the model as a orthogonal basis of the
orthogonal space spaned by \code{V}.
}
\description{
This version uses a "simple" stiefel optimization schema.
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/datasets.R
\name{dataset}
\alias{dataset}
\title{Generates test datasets.}
\usage{
dataset(name = "M1", n, B, p.mix = 0.3, lambda = 1)
}
\arguments{
\item{name}{One of \code{"M1"}, \code{"M2"}, \code{"M3"}, \code{"M4"} or \code{"M5"}}
\item{n}{nr samples}
\item{p.mix}{Only for \code{"M4"}, see: below.}
\item{lambda}{Only for \code{"M4"}, see: below.}
\item{p}{Dim. of random variable \code{X}.}
}
\value{
List with elements
\item{X}{data}
\item{Y}{response}
\item{B}{Used dim-reduction matrix}
\item{name}{Name of the dataset (name parameter)}
}
\description{
Provides sample datasets. There are 5 different datasets named
M1, M2, M3, M4 and M5 describet in the paper references below.
The general model is given by:
\deqn{Y ~ g(B'X) + \epsilon}
}
\section{M1}{
The data follows \eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} for a subspace
dimension of \eqn{k = 2} with a default of \eqn{n = 200} data points.
The link function \eqn{g} is given as
\deqn{g(x) = \frac{x_1}{0.5 + (x_2 + 1.5)^2} + 0.5\epsilon}{g(x) = x_1 / (0.5 + (x_2 + 1.5)^2) + 0.5 epsilon}
}
\section{M2}{
\eqn{X\sim N_p(0, \Sigma)}{X ~ N_p(0, Sigma)} with \eqn{k = 2} with a default of \eqn{n = 200} data points.
The link function \eqn{g} is given as
\deqn{g(x) = x_1 x_2^2 + 0.5\epsilon}{g(x) = x_1 x_2^2 + 0.5 epsilon}
}
\section{M3}{
TODO:
}
\section{M4}{
TODO:
}
\section{M5}{
TODO:
}
\references{
Fertl Likas, Bura Efstathia. Conditional Variance Estimation for Sufficient Dimension Reduction, 2019
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/RcppExports.R
\name{estimateBandwidth}
\alias{estimateBandwidth}
\title{Estimated bandwidth for CVE.}
\usage{
estimateBandwidth(X, k, nObs)
}
\arguments{
\item{X}{data matrix of dimension (n x p) with n data points X_i of dimension
q. Therefor each row represents a datapoint of dimension p.}
\item{k}{Guess for rank(B).}
\item{nObs}{Ether numeric of a function. If specified as numeric value
its used in the computation of the bandwidth directly. If its a function
`nObs` is evaluated as \code{nObs(nrow(x))}. The default behaviou if not
supplied at all is to use \code{nObs <- nrow(x)^0.5}.}
}
\description{
Estimates a propper bandwidth \code{h} according
\deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
}
\seealso{
[qchisq()]
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/RcppExports.R
\name{optStiefel}
\alias{optStiefel}
\title{Stiefel Optimization.}
\arguments{
\item{X}{data points}
\item{Y}{response}
\item{k}{assumed \eqn{rank(B)}}
\item{nObs}{parameter for bandwidth estimation, typical value
\code{nObs = nrow(X)^lambda} with \code{lambda} in the range [0.3, 0.8].}
\item{tau}{Initial step size}
\item{tol}{Tolerance for update error used for stopping criterion
\eqn{|| V(j) V(j)' - V(j+1) V(j+1)' ||_2 < tol}{%
\| V_j V_j' - V_{j+1} V_{j+1}' \|_2 < tol}.}
\item{maxIter}{Upper bound of optimization iterations}
}
\value{
List containing the bandwidth \code{h}, optimization objective \code{V}
and the matrix \code{B} estimated for the model as a orthogonal basis of the
orthogonal space spaned by \code{V}.
}
\description{
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}}{%
span(B) = orth(span(B))}.
}
\keyword{internal}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/RcppExports.R
\name{rStiefel}
\alias{rStiefel}
\title{Random element from Stiefel Manifold `S(p, q)`.}
\usage{
rStiefel(p, q)
}
\arguments{
\item{p}{Row dimension}
\item{q}{Column dimension}
}
\value{
Matrix of dim `(p, q)`.
}
\description{
Draws an element of \eqn{S(p, q)} which is the Stiefel Manifold.
This is done by taking the Q-component of the QR decomposition
from a `(p, q)` Matrix with independent standart normal entries.
As a semi-orthogonal Matrix the result `V` satisfies \eqn{V'V = I_q}.
}
\seealso{
<https://en.wikipedia.org/wiki/Stiefel_manifold>
}

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//
// Usage:
// ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V1.cpp')"
//
// only `RcppArmadillo.h` which includes `Rcpp.h`
#include <RcppArmadillo.h>
// through the depends attribute `Rcpp` is tolled to create
// hooks for `RcppArmadillo` needed by the build process.
//
// [[Rcpp::depends(RcppArmadillo)]]
// required for `R::qchisq()` used in `estimateBandwidth()`
#include <Rmath.h>
//' Estimated bandwidth for CVE.
//'
//' Estimates a propper bandwidth \code{h} according
//' \deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
//' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
//'
//' @param X data matrix of dimension (n x p) with n data points X_i of dimension
//' q. Therefor each row represents a datapoint of dimension p.
//' @param k Guess for rank(B).
//' @param nObs Ether numeric of a function. If specified as numeric value
//' its used in the computation of the bandwidth directly. If its a function
//' `nObs` is evaluated as \code{nObs(nrow(x))}. The default behaviou if not
//' supplied at all is to use \code{nObs <- nrow(x)^0.5}.
//'
//' @seealso [qchisq()]
//'
//' @export
// [[Rcpp::export]]
double estimateBandwidth(const arma::mat& X, arma::uword k, double nObs) {
using namespace arma;
uword n = X.n_rows; // nr samples
uword p = X.n_cols; // dimension of rand. var. `X`
// column mean
mat M = mean(X);
// center `X`
mat C = X.each_row() - M;
// trace of covariance matrix, `traceSigma = Tr(C' C)`
double traceSigma = accu(C % C);
// compute estimated bandwidth
double qchi2 = R::qchisq((nObs - 1.0) / (n - 1), static_cast<double>(k), 1, 0);
return 2.0 * qchi2 * traceSigma / (p * n);
}
//' Random element from Stiefel Manifold `S(p, q)`.
//'
//' Draws an element of \eqn{S(p, q)} which is the Stiefel Manifold.
//' This is done by taking the Q-component of the QR decomposition
//' from a `(p, q)` Matrix with independent standart normal entries.
//' As a semi-orthogonal Matrix the result `V` satisfies \eqn{V'V = I_q}.
//'
//' @param p Row dimension
//' @param q Column dimension
//'
//' @return Matrix of dim `(p, q)`.
//'
//' @seealso <https://en.wikipedia.org/wiki/Stiefel_manifold>
//'
//' @export
// [[Rcpp::export]]
arma::mat rStiefel(arma::uword p, arma::uword q) {
arma::mat Q, R;
arma::qr_econ(Q, R, arma::randn<arma::mat>(p, q));
return Q;
}
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
) {
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());
Q.diag() += 1;
// calc pairwise distances as `D` with `D(i, j) = d_i(V, X_j)`
vec D_vec = sum(square(X_diff * Q), 1);
mat D = reshape(D_vec, n, n);
// calc weights as `W` with `W(i, j) = w_i(V, X_j)`
mat W = exp(D / (-2.0 * h));
// column-wise normalization via 1-norm
W = normalise(W, 1);
vec W_vec = vectorise(W);
// weighted `Y` means (first and second order)
vec y1 = W.t() * Y;
vec y2 = W.t() * square(Y);
// loss for each `X_i`, meaning `L(i) = L_n(V, X_i)`
vec L = y2 - square(y1);
// `loss = L_n(V)`
double loss = mean(L);
// check if gradient as output variable is set
if (G != 0) {
// `G = grad(L_n(V))` a.k.a. gradient of `L` with respect to `V`
vec scale = (repelem(L, n, 1) - square(Y_rep - repelem(y1, n, 1))) % W_vec % D_vec;
mat X_diff_scale = X_diff.each_col() % scale;
(*G) = X_diff_scale.t() * X_diff * V;
(*G) *= -2.0 / (h * h * n);
}
return loss;
}
//' Stiefel Optimization.
//'
//' 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}}{%
//' span(B) = orth(span(B))}.
//'
//' @param X data points
//' @param Y response
//' @param k assumed \eqn{rank(B)}
//' @param nObs parameter for bandwidth estimation, typical value
//' \code{nObs = nrow(X)^lambda} with \code{lambda} in the range [0.3, 0.8].
//' @param tau Initial step size
//' @param tol Tolerance for update error used for stopping criterion
//' \eqn{|| V(j) V(j)' - V(j+1) V(j+1)' ||_2 < tol}{%
//' \| V_j V_j' - V_{j+1} V_{j+1}' \|_2 < tol}.
//' @param maxIter Upper bound of optimization iterations
//'
//' @return List containing the bandwidth \code{h}, optimization objective \code{V}
//' and the matrix \code{B} estimated for the model as a orthogonal basis of the
//' orthogonal space spaned by \code{V}.
//'
//' @rdname optStiefel
//' @name optStiefel
//' @keywords internal
double optStiefel(
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
) {
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);
// initial start value for `V`
V = rStiefel(p, q);
// init optimization `loss`es, `error` and stepsize `tau`
// double loss_next = datum::inf;
double loss;
double error = datum::inf;
double tau = tauInitial;
int count;
// main optimization loop
for (count = 0; count < maxIter && error > tol; ++count) {
// calc gradient `G = grad_V(L)(V)`
mat G;
loss = gradient(X, X_diff, Y, Y_rep, V, h, &G);
// matrix `A` for colescy-transform of the gradient
mat A = tau * ((G * V.t()) - (V * G.t()));
// next iteration step of `V`
mat V_tau = inv(I_p + A) * (I_p - A) * V;
// 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;
// validate if loss decreased
if ((loss_tau - loss) > slack * loss) {
// ignore step, retry with half the step size
tau = tau / 2.;
error = datum::inf;
} else {
// compute step error (break condition)
error = norm((V * V.t()) - (V_tau * V_tau.t()), 2) / (2 * q);
// shift for next iteration
V = V_tau;
loss = loss_tau;
}
}
// store final `loss`
history(count) = loss;
return loss;
}
//' Conditional Variance Estimation (CVE) method.
//'
//' This version uses a "simple" stiefel optimization schema.
//'
//' @param X data points
//' @param Y response
//' @param k assumed \eqn{rank(B)}
//' @param nObs parameter for bandwidth estimation, typical value
//' \code{nObs = nrow(X)^lambda} with \code{lambda} in the range [0.3, 0.8].
//' @param tau Initial step size (default 1)
//' @param tol Tolerance for update error used for stopping criterion (default 1e-5)
//' @param slack Ratio of small negative error allowed in loss optimization (default -1e-10)
//' @param maxIter Upper bound of optimization iterations (default 50)
//' @param attempts Number of tryes with new random optimization starting points (default 10)
//'
//' @return List containing the bandwidth \code{h}, optimization objective \code{V}
//' 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
// [[Rcpp::export]]
Rcpp::List cve_cpp(
const arma::mat& X,
const arma::vec& Y,
const int k,
const double nObs,
const double tauInitial = 1.,
const double tol = 1e-5,
const double slack = -1e-10,
const int maxIter = 50,
const int attempts = 10
) {
using namespace arma;
// tracker of current best results
mat V_best;
double loss_best = datum::inf;
// estimate bandwidth
double h = estimateBandwidth(X, k, nObs);
// loss history for each optimization attempt
// each column contaions the iteration history for the loss
mat history = mat(maxIter + 1, attempts);
// multiple stiefel optimization attempts
for (int i = 0; i < attempts; ++i) {
// 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);
if (loss < loss_best) {
loss_best = loss;
V_best = V;
}
// write history to history collection
history.col(i) = hist;
}
// get `B` as kernal of `V.t()`
mat B = null(V_best.t());
return Rcpp::List::create(
Rcpp::Named("history") = history,
Rcpp::Named("loss") = loss_best,
Rcpp::Named("h") = h,
Rcpp::Named("V") = V_best,
Rcpp::Named("B") = B
);
}

64
CVE/src/RcppExports.cpp Normal file
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@ -0,0 +1,64 @@
// Generated by using Rcpp::compileAttributes() -> do not edit by hand
// Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393
#include <RcppArmadillo.h>
#include <Rcpp.h>
using namespace Rcpp;
// estimateBandwidth
double estimateBandwidth(const arma::mat& X, arma::uword k, double nObs);
RcppExport SEXP _CVE_estimateBandwidth(SEXP XSEXP, SEXP kSEXP, SEXP nObsSEXP) {
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< arma::uword >::type k(kSEXP);
Rcpp::traits::input_parameter< double >::type nObs(nObsSEXP);
rcpp_result_gen = Rcpp::wrap(estimateBandwidth(X, k, nObs));
return rcpp_result_gen;
END_RCPP
}
// rStiefel
arma::mat rStiefel(arma::uword p, arma::uword q);
RcppExport SEXP _CVE_rStiefel(SEXP pSEXP, SEXP qSEXP) {
BEGIN_RCPP
Rcpp::RObject rcpp_result_gen;
Rcpp::RNGScope rcpp_rngScope_gen;
Rcpp::traits::input_parameter< arma::uword >::type p(pSEXP);
Rcpp::traits::input_parameter< arma::uword >::type q(qSEXP);
rcpp_result_gen = Rcpp::wrap(rStiefel(p, q));
return rcpp_result_gen;
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) {
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 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 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 attempts(attemptsSEXP);
rcpp_result_gen = Rcpp::wrap(cve_cpp(X, Y, k, nObs, tauInitial, tol, slack, maxIter, attempts));
return rcpp_result_gen;
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},
{NULL, NULL, 0}
};
RcppExport void R_init_CVE(DllInfo *dll) {
R_registerRoutines(dll, NULL, CallEntries, NULL, NULL);
R_useDynamicSymbols(dll, FALSE);
}

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@ -2,14 +2,14 @@
#' Euclidean vector norm (2-norm) #' Euclidean vector norm (2-norm)
#' #'
#' @param x Numeric vector #' @param x Numeric vector
#' @returns Numeric #' @return Numeric
norm2 <- function(x) { return(sum(x^2)) } norm2 <- function(x) { return(sum(x^2)) }
#' Samples uniform from the Stiefel Manifold #' Samples uniform from the Stiefel Manifold
#' #'
#' @param p row dim. #' @param p row dim.
#' @param q col dim. #' @param q col dim.
#' @returns `(p, q)` semi-orthogonal matrix #' @return `(p, q)` semi-orthogonal matrix
rStiefl <- function(p, q) { rStiefl <- function(p, q) {
return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q)))) return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q))))
} }
@ -17,7 +17,7 @@ rStiefl <- function(p, q) {
#' Matrix Trace #' Matrix Trace
#' #'
#' @param M Square matrix #' @param M Square matrix
#' @returns Trace \eqn{Tr(M)} #' @return Trace \eqn{Tr(M)}
Tr <- function(M) { Tr <- function(M) {
return(sum(diag(M))) return(sum(diag(M)))
} }
@ -25,7 +25,7 @@ Tr <- function(M) {
#' Null space basis of given matrix `B` #' Null space basis of given matrix `B`
#' #'
#' @param B `(p, q)` matrix #' @param B `(p, q)` matrix
#' @returns Semi-orthogonal `(p, p - q)` matrix `Q` spaning the null space of `B` #' @return Semi-orthogonal `(p, p - q)` matrix `Q` spaning the null space of `B`
null <- function(M) { null <- function(M) {
tmp <- qr(M) tmp <- qr(M)
set <- if(tmp$rank == 0L) seq_len(ncol(M)) else -seq_len(tmp$rank) set <- if(tmp$rank == 0L) seq_len(ncol(M)) else -seq_len(tmp$rank)
@ -60,8 +60,7 @@ estimateBandwidth<-function(X, k, nObs) {
# if grad=T, gradient of L(V) also returned # if grad=T, gradient of L(V) also returned
LV <- function(V, Xl, dtemp, h, q, Y, grad = TRUE) { LV <- function(V, Xl, dtemp, h, q, Y, grad = TRUE) {
N <- length(Y) N <- length(Y)
if (is.vector(V)) { k <- 1 } k <- if (is.vector(V)) { 1 } else { ncol(V) }
else { k <- length(V[1,]) }
Xlv <- Xl %*% V Xlv <- Xl %*% V
d <- dtemp - ((Xlv^2) %*% rep(1, k)) d <- dtemp - ((Xlv^2) %*% rep(1, k))
w <- dnorm(d / h) / dnorm(0) w <- dnorm(d / h) / dnorm(0)
@ -108,7 +107,7 @@ LV <- function(V, Xl, dtemp, h, q, Y, grad = TRUE) {
#aov_dat... (L_tilde_n(Vhat_k,X_i))_{i=1,..,N} #aov_dat... (L_tilde_n(Vhat_k,X_i))_{i=1,..,N}
#count...number of iterations #count...number of iterations
#h...bandwidth #h...bandwidth
cve_legacy <- function( cve_R <- function(
X, Y, k, X, Y, k,
nObs = sqrt(nrow(X)), nObs = sqrt(nrow(X)),
tauInitial = 1.0, tauInitial = 1.0,

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@ -1,4 +1,6 @@
// //
// Standalone implementation for development.
//
// Usage: // Usage:
// ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V1.cpp')" // ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V1.cpp')"
// //
@ -17,7 +19,7 @@
//' Estimated bandwidth for CVE. //' Estimated bandwidth for CVE.
//' //'
//' Estimates a propper bandwidth \code{h} according //' Estimates a propper bandwidth \code{h} according
//' \deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)}\frac{2 tr(\Sigma)}{p}}{% //' \deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
//' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p} //' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
//' //'
//' @param X data matrix of dimension (n x p) with n data points X_i of dimension //' @param X data matrix of dimension (n x p) with n data points X_i of dimension
@ -60,7 +62,7 @@ double estimateBandwidth(const arma::mat& X, arma::uword k, double nObs) {
//' @param p Row dimension //' @param p Row dimension
//' @param q Column dimension //' @param q Column dimension
//' //'
//' @returns Matrix of dim `(p, q)`. //' @return Matrix of dim `(p, q)`.
//' //'
//' @seealso <https://en.wikipedia.org/wiki/Stiefel_manifold> //' @seealso <https://en.wikipedia.org/wiki/Stiefel_manifold>
//' //'
@ -138,6 +140,7 @@ double gradient(const arma::mat& X,
//' orthogonal space spaned by \code{V}. //' orthogonal space spaned by \code{V}.
//' //'
//' @rdname optStiefel //' @rdname optStiefel
//' @keywords internal
double optStiefel( double optStiefel(
const arma::mat& X, const arma::mat& X,
const arma::vec& Y, const arma::vec& Y,

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@ -1,4 +1,5 @@
// -*- mode: C++; c-indent-level: 4; c-basic-offset: 4; indent-tabs-mode: nil; -*- //
// Standalone implementation for development.
// //
// Usage: // Usage:
// ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V2.cpp')" // ~$ R -e "library(Rcpp); Rcpp::sourceCpp('cve_V2.cpp')"
@ -18,7 +19,7 @@
//' Estimated bandwidth for CVE. //' Estimated bandwidth for CVE.
//' //'
//' Estimates a propper bandwidth \code{h} according //' Estimates a propper bandwidth \code{h} according
//' \deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)}\frac{2 tr(\Sigma)}{p}}{% //' \deqn{h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
//' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p} //' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
//' //'
//' @param X data matrix of dimension (n x p) with n data points X_i of dimension //' @param X data matrix of dimension (n x p) with n data points X_i of dimension
@ -61,7 +62,7 @@ double estimateBandwidth(const arma::mat& X, arma::uword k, double nObs) {
//' @param p Row dimension //' @param p Row dimension
//' @param q Column dimension //' @param q Column dimension
//' //'
//' @returns Matrix of dim `(p, q)`. //' @return Matrix of dim `(p, q)`.
//' //'
//' @seealso <https://en.wikipedia.org/wiki/Stiefel_manifold> //' @seealso <https://en.wikipedia.org/wiki/Stiefel_manifold>
//' //'
@ -141,6 +142,7 @@ double gradient(const arma::mat& X,
//' orthogonal space spaned by \code{V}. //' orthogonal space spaned by \code{V}.
//' //'
//' @rdname optStiefel //' @rdname optStiefel
//' @keywords internal
double optStiefel( double optStiefel(
const arma::mat& X, const arma::mat& X,
const arma::vec& Y, const arma::vec& Y,