Cross-Validated Covariance Matrix Estimation
Authors: Philippe Boileau, Brian Collica, and Nima Hejazi
cvCovEst
?cvCovEst
implements an efficient cross-validated procedure for covariance matrix estimation, particularly useful in high-dimensional settings. The general methodology allows for cross-validation to be used to data adaptively identify the optimal estimator of the covariance matrix from a prespecified set of candidate estimators. An overview of the framework is provided in the package vignette. For a more detailed description, see Boileau et al. (2021). A suite of plotting and diagnostic tools are also included.
For standard use, install cvCovEst
from CRAN:
install.packages("cvCovEst")
The development version of the package may be installed from GitHub using remotes
:
remotes::install_github("PhilBoileau/cvCovEst")
To illustrate how cvCovEst
may be used to select an optimal covariance matrix estimator via cross-validation, consider the following toy example:
library(MASS)
library(cvCovEst)
set.seed(1584)
# generate a 50x50 covariance matrix with unit variances and off-diagonal
# elements equal to 0.5
Sigma <- matrix(0.5, nrow = 50, ncol = 50) + diag(0.5, nrow = 50)
# sample 50 observations from multivariate normal with mean = 0, var = Sigma
dat <- mvrnorm(n = 50, mu = rep(0, 50), Sigma = Sigma)
# run CV-selector
cv_cov_est_out <- cvCovEst(
dat = dat,
estimators = c(linearShrinkLWEst, denseLinearShrinkEst,
thresholdingEst, poetEst, sampleCovEst),
estimator_params = list(
thresholdingEst = list(gamma = c(0.2, 2)),
poetEst = list(lambda = c(0.1, 0.2), k = c(1L, 2L))
),
cv_loss = cvMatrixFrobeniusLoss,
cv_scheme = "v_fold",
v_folds = 5,
)
# print the table of risk estimates
# NOTE: the estimated covariance matrix is accessible via the `$estimate` slot
cv_cov_est_out$risk_df
#> # A tibble: 9 x 3
#> estimator hyperparameters cv_risk
#> <chr> <chr> <dbl>
#> 1 linearShrinkLWEst hyperparameters = NA 357.
#> 2 poetEst lambda = 0.2, k = 1 369.
#> 3 poetEst lambda = 0.2, k = 2 372.
#> 4 poetEst lambda = 0.1, k = 2 375.
#> 5 poetEst lambda = 0.1, k = 1 376.
#> 6 denseLinearShrinkEst hyperparameters = NA 379.
#> 7 sampleCovEst hyperparameters = NA 379.
#> 8 thresholdingEst gamma = 0.2 384.
#> 9 thresholdingEst gamma = 2 826.
Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.
Please cite the following paper when using the cvCovEst
R software package.
@misc{boileau2021,
={Cross-Validated Loss-Based Covariance Matrix Estimator Selection in High Dimensions},
title={Philippe Boileau and Nima S. Hejazi and Mark J. van der Laan and Sandrine Dudoit},
author={2021},
year={2102.09715},
eprint={arXiv},
archivePrefix={stat.ME}
primaryClass }
© 2020-2021 Philippe Boileau
The contents of this repository are distributed under the MIT license. See file LICENSE.md
for details.