covboost

Estimate (possibly sparse, high dimensional) covariance matrix through boosting

covboost boosts out the path of the correlation matrix starting from the Identity matrix and eventual convergence (if enough iterations are used) at the ordinary covariance matrix estimate.

Installation

Install the development version from GitHub

devtools::install_github("Blunde1/covboost")

The package is hopefully soon on CRAN.

Example code and documentation

There are two main functions

• covboost_cv: Boosts out the covariance matrix using k-fold cross validation.
• covboost: Boosts out the covariance matrix.

The CV function runs in parallel (OpenMP), and returns useful information and plots from cross validation and the best (in terms of Gaussian loss) covariance matrix. See the example below. This is information is in the next step used to run covboost, which works on the full dataset.

library(covboost)

# -- Generate some Gaussian data with a few (random) non-zero correlations --
p <- 50
n <- 50
x <- matrix(nrow=n, ncol=p)
x[,1] <- rnorm(n)
for(j in 2:p){
    rho <- runif(1,-1,1)*rbinom(1,1,0.5)
    col_dependence <- sample(j-1,1)
    x[,j] <- rnorm(n, mean=rho*x[,col_dependence], sd=(1-rho^2))
}

# -- Run `covboost_cv` to find the best iteration and check convergence --
lrn_rate <- 0.5
cov_cv <- covboost_cv(x, learning_rate=lrn_rate)

# -- Plot to check convergence --
cov_cv$cvplot
cov_cv$opt_iter

# -- Run `covboost` with the best iteration and shrinkage --
sigma <- covboost(x, niter=cov_cv$opt_iter, learning_rate=lrn_rate)
sigma$cov
sigma$cor
sigma$plot # plot (sparse) covariance matrix

The code above generates the convergence plot (top), and images of the obtained (sparse) boosted covariance matrix. For reference, here is the ordinary (dense) covariance matrix estimate (bottom right). Note a few significant non-zero correlations in the boosted covariance estimate (bottom left).