Benchmarks

This is a short effort to give users an idea of how long the functions take to process. The benchmark examples below are illustrative; exact timings vary by platform and R version.

We will be estimating a tri-diagonal precision matrix with dimension \(p = 100\):

library(CVglasso)

#  generate data from tri-diagonal (sparse) matrix
# compute covariance matrix (can confirm inverse is tri-diagonal)
S = matrix(0, nrow = 100, ncol = 100)

for (i in 1:100){
  for (j in 1:100){
    S[i, j] = 0.7^(abs(i - j))
  }
}

# generate 1000 x 100 matrix with rows drawn from iid N_p(0, S)
set.seed(123)
Z = matrix(rnorm(1000*100), nrow = 1000, ncol = 100)
out = eigen(S, symmetric = TRUE)
S.sqrt = out$vectors %*% diag(out$values^0.5) %*% t(out$vectors)
X = Z %*% S.sqrt

# calculate sample covariance matrix
sample = (nrow(X) - 1)/nrow(X)*cov(X)

The code chunks below show how to run local benchmarks. To keep CRAN vignette builds fast and deterministic, these chunks are not evaluated during rendering.

Default convergence tolerance with specified tuning parameter (no cross validation):

# benchmark CVglasso - defaults
library(microbenchmark)
microbenchmark(CVglasso(S = sample, lam = 0.1, trace = "none"))

Stricter convergence tolerance with specified tuning parameter (no cross validation):

# benchmark CVglasso - tolerance 1e-6
microbenchmark(CVglasso(S = sample, lam = 0.1, tol = 1e-6, trace = "none"))

Default convergence tolerance with cross validation for lam:

# benchmark CVglasso CV - default parameter grid
microbenchmark(CVglasso(X, trace = "none"), times = 5)

Parallel (cores = 2) cross validation:

# benchmark CVglasso parallel CV
microbenchmark(CVglasso(X, cores = 2, trace = "none"), times = 5)