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 \(p = 100\):

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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)

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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):

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

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

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# benchmark CVglasso - tolerance 1e-6
microbenchmark(CVglasso(S = sample, lam = 0.1, tol = 1e-06, trace = "none"))

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• Default convergence tolerance with cross validation for lam:

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

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• Parallel (cores = 2) cross validation:

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

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