Benchmarks

This is a short effort to give users an idea of how long the functions take to process. The benchmarks were performed using the default R install on Travis CI.

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

library(CVglasso)
library(microbenchmark)

#  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)

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

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

## Unit: milliseconds
##                                             expr      min       lq
##  CVglasso(S = sample, lam = 0.1, trace = "none") 38.30081 39.01058
##      mean  median       uq      max neval
##  39.54015 39.3403 39.73937 47.16266   100

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"))

## Unit: milliseconds
##                                                          expr      min
##  CVglasso(S = sample, lam = 0.1, tol = 1e-06, trace = "none") 65.30402
##        lq     mean   median      uq      max neval
##  67.33803 68.55631 67.86555 68.5757 84.47638   100

Default convergence tolerance with cross validation for lam:

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

## Unit: seconds
##                         expr      min       lq     mean   median       uq
##  CVglasso(X, trace = "none") 1.980687 1.993587 2.007446 2.015235 2.023801
##       max neval
##  2.023918     5

Parallel (cores = 2) cross validation:

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

## Unit: seconds
##                                    expr      min       lq     mean
##  CVglasso(X, cores = 2, trace = "none") 2.583931 2.629241 2.647991
##    median       uq     max neval
##  2.641509 2.656996 2.72828     5

Matt Galloway