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(GLASSOO)
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(GLASSO(S = sample, lam = 0.1, trace = "none"))

## Unit: milliseconds
##                                           expr      min       lq     mean
##  GLASSO(S = sample, lam = 0.1, trace = "none") 169.3704 173.3424 175.9905
##    median       uq      max neval
##  174.9908 177.0388 199.4217   100

Default convergence tolerance with cross validation for lam:

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

## Unit: seconds
##                       expr      min       lq     mean   median       uq
##  GLASSO(X, trace = "none") 9.408677 9.451392 9.946536 10.09357 10.24701
##       max neval
##  10.53203     5

Parallel (cores = 2) cross validation:

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

## Unit: seconds
##                                  expr      min       lq     mean   median
##  GLASSO(X, cores = 2, trace = "none") 7.057724 7.063606 7.374455 7.322304
##        uq      max neval
##  7.337788 8.090854     5

Matt Galloway