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.
Note: the benchmarks run significantly faster on my personal machine (MacBook Pro Late 2016). In most cases, the processes take \(\approx\) 25% of the time.
We will be estimating a tri-diagonal precision matrix with dimension \(p = 100\):
library(SCPME)
library(microbenchmark)
# generate data from tri-diagonal (sparse) matrix
data = data_gen(p = 100, n = 1000, r = 5)
# calculate sample covariance matrix
sample = (nrow(data$X) - 1)/nrow(data$X)*cov(data$X)
# benchmark shrink - default tolerance
microbenchmark(shrink(S = sample, crit.cv = "loglik", lam = 0.1, tol.abs = 1e-4, tol.rel = 1e-4, trace = "none"))
## Unit: milliseconds
## expr
## shrink(S = sample, crit.cv = "loglik", lam = 0.1, tol.abs = 1e-04, tol.rel = 1e-04, trace = "none")
## min lq mean median uq max neval
## 443.3506 450.3688 463.6747 461.9791 473.2268 496.8634 100
# benchmark shrink - tolerance 1e-8
microbenchmark(shrink(S = sample, crit.cv = "loglik", lam = 0.1, tol.abs = 1e-8, tol.rel = 1e-8, trace = "none"))
## Unit: seconds
## expr
## shrink(S = sample, crit.cv = "loglik", lam = 0.1, tol.abs = 1e-08, tol.rel = 1e-08, trace = "none")
## min lq mean median uq max neval
## 1.600358 1.646749 1.670888 1.669327 1.690355 1.778268 100
lam
:# benchmark shrink CV - default parameter grid
microbenchmark(shrink(X = data$X, Y = data$Y, trace = "none"), times = 5)
## Unit: seconds
## expr min lq mean
## shrink(X = data$X, Y = data$Y, trace = "none") 16.06304 16.36117 16.61059
## median uq max neval
## 16.43248 16.60028 17.59596 5
cores = 2
) cross validation:# benchmark shrink parallel CV
microbenchmark(shrink(X = data$X, Y = data$Y, cores = 2, trace = "none"), times = 5)
## Unit: seconds
## expr min
## shrink(X = data$X, Y = data$Y, cores = 2, trace = "none") 12.25516
## lq mean median uq max neval
## 12.37918 12.50935 12.4228 12.65463 12.83499 5
# benchmark shrink penalizing beta
lam_max = max(abs(crossprod(data$X, data$Y)))
microbenchmark(shrink(X = data$X, Y = data$Y, B = cov(data$X, data$Y), lam.max = lam_max, lam.min.ratio = 1e-4, trace = "none"), times = 5)
## Unit: seconds
## expr
## shrink(X = data$X, Y = data$Y, B = cov(data$X, data$Y), lam.max = lam_max, lam.min.ratio = 1e-04, trace = "none")
## min lq mean median uq max neval
## 19.4061 19.87525 20.09298 20.10041 20.47427 20.60889 5
# benchmark shrink penalizing beta and omega
microbenchmark(shrink(X = data$X, Y = data$Y, B = cbind(cov(data$X, data$Y), diag(ncol(data$X))), lam.max = 10, lam.min.ratio = 1e-4, trace = "none"), times = 5)
## Unit: seconds
## expr
## shrink(X = data$X, Y = data$Y, B = cbind(cov(data$X, data$Y), diag(ncol(data$X))), lam.max = 10, lam.min.ratio = 1e-04, trace = "none")
## min lq mean median uq max neval
## 64.52161 65.65382 66.49351 65.99164 67.67487 68.6256 5