Performance

Eunseop Kim

All the tests were done on an Arch Linux x86_64 machine with an Intel(R) Core(TM) i7 CPU (1.90GHz).

Empirical likelihood computation

We show the performance of computing empirical likelihood with el_mean(). We test the computation speed with simulated data sets in two different settings: 1) the number of observations increases with the number of parameters fixed, and 2) the number of parameters increases with the number of observations fixed.

Increasing the number of observations

We fix the number of parameters at $p = 10$, and simulate the parameter value and $n \times p$ matrices using rnorm(). In order to ensure convergence with a large $n$, we set a large threshold value using el_control().

library(ggplot2)
library(microbenchmark)
set.seed(3175775)
p <- 10
par <- rnorm(p, sd = 0.1)
ctrl <- el_control(th = 1e+10)
result <- microbenchmark(
  n1e2 = el_mean(matrix(rnorm(100 * p), ncol = p), par = par, control = ctrl),
  n1e3 = el_mean(matrix(rnorm(1000 * p), ncol = p), par = par, control = ctrl),
  n1e4 = el_mean(matrix(rnorm(10000 * p), ncol = p), par = par, control = ctrl),
  n1e5 = el_mean(matrix(rnorm(100000 * p), ncol = p), par = par, control = ctrl)
)

Below are the results:

result
#> Unit: microseconds
#>  expr        min          lq       mean     median         uq        max neval
#>  n1e2    435.469    476.8905    522.720    500.290    557.626    757.258   100
#>  n1e3   1267.758   1446.8045   1580.421   1547.079   1673.818   2709.245   100
#>  n1e4  11393.587  13138.8710  15475.314  15941.224  16947.373  22562.019   100
#>  n1e5 184991.234 221522.1545 255491.712 251015.169 275534.833 410394.558   100
#>  cld
#>  a  
#>  a  
#>   b 
#>    c
autoplot(result)
#> Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
#> ℹ Please use tidy evaluation idioms with `aes()`.
#> ℹ See also `vignette("ggplot2-in-packages")` for more information.
#> ℹ The deprecated feature was likely used in the microbenchmark package.
#>   Please report the issue at
#>   <https://github.com/joshuaulrich/microbenchmark/issues/>.
#> This warning is displayed once per session.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

Increasing the number of parameters

This time we fix the number of observations at $n = 1000$, and evaluate empirical likelihood at zero vectors of different sizes.

n <- 1000
result2 <- microbenchmark(
  p5 = el_mean(matrix(rnorm(n * 5), ncol = 5),
    par = rep(0, 5),
    control = ctrl
  ),
  p25 = el_mean(matrix(rnorm(n * 25), ncol = 25),
    par = rep(0, 25),
    control = ctrl
  ),
  p100 = el_mean(matrix(rnorm(n * 100), ncol = 100),
    par = rep(0, 100),
    control = ctrl
  ),
  p400 = el_mean(matrix(rnorm(n * 400), ncol = 400),
    par = rep(0, 400),
    control = ctrl
  )
)

result2
#> Unit: microseconds
#>  expr        min         lq        mean     median         uq        max neval
#>    p5    711.149    774.203    867.1492    816.441    876.220   4686.820   100
#>   p25   2902.883   2983.633   3084.4227   3028.565   3095.715   6833.586   100
#>  p100  23114.201  25948.242  28258.3973  26421.422  30745.145  48674.835   100
#>  p400 257745.096 283658.526 321392.8748 306667.650 350381.443 479396.343   100
#>  cld
#>  a  
#>  a  
#>   b 
#>    c
autoplot(result2)

On average, evaluating empirical likelihood with a 100000×10 or 1000×400 matrix at a parameter value satisfying the convex hull constraint takes less than a second.