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    452.394    480.847    584.1662    496.792    545.262   5342.134   100
#>  n1e3   1174.021   1401.068   2335.1833   1480.862   1632.074  71679.459   100
#>  n1e4  10704.276  12985.917  14564.7576  14971.992  15825.298  21564.293   100
#>  n1e5 167806.739 204826.742 238350.7291 231367.897 259028.736 339755.596   100
#>  cld
#>  a  
#>  a  
#>   b 
#>    c
autoplot(result)

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    732.366    757.488    798.6717    790.935    835.243    909.567   100
#>   p25   2903.095   2925.156   3056.6724   2949.862   3016.091   8085.471   100
#>  p100  23376.864  25868.997  28081.8670  26710.607  30829.069  49931.525   100
#>  p400 266781.732 292708.517 326423.1932 312793.054 341474.797 574291.591   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.