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
#>  n1e2    431.395    469.2555    504.4113    488.055    542.7975    668.017
#>  n1e3   1140.227   1350.5890   1459.7935   1425.318   1541.1745   2284.662
#>  n1e4  10472.233  12808.1105  15817.5770  14815.454  15702.6790  90502.589
#>  n1e5 158213.415 205709.0565 241115.2185 240662.913 277792.0530 339345.141
#>  neval cld
#>    100 a  
#>    100 a  
#>    100  b 
#>    100   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
#>    p5    706.498    747.5295    877.7997    778.357    825.2345   3876.651
#>   p25   2673.407   2780.3510   2974.6349   2827.033   2881.4445   6080.111
#>  p100  21291.333  23724.5320  26122.3424  24711.022  28959.4760  47624.822
#>  p400 236755.986 264297.5485 298386.0130 286411.401 313203.0335 477978.723
#>  neval cld
#>    100 a  
#>    100 a  
#>    100  b 
#>    100   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.