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    471.208    534.686    642.0046    590.6805    663.5565   2547.809
#>  n1e3   1306.451   1543.368   1865.0289   1753.3175   1948.1420   4835.856
#>  n1e4  11980.556  15318.528  18041.1383  17403.4760  19572.6080  34205.827
#>  n1e5 249800.349 300236.748 363823.3686 351242.7685 410751.0255 677121.897
#>  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 neval
#>    p5    836.605    957.967   1173.603   1034.581   1146.942   3507.973   100
#>   p25   2972.009   3434.618   3974.785   3608.974   4209.010   7394.445   100
#>  p100  24543.118  30161.395  34809.507  32883.622  38059.852  59219.304   100
#>  p400 313662.409 361374.363 411516.334 388878.859 456629.373 673508.962   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.