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    447.765    479.5535    587.5175    496.9715    557.4085   5244.464
#>  n1e3   1174.409   1404.9330   2380.0707   1493.8845   1703.8805  70913.487
#>  n1e4  10670.295  13208.4110  14597.3124  14988.4280  15842.7155  20972.755
#>  n1e5 167814.065 205348.5600 238347.1048 228291.6180 277206.9785 327150.500
#>  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    723.859    775.0695    814.9904    800.728    850.2345   1207.070
#>   p25   2896.979   2955.4480   3101.5832   3015.425   3051.4720   7878.714
#>  p100  23360.606  25901.6760  28450.8048  26801.859  31062.2935  51156.347
#>  p400 269599.005 292393.8260 326972.4845 314499.289 342746.1685 571642.475
#>  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.