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Performance

Eunseop Kim

Source: vignettes/performance.Rmd
performance.Rmd

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=10p = 10, and simulate the parameter value and n×pn \times p matrices using rnorm(). In order to ensure convergence with a large nn, 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    439.620    472.7165    506.0363    494.6875    528.977    654.570
#>  n1e3   1154.954   1367.7860   1479.0371   1460.9445   1557.775   2358.138
#>  n1e4  10553.522  12686.8755  15824.2599  14812.6500  15712.654  89249.405
#>  n1e5 154941.097 203060.9330 239495.4004 239551.3255 270962.902 340917.383
#>  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=1000n = 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    720.293    758.980    889.3308    790.1985    840.267   3909.551   100
#>   p25   2768.403   2812.815   3020.0503   2856.8435   2921.363   6031.418   100
#>  p100  21288.712  23891.342  26240.2582  24687.3855  29055.191  46822.833   100
#>  p400 239248.918 265062.488 299138.3089 285713.0250 315636.696 486046.792   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.