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    437.406    476.2775    586.9647    495.799    553.131   5280.724   100
#>  n1e3   1174.870   1398.5070   2337.5614   1488.365   1645.697  71417.517   100
#>  n1e4  10671.322  13061.4930  14545.1050  14970.731  15773.828  21142.201   100
#>  n1e5 168103.418 204650.5240 236256.0643 226905.168 261474.538 333851.274   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    714.752    767.6915    804.5887    798.433    836.885    944.330   100
#>   p25   2900.096   2941.7185   3128.5123   3000.734   3043.704   8278.422   100
#>  p100  23254.398  25821.4230  28125.4062  26733.429  30922.938  50002.319   100
#>  p400 266463.668 292106.9235 325892.9611 312605.600 341818.385 567187.310   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.