All the tests were done on an Arch Linux x86_64 machine with an Intel(R) Core(TM) i7 CPU (1.90GHz).
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.
We fix the number of parameters at p = 10, and simulate the parameter
value and n × 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 436.735 469.4955 509.8965 490.660 548.3175 819.829
#> n1e3 1191.562 1359.6805 1588.1001 1449.614 1650.8245 5582.150
#> n1e4 10420.193 12382.9380 14520.1949 14776.578 15705.6650 28453.073
#> n1e5 159142.973 181864.8840 214987.5162 210712.082 243056.3325 375463.484
#> neval cld
#> 100 a
#> 100 a
#> 100 b
#> 100 c
autoplot(result)
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 714.051 755.739 826.7829 790.8055 832.5525 3689.10 100
#> p25 2732.957 2778.617 3006.2785 2807.8065 2871.2555 9866.17 100
#> p100 21143.551 23643.669 25765.0891 24130.3925 28691.7330 44744.18 100
#> p400 239251.732 263440.302 296609.6124 284875.0475 309075.4735 474184.04 100
#> 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.