Movatterモバイル変換

All the tests were done on an Arch Linux x86_64 machine with anIntel(R) Core(TM) i7 CPU (1.90GHz).

Empirical likelihood computation

We show the performance of computing empirical likelihood withel_mean(). We test the computation speed with simulateddata sets in two different settings: 1) the number of observationsincreases with the number of parameters fixed, and 2) the number ofparameters 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 usingrnorm(). In order to ensure convergence with a large\(n\), we set a large threshold value usingel_control().

library(ggplot2)library(microbenchmark)set.seed(3175775)p<-10par<-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    480.259    552.6765    605.5336    605.2785    663.4835    747.412#>  n1e3   1341.880   1584.8560   1817.1119   1755.0720   1923.7255   4458.305#>  n1e4  12227.928  15504.0695  18338.3115  17224.0770  19222.8105 104056.099#>  n1e5 248277.438 284915.2620 333091.8719 327406.7725 390166.0540 492460.706#>  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 empiricallikelihood at zero vectors of different sizes.

n<-1000result2<-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    776.637    857.5115   1047.512    954.4555   1097.735   2311.881   100#>   p25   2995.186   3093.3480   3720.127   3245.1005   3945.950   7162.429   100#>  p100  23567.613  26633.9825  33190.404  31544.7910  37026.504  73363.918   100#>  p400 276768.597 329771.0900 417690.242 398333.6365 474940.140 737572.795   100#>  cld#>  a#>  a#>   b#>    c

autoplot(result2)

On average, evaluating empirical likelihood with a 100000×10 or1000×400 matrix at a parameter value satisfying the convex hullconstraint takes less than a second.

Movatterモバイル変換

Performance

Eunseop Kim

Empirical likelihood computation

Increasing the number of observations

Increasing the number of parameters