Efficiently apply sample() in R

Question

I need to sample an outcome variable given a matrix with row-wise outcome probabilities.

set.seed(1010) #reproducibility

#create a matrix of probabilities
#three possible outcomes, 10.000 cases
probabilities <- matrix(runif(10000*3),nrow=10000,ncol=3)
probabilities <- probabilities / Matrix::rowSums(probabilities)

The fastest way I could come up with is a combination of apply() and sample().

#row-wise sampling using these probabilities
classification <- apply(probabilities, 1, function(x) sample(1:3, 1, prob = x))

However, in what I'm doing, this is the computational bottleneck. Do you have an idea how to speed this code up / how to sample more efficiently?

Thanks!

Answer 1

RLave's comment that Rcpp could be the way to go is spot on (you also need RcppArmadillo for sample()); I used the following C++ code to create such a function:

// [[Rcpp::depends(RcppArmadillo)]]
#include <RcppArmadilloExtensions/sample.h>

using namespace Rcpp;

// [[Rcpp::export]]
IntegerVector sample_matrix(NumericMatrix x, IntegerVector choice_set) {
    int n = x.nrow();
    IntegerVector result(n);
    for ( int i = 0; i < n; ++i ) {
        result[i] = RcppArmadillo::sample(choice_set, 1, false, x(i, _))[0];
    }
    return result;
}

I then made that function available in my R session via

Rcpp::sourceCpp("sample_matrix.cpp")

Now we can test it in R against your initial approach, as well as the other suggestions to use purrr::map() and lapply():

set.seed(1010) #reproducibility

#create a matrix of probabilities
#three possible outcomes, 10.000 cases
probabilities <- matrix(runif(10000*3),nrow=10000,ncol=3)
probabilities <- probabilities / Matrix::rowSums(probabilities)
probabilities_list <- split(probabilities, seq(nrow(probabilities)))

library(purrr)
library(microbenchmark)

microbenchmark(
    apply = apply(probabilities, 1, function(x) sample(1:3, 1, prob = x)),
    map = map(probabilities_list, function(x) sample(1:3, 1, prob = x)),
    lapply = lapply(probabilities_list, function(x) sample(1:3, 1, prob = x)),
    rcpp = sample_matrix(probabilities, 1:3),
    times = 100
)

Unit: milliseconds
   expr       min        lq      mean    median        uq       max neval
  apply 307.44702 321.30051 339.85403 342.36421 350.86090 434.56007   100
    map 254.69721 265.10187 282.85592 286.21680 295.48886 363.95898   100
 lapply 249.68224 259.70178 280.63066 279.87273 287.10062 691.21359   100
   rcpp  12.16787  12.55429  13.47837  13.81601  14.25198  16.84859   100
 cld
   c
  b 
  b 
 a  

The time savings are considerable.

Answer 2

If you are willing to put probabilities in list, purrr::map or lapply seem a little faster:

probabilities <- matrix(runif(10000*3),nrow=10000,ncol=3)
probabilities <- probabilities / Matrix::rowSums(probabilities)
probabilities_list <- split(probabilities, seq(nrow(probabilities)))

library(purrr)
set.seed(1010)
classification_list <- map(probabilities_list, function(x) sample(1:3, 1, prob = x))

set.seed(1010)
classification_list <- lapply(probabilities_list, function(x) sample(1:3, 1, prob = x))

Benchmarking:

microbenchmark::microbenchmark(
  apply = {classification = apply(probabilities, 1, function(x) sample(1:3, 1, prob = x))},
  map = {classification = map(probabilities_list, function(x) sample(1:3, 1, prob = x))},
  lapply = {classification = lapply(probabilities_list, function(x) sample(1:3, 1, prob = x))},
  times = 100
)
# Unit: milliseconds
#  expr      min       lq     mean   median       uq      max neval
# apply 39.92883 42.59249 48.39247 45.03080 47.86648 94.39828   100
#   map 35.54077 37.13866 42.19719 39.95046 41.56323 66.05167   100
#lapply 34.54861 36.48664 42.69512 39.20139 52.31494 59.29200   100

With 100.000 cases

# Unit: milliseconds
# expr      min       lq     mean   median       uq      max neval
# apply 457.5310 520.4926 572.5974 552.1674 611.5640 957.3997   100
#   map 391.4751 457.7326 488.3286 482.1459 512.2054 899.1380   100
#lapply 386.2698 443.6732 491.9957 475.4160 507.3677 868.6725   100

Answer 3

You can consider

• vapply and
• parallization: parallel::parApply

With your probabilities matrix:

set.seed(1010) #reproducibility

#create a matrix of probabilities
#three possible outcomes, 10.000 cases
probabilities <- matrix(runif(10000*3), nrow=10000,ncol=3)
probabilities <- probabilities / Matrix::rowSums(probabilities)
classification <- apply(probabilities, 1, function(x) sample(1:3, 1, prob = x))

vapply

By specifying the class for FUN.VALUE, you might be able to make it fast.

classification2 <- vapply(split(probabilities, 1:nrow(probabilities)),
                          function(x) sample(1:3, 1, prob = x),
                          FUN.VALUE = integer(1), USE.NAMES = FALSE)
head(classification2)
#> [1] 1 3 3 1 2 3

parallel package

benchmarkme::get_cpu()
#> $vendor_id
#> [1] "GenuineIntel"
#> 
#> $model_name
#> [1] "Intel(R) Core(TM) i5-4288U CPU @ 2.60GHz"
#> 
#> $no_of_cores
#> [1] 4

In the above environment,

cl <- parallel::makeCluster(4)
doParallel::registerDoParallel(cl, cores = 4)

parApply() can do what apply() do.

classification3 <- parallel::parApply(cl, probabilities, 1, function(x) sample(1:3, 1, prob = x))
head(classification3)
#> [1] 2 2 2 2 3 3

Comparing the three, including apply() solution,

microbenchmark::microbenchmark(
  question = { # yours
    apply(probabilities, 1, function(x) sample(1:3, 1, prob = x))
  },
  vapp = {
    vapply(split(probabilities, 1:nrow(probabilities)), function(x) sample(1:3, 1, prob = x), FUN.VALUE = integer(1), USE.NAMES = FALSE)
  },
  parr = {
    parallel::parApply(cl, probabilities, 1, function(x) sample(1:3, 1, prob = x))
  }
)
#> Unit: milliseconds
#>      expr      min       lq     mean   median       uq       max neval
#>  question 49.93853 58.39965 65.05360 62.98119 68.28044 182.03267   100
#>      vapp 44.19828 54.84294 59.47109 58.56739 62.05269 146.14792   100
#>      parr 43.33227 48.16840 53.26599 50.87995 54.17286  98.67692   100

parallel::stopCluster(cl)