R:使用 Mersenne-Twister 种子将来自 runif 的随机值极端聚集

Question

我们在使用 R 的 runif 时，在我们的代码中遇到了一个奇怪的情况。并用 set.seed 设置种子与 kind = NULL选项(除非我弄错了，否则解析为 kind = "default" ；默认值为 "Mersenne-Twister" )。

在调用 runif 之前，我们使用上游系统生成的(8 位)唯一 ID 设置种子。 :

seeds = c(
  "86548915", "86551615", "86566163", "86577411", "86584144", 
  "86584272", "86620568", "86724613", "86756002", "86768593", "86772411", 
  "86781516", "86794389", "86805854", "86814600", "86835092", "86874179", 
  "86876466", "86901193", "86987847", "86988080")

random_values = sapply(seeds, function(x) {
  set.seed(x)
  y = runif(1, 17, 26)
  return(y)
})

这给出了 的值极挤在一起。

> summary(random_values)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  25.13   25.36   25.66   25.58   25.83   25.94 

runif的这种行为当我们使用 kind = "Knuth-TAOCP-2002" 时消失，我们得到的值似乎分布得更均匀。

random_values = sapply(seeds, function(x) {
  set.seed(x, kind = "Knuth-TAOCP-2002")
  y = runif(1, 17, 26)
  return(y)
})

输出省略。

这里最有趣的是，这不会发生在 Windows 上——只发生在 Ubuntu 上。 ( sessionInfo 下面是 Ubuntu 和 Windows 的输出)。

窗口输出:

> seeds = c(
+   "86548915", "86551615", "86566163", "86577411", "86584144", 
+   "86584272", "86620568", "86724613", "86756002", "86768593", "86772411", 
+   "86781516", "86794389", "86805854", "86814600", "86835092", "86874179", 
+   "86876466", "86901193", "86987847", "86988080")
> 
> random_values = sapply(seeds, function(x) {
+   set.seed(x)
+   y = runif(1, 17, 26)
+   return(y)
+ })
> 
> summary(random_values)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  17.32   20.14   23.00   22.17   24.07   25.90 

有人可以帮助了解发生了什么吗？

Ubuntu

R version 3.4.0 (2017-04-21)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 16.04.2 LTS

Matrix products: default
BLAS: /usr/lib/libblas/libblas.so.3.6.0
LAPACK: /usr/lib/lapack/liblapack.so.3.6.0

locale:
[1] LC_CTYPE=en_US.UTF-8          LC_NUMERIC=C                 
 [3] LC_TIME=en_US.UTF-8           LC_COLLATE=en_US.UTF-8       
 [5] LC_MONETARY=en_US.UTF-8       LC_MESSAGES=en_US.UTF-8      
 [7] LC_PAPER=en_US.UTF-8          LC_NAME=en_US.UTF-8          
 [9] LC_ADDRESS=en_US.UTF-8        LC_TELEPHONE=en_US.UTF-8     
[11] LC_MEASUREMENT=en_US.UTF-8    LC_IDENTIFICATION=en_US.UTF-8

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] RMySQL_0.10.8               DBI_0.6-1                  
 [3] jsonlite_1.4                tidyjson_0.2.2             
 [5] optiRum_0.37.3              lubridate_1.6.0            
 [7] httr_1.2.1                  gdata_2.18.0               
 [9] XLConnect_0.2-12            XLConnectJars_0.2-12       
[11] data.table_1.10.4           stringr_1.2.0              
[13] readxl_1.0.0                xlsx_0.5.7                 
[15] xlsxjars_0.6.1              rJava_0.9-8                
[17] sqldf_0.4-10                RSQLite_1.1-2              
[19] gsubfn_0.6-6                proto_1.0.0                
[21] dplyr_0.5.0                 purrr_0.2.4                
[23] readr_1.1.1                 tidyr_0.6.3                
[25] tibble_1.3.0                tidyverse_1.1.1            
[27] rBayesianOptimization_1.1.0 xgboost_0.6-4              
[29] MLmetrics_1.1.1             caret_6.0-76               
[31] ROCR_1.0-7                  gplots_3.0.1               
[33] effects_3.1-2               pROC_1.10.0                
[35] pscl_1.4.9                  lattice_0.20-35            
[37] MASS_7.3-47                 ggplot2_2.2.1              

loaded via a namespace (and not attached):
[1] splines_3.4.0      foreach_1.4.3      AUC_0.3.0          modelr_0.1.0      
 [5] gtools_3.5.0       assertthat_0.2.0   stats4_3.4.0       cellranger_1.1.0  
 [9] quantreg_5.33      chron_2.3-50       digest_0.6.10      rvest_0.3.2       
[13] minqa_1.2.4        colorspace_1.3-2   Matrix_1.2-10      plyr_1.8.4        
[17] psych_1.7.3.21     XML_3.98-1.7       broom_0.4.2        SparseM_1.77      
[21] haven_1.0.0        scales_0.4.1       lme4_1.1-13        MatrixModels_0.4-1
[25] mgcv_1.8-17        car_2.1-5          nnet_7.3-12        lazyeval_0.2.0    
[29] pbkrtest_0.4-7     mnormt_1.5-5       magrittr_1.5       memoise_1.0.0     
[33] nlme_3.1-131       forcats_0.2.0      xml2_1.1.1         foreign_0.8-69    
[37] tools_3.4.0        hms_0.3            munsell_0.4.3      compiler_3.4.0    
[41] caTools_1.17.1     rlang_0.1.1        grid_3.4.0         nloptr_1.0.4      
[45] iterators_1.0.8    bitops_1.0-6       tcltk_3.4.0        gtable_0.2.0      
[49] ModelMetrics_1.1.0 codetools_0.2-15   reshape2_1.4.2     R6_2.2.0          
[53] knitr_1.15.1       KernSmooth_2.23-15 stringi_1.1.5      Rcpp_0.12.11  

视窗

> sessionInfo()
R version 3.3.2 (2016-10-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows >= 8 x64 (build 9200)

locale:
[1] LC_COLLATE=English_India.1252  LC_CTYPE=English_India.1252    LC_MONETARY=English_India.1252
[4] LC_NUMERIC=C                   LC_TIME=English_India.1252    

attached base packages:
[1] graphics  grDevices utils     datasets  grid      stats     methods   base     

other attached packages:
 [1] bindrcpp_0.2         h2o_3.14.0.3         ggrepel_0.6.5        eulerr_1.1.0         VennDiagram_1.6.17  
 [6] futile.logger_1.4.3  scales_0.4.1         FinCal_0.6.3         xml2_1.0.0           httr_1.3.0          
[11] wesanderson_0.3.2    wordcloud_2.5        RColorBrewer_1.1-2   htmltools_0.3.6      urltools_1.6.0      
[16] timevis_0.4          dtplyr_0.0.1         magrittr_1.5         shiny_1.0.5          RODBC_1.3-14        
[21] zoo_1.8-0            sqldf_0.4-10         RSQLite_1.1-2        gsubfn_0.6-6         proto_1.0.0         
[26] gdata_2.17.0         stringr_1.2.0        XLConnect_0.2-12     XLConnectJars_0.2-12 data.table_1.10.4   
[31] xlsx_0.5.7           xlsxjars_0.6.1       rJava_0.9-8          readxl_0.1.1         googlesheets_0.2.1  
[36] jsonlite_1.5         tidyjson_0.2.1       RMySQL_0.10.9        RPostgreSQL_0.4-1    DBI_0.5-1           
[41] dplyr_0.7.2          purrr_0.2.3          readr_1.1.1          tidyr_0.7.0          tibble_1.3.3        
[46] ggplot2_2.2.0        tidyverse_1.0.0      lubridate_1.6.0     

loaded via a namespace (and not attached):
 [1] gtools_3.5.0         assertthat_0.2.0     triebeard_0.3.0      cellranger_1.1.0     yaml_2.1.14         
 [6] slam_0.1-40          lattice_0.20-34      glue_1.1.1           chron_2.3-48         digest_0.6.12.1     
[11] colorspace_1.3-1     httpuv_1.3.5         plyr_1.8.4           pkgconfig_2.0.1      xtable_1.8-2        
[16] lazyeval_0.2.0       mime_0.5             memoise_1.0.0        tools_3.3.2          hms_0.3             
[21] munsell_0.4.3        lambda.r_1.1.9       rlang_0.1.1          RCurl_1.95-4.8       labeling_0.3        
[26] bitops_1.0-6         tcltk_3.3.2          gtable_0.2.0         reshape2_1.4.2       R6_2.2.0            
[31] bindr_0.1            futile.options_1.0.0 stringi_1.1.2        Rcpp_0.12.12.1      

Answer 1

注意:这个答案总结了在 R-devel 邮件列表上发生的关于这个问题的讨论的元素。我只是试图捕捉和总结最初在那里表达的想法。

尽管您保证这些数字不是特殊构造的边缘情况，但它们的外观看起来就是这样。这是原始序列加代码，用于检查产生的值的分布:

seeds = c(
    86548915, 86551615, 86566163, 86577411, 86584144, 86584272,
    86620568, 86724613, 86756002, 86768593, 86772411, 86781516,
    86794389, 86805854, 86814600, 86835092, 86874179, 86876466,
    86901193, 86987847, 86988080)
checkit <- function(seeds) {
    sapply(seeds, function(x) {
        set.seed(x)
        y = runif(1, 17, 26)
        return(y)
    })}

正如所指出的，原始序列的变化令人惊讶地很小:

  summary(checkit(seeds+0))
  ## Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  ##25.13   25.36   25.66   25.58   25.83   25.94 

原始序列似乎确实有一些特别之处，因为对它的最小修改不会产生同样令人惊讶的结果:

summary(checkit(seeds+1))
## Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 17.18   19.65   22.75   22.02   24.37   25.79

summary(checkit(seeds-1))
## Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##17.15   18.44   19.92   20.77   22.97   25.95 

在原始序列跨越的范围内的所有种子中，预期数量产生观察范围内的值:

possible.seeds <- min(seeds):max(seeds)

s25 <- Filter(function(s){
    set.seed(s)
    x <- runif(1,17,26)
    x > 25.12 & x < 25.95},
    possible.seeds)

length(s25)/length(possible.seeds)
##[1] 0.09175801

然而，原始序列中的所有值都在这个子集中(当然我们已经知道了......)。

table(seeds %in% s25)

##TRUE 
##  21 

所有这些都表明原始序列实际上可能是(可能是无意的)特殊构造的边缘情况。