Extreme bunching of random values from runif with Mersenne-Twister seed

Fri, Nov 3, 2017 10:31 AM

Bill,

I have clarified this on SO, and I will copy that clarification in here:

"Sure, we tested them on other 8-digit numbers as well & we could not
replicate. However, these are honest-to-goodness numbers generated by a
non-adversarial system that has no conception of these numbers being used
for anything other than a unique key for an entity -- these are not a
specially constructed edge case. Would be good to know what seeds will and
will not work, and why."

These numbers are generated by an application that serves a form, and
associates form IDs in a sequence. The application calls our API depending
on the form values entered by users, which in turn calls our R code that
executes some code that needs an RNG. Since the API has to be stateless, to
be able to replicate the results for possible debugging, we need to draw
random numbers in a way that we can replicate the results of the API
response -- we use the form ID as seeds.

I repeat, there is no design or anything adversarial about the way that
these numbers were generated -- the system generating these numbers and the
users entering inputs have no conception of our use of an RNG -- this is
meant to just be a random sequence of form IDs. This issue was discovered
completely by chance when the output of the API was observed to be highly
non-random. It is possible that it is a 1/10^8 chance, but that is hard to
believe, given that the API hit depends on user input. Note also that the
issue goes away when we use a different RNG as mentioned below.

T

On Fri, Nov 3, 2017 at 9:58 PM, William Dunlap <wdunlap at tibco.com> wrote:

The random numbers in a stream initialized with one seed should have about
the desired distribution.  You don't win by changing the seed all the
time.  Your seeds caused the first numbers of a bunch of streams to be
about the same, but the second and subsequent entries in each stream do
look uniformly distributed.

You didn't say what your 'upstream process' was, but it is easy to come up
with seeds that give about the same first value:

Filter(function(s){set.seed(s);runif(1,17,26)>25.99}, 1:10000)

 [1]  514  532 1951 2631 3974 4068 4229 6092 6432 7264 9090



Bill Dunlap
TIBCO Software
wdunlap tibco.com

On Fri, Nov 3, 2017 at 12:49 AM, Tirthankar Chakravarty <
tirthankar.lists at gmail.com> wrote:

This is cross-posted from SO (https://stackoverflow.com/q/4
7079702/1414455),
but I now feel that this needs someone from R-Devel to help understand why
this is happening.

We are facing a weird situation in our code when using R's [`runif`][1]
and
setting seed with `set.seed` with the `kind = NULL` option (which
resolves,
unless I am mistaken, to `kind = "default"`; the default being
`"Mersenne-Twister"`).

We set the seed using (8 digit) unique IDs generated by an upstream
system,
before calling `runif`:

    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)
    })

This gives values that are **extremely** bunched together.

    > summary(random_values)

       Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
      25.13   25.36   25.66   25.58   25.83   25.94

This behaviour of `runif` goes away when we use `kind =
"Knuth-TAOCP-2002"`, and we get values that appear to be much more evenly
spread out.

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

*Output omitted.*

---

**The most interesting thing here is that this does not happen on Windows
-- only happens on Ubuntu** (`sessionInfo` output for Ubuntu & Windows
below).

# Windows output: #

    > 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

Can someone help understand what is going on?

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



Windows
-------

    > 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

  [1]: http://stat.ethz.ch/R-manual/R-devel/library/stats/html/Unif
orm.html

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Extreme bunching of random values from runif with Mersenne-Twister seed

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