bug in RandomChoice if weight is zero?
Matthias Greiff
In[62]:= RandomChoice[{0, 0, 3} -> {3, 2, 1}, 5]
Out[62]= {1, 1, 1, 1, 1}
Why is it not the same if I use RandomSample?
The following command
RandomSample[{1, 2, 0} -> Range[3], 2]
returns either {1,2} or {2,1}. But when I change the command to sample size 3 I get the following.
In[60]:= RandomSample[{1, 2, 0} -> Range[3], 3]
Out[60]= {2, 1, 3}
Why is the third element selected? Shouldn't Mathematica return an error message because the sample size is larger than the population size?
Appreciate your answers.
Merry Christmas!
Matthias
dh
from the manual:
"RandomSample[{Subscript[e, 1],Subscript[e, 2],\[Ellipsis]},n] never
samples any of the Subscript[e, i] more than once."
Daniel
Leonid Shifrin
presumably this is because RandomSample never samples any given element more
than once - in that case it has no other choice, regardless of the weight.
Perhaps, the error message might be added for exact symbolic zero appearing
somewhere in the wieights for the case where the size of the desired sample
is larger than the number of non-zero weights (non-zero means
UnsameQ[weight,0]). It is not clear however whether it is worth it given
the overhead of such an analysis. Besides, this will be a point solution
anyway, since some expressions that might be used for weights may be in fact
identically equal to zero but just not simplified to zero - these cases
would not be caught by such an analysis.
OTOH, it is hard to make a formal (not based on syntax) distinction between
zero and some very small weight close to zero (which may be expressed not
necessarily with machine precision). This of course depends on the
implementation of the underlying algorithm used to do the sampling - whether
or not it treats weights smaller than machine epsilon as zero. From the
point of view of the abstract interface of RandomSample, there is no reason
why it should do that, even if such events are highly unlikely to be
sampled.
Generally, what you ask for should be possible once you give a specific
interpretation of what you mean by zero, but arguably this would add more
ambiguities/restrictions than it is worth for a kind of a general-purpose
function that RandomSample is. After all, you can always wrap RandomSample
in your own wrapper function which will implement this functionality in the
way you want it (consistent with your definition of zero), while preserving
the syntax of the original RandomSample.
Regards,
Leonid
Daniel Lichtblau
> If I use RandomChoice with weights of zero the corresponding elements will never be selected.
>
> In[62]:= RandomChoice[{0, 0, 3} -> {3, 2, 1}, 5]
> Out[62]= {1, 1, 1, 1, 1}
>
> Why is it not the same if I use RandomSample?
> The following command
>
> RandomSample[{1, 2, 0} -> Range[3], 2]
>
> returns either {1,2} or {2,1}. But when I change the command to sample size 3 I get the following.
>
> In[60]:= RandomSample[{1, 2, 0} -> Range[3], 3]
> Out[60]= {2, 1, 3}
>
> Why is the third element selected? Shouldn't Mathematica return an error message because the sample size is larger than the population size?
>
> Appreciate your answers.
>
> Merry Christmas!
>
> Matthias
I see your bug, and raise you another.
In[25]:= TimeConstrained[
RandomSample[UnitVector[100,1]->Range[100], 2], 10] (* hangs *)
Actually that's two more bugs, because it is both in some infinite
cycling and also not responding to aborts.
I'll look into repair today. Alternatively, I might go home and have a
good sob.
Daniel Lichtblau
Wolfram Research
Leonid Shifrin
seems to me like a point solution, given that there may be extremely small
non-zero weights expressed analytically (as a rational for example). I may
be wrong of course.
On Wed, Dec 30, 2009 at 8:29 AM, DrMajorBob <btr...@austin.rr.com> wrote:
> Generally, what you ask for should be possible once you give a specific
>> interpretation of what you mean by zero
>>
>
> What's ambiguous about the Integer 0?
>
> Bobby
>> On Tue, Dec 29, 2009 at 9:17 AM, Matthias Greiff <gre...@mac.com> wrote:
>>
>> If I use RandomChoice with weights of zero the corresponding elements
>>> will
>>> never be selected.
>>>
>>> In[62]:= RandomChoice[{0, 0, 3} -> {3, 2, 1}, 5]
>>> Out[62]= {1, 1, 1, 1, 1}
>>>
>>> Why is it not the same if I use RandomSample?
>>> The following command
>>>
>>> RandomSample[{1, 2, 0} -> Range[3], 2]
>>>
>>> returns either {1,2} or {2,1}. But when I change the command to sample
>>> size
>>> 3 I get the following.
>>>
>>> In[60]:= RandomSample[{1, 2, 0} -> Range[3], 3]
>>> Out[60]= {2, 1, 3}
>>>
>>> Why is the third element selected? Shouldn't Mathematica return an error
>>> message because the sample size is larger than the population size?
>>>
>>> Appreciate your answers.
>>>
>>> Merry Christmas!
>>>
>>> Matthias
>>>
>>>
>>>
>
> --
> DrMaj...@yahoo.com
>
DrMajorBob
verified as such, you have a point.
But the OP's example had an explicit integer 0. Mathematica should have
thrown an error.
Bobby
On Wed, 30 Dec 2009 14:47:42 -0600, Leonid Shifrin <lsh...@gmail.com>
wrote:
DrMajorBob
Hence, the documentation simply contradicts itself.
Bobby
On Wed, 30 Dec 2009 03:16:58 -0600, dh <d...@metrohm.com> wrote:
> Hi Mathias,
> from the manual:
> "RandomSample[{Subscript[e, 1],Subscript[e, 2],\[Ellipsis]},n] never
> samples any of the Subscript[e, i] more than once."
> Daniel
>
> On 29 Dez., 07:20, Matthias Greiff <gre...@mac.com> wrote:
DrMajorBob
> interpretation of what you mean by zero
What's ambiguous about the Integer 0?
Bobby
On Wed, 30 Dec 2009 03:17:21 -0600, Leonid Shifrin <lsh...@gmail.com>
wrote:
Matthias
In[171]:= RandomSample[{0, 0, 0, 1, 0} -> {1, 2, 3, 4, 5}, 1]
RandomSample[{0, 0, 0, 1, 0} -> {1, 2, 3, 4, 5}, 2]
RandomSample[{0, 0, 0, 1, 0} -> {1, 2, 3, 4, 5}, 3]
RandomSample[{0, 0, 0, 1, 0} -> {1, 2, 3, 4, 5}, 5]
Out[171]= {4}
Out[172]= {4, 5}
Out[173]= {4, 5, 5}
Out[174]= {4, 5, 5, 5, 5}
Although the fifth element has weight zero it is selected multiple
times? Is that only in my version of Mathematica (Version 7.0.1.0 on
Max OS X 10.6.2)?
Of course there are ways to work around that but, as DrMajorBob,
already pointed out, this contradicts the documentation.