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digitalmars.D - randomSample with unknown length

reply Magnus Lie Hetland <magnus hetland.org> writes:
Reading the doc for std.random.randomSample, I saw that "The total 
length of r must be known". There are rather straightforward algorithms 
for drawing random samples *without* knowing this. This might be useful 
if one wants to support input ranges, I guess?

Take, for example, the method described by Knuth (TAoP 2), for 
selecting n elements uniformly at random from an input range:

- Select the first n elements as the current sample.
- Each subsequent element is rejected with a probability of 1 - n/t, 
where t is the number seen so far.
- If a new item is selected, it replaces a random item in the current sample.

A cool property of this is that at any time, the current sample is one 
drawn randomly (i.e., uniformly, without replacement) from the items 
you've seen so far, so you could really stop at any point. That is, 
stop iterating over the input; you can't really give the output as a 
small-footprint range here (as far as I can see). Seems you have to 
allocate room for n pointers. (Or you *could* just keep track of which 
objects were swapped in -- might be worth the overhead if n is large 
compared to the input size.)

-- 
Magnus Lie Hetland
http://hetland.org
Feb 02 2011
parent reply Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> writes:
On 2/2/11 6:03 AM, Magnus Lie Hetland wrote:
 Reading the doc for std.random.randomSample, I saw that "The total
 length of r must be known". There are rather straightforward algorithms
 for drawing random samples *without* knowing this. This might be useful
 if one wants to support input ranges, I guess?

 Take, for example, the method described by Knuth (TAoP 2), for selecting
 n elements uniformly at random from an input range:

 - Select the first n elements as the current sample.
 - Each subsequent element is rejected with a probability of 1 - n/t,
 where t is the number seen so far.
 - If a new item is selected, it replaces a random item in the current
 sample.

 A cool property of this is that at any time, the current sample is one
 drawn randomly (i.e., uniformly, without replacement) from the items
 you've seen so far, so you could really stop at any point. That is, stop
 iterating over the input; you can't really give the output as a
 small-footprint range here (as far as I can see). Seems you have to
 allocate room for n pointers. (Or you *could* just keep track of which
 objects were swapped in -- might be worth the overhead if n is large
 compared to the input size.)

I posted a problem solved by the algorithm above (and others, more sophisticated ones) as a challenge to this group a couple of years ago. randomSample is designed to subsample a large stream in constant space and without needing to scan the entire stream in order to output the first element. I used in in my dissertation where e.g. I had to select 100K samples from a stream of many millions. Having a reservoir sample available would be nice. I'd be thrilled if you coded up a reservoirSample(r, n) function for addition to std.random. Andrei
Feb 02 2011
next sibling parent "Simen kjaeraas" <simen.kjaras gmail.com> writes:
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Andrei Alexandrescu <SeeWebsiteForEmail erdani.org> wrote:

 Having a reservoir sample available would be nice. I'd be thrilled if  
 you coded up a reservoirSample(r, n) function for addition to std.random.

Done. No comments or unittests yet, though. randomSampleRange( R, num ) takes num samples from an input range, and keeps a reservoir that is updated as you traverse the range (lazy, if you wish). randomSample( R, num ) takes num samples from all over a range (eager). -- Simen ------------xSiOOR6ZU4bV01lWI6ZjHX Content-Disposition: attachment; filename=RandomSample.d Content-Type: application/octet-stream; name="RandomSample.d" Content-Transfer-Encoding: Base64 77u/bW9kdWxlIFJhbmRvbVNhbXBsZTsNCg0KaW1wb3J0IHN0ZC5yYW5nZTsNCmlt cG9ydCBzdGQucmFuZG9tOw0KaW1wb3J0IHN0ZC5zdGRpbzsNCg0Kc3RydWN0IFJh bmRvbVNhbXBsZSggUiApIGlmICggaXNJbnB1dFJhbmdlIVIgKSB7DQoJUiByYW5n ZTsNCglFbGVtZW50VHlwZSEoIFIgKVtdIF9mcm9udDsNCglib29sIGVtcHR5Ow0K CVJhbmRvbSBybmQ7DQoJdWxvbmcgcG9zOw0KCQ0KCXRoaXMoIFIgciwgc2l6ZV90 IG51bSApIHsNCgkJc3RhdGljIGlmICggaXNGb3J3YXJkUmFuZ2UhUiApIHsNCgkJ CXJhbmdlID0gci5zYXZlOw0KCQl9IGVsc2Ugew0KCQkJcmFuZ2UgPSByOw0KCQl9 DQoJCV9mcm9udCA9IGFycmF5KCB0YWtlKCByYW5nZSwgbnVtICkgKTsNCgkJc3Rh dGljIGlmICggaXNGb3J3YXJkUmFuZ2UhUiApIHsNCgkJCXBvcEZyb250TiggcmFu Z2UsIG51bSApOw0KCQl9DQoJCQ0KCQllbXB0eSA9IGZhbHNlOw0KCQlybmQgPSBS YW5kb20oIHVucHJlZGljdGFibGVTZWVkICk7DQoJCXBvcyA9IG51bTsNCgl9DQoJ DQoJQHByb3BlcnR5IEVsZW1lbnRUeXBlIShSKVtdIGZyb250KCApIHsNCgkJcmV0 dXJuIF9mcm9udC5kdXA7DQoJfQ0KCQ0KCXZvaWQgcG9wRnJvbnQoICkgew0KCQlh c3NlcnQoICFlbXB0eSApOw0KCQlpZiAoIHVuaWZvcm0oIDAsIHBvcywgcm5kICkg PCBfZnJvbnQubGVuZ3RoICkgew0KCQkJX2Zyb250WyB1bmlmb3JtKCAwLCBfZnJv bnQubGVuZ3RoLCBybmQgKSBdID0gcmFuZ2UuZnJvbnQ7DQoJCX0NCgkJcmFuZ2Uu cG9wRnJvbnQoICk7DQoJCXBvcysrOw0KCQllbXB0eSA9IHJhbmdlLmVtcHR5Ow0K CX0NCn0NCg0KUmFuZG9tU2FtcGxlIVIgcmFuZG9tU2FtcGxlUmFuZ2UoIFIgKSgg UiByLCBzaXplX3QgbnVtID0gMSApIGlmICggaXNJbnB1dFJhbmdlIVIgKSB7DQoJ cmV0dXJuIFJhbmRvbVNhbXBsZSFSKCByLCBudW0gKTsNCn0NCg0KVFtdIHJhbmRv bVNhbXBsZUltcGwoIFQsIFIgKSggVFtdIHJlc3VsdCwgUiByICkgew0KCWF1dG8g cm5kID0gUmFuZG9tKCB1bnByZWRpY3RhYmxlU2VlZCApOw0KCWZvcmVhY2ggKCBp LCBlOyByICkgew0KCQlpZiAoIHVuaWZvcm0oIDAsIHJlc3VsdC5sZW5ndGggKyBp ICsgMSwgcm5kICkgPCByZXN1bHQubGVuZ3RoICkgew0KCQkJcmVzdWx0WyB1bmlm b3JtKCAwLCByZXN1bHQubGVuZ3RoLCBybmQgKSBdID0gZTsNCgkJfQ0KCX0NCgly ZXR1cm4gcmVzdWx0Ow0KfQ0KDQpFbGVtZW50VHlwZSEoIFIgKVtdIHJhbmRvbVNh bXBsZSggUiApKCBSIHIsIHNpemVfdCBudW0gPSAxICkgaWYgKCBpc0lucHV0UmFu Z2UhUiAmJiAhaXNGb3J3YXJkUmFuZ2UhUiApIHsNCglhdXRvIHJlc3VsdCA9IGFy cmF5KCB0YWtlKCByLCBudW0gKSApOw0KCXJldHVybiByYW5kb21TYW1wbGVJbXBs KCByZXN1bHQsIHJyICk7DQp9DQoNCkVsZW1lbnRUeXBlISggUiApW10gcmFuZG9t U2FtcGxlKCBSICkoIFIgciwgc2l6ZV90IG51bSA9IDEgKSBpZiAoIGlzRm9yd2Fy ZFJhbmdlIVIgKSB7DQoJYXV0byByciA9IHIuc2F2ZTsNCglhdXRvIHJlc3VsdCA9 IGFycmF5KCB0YWtlKCByciwgbnVtICkgKTsNCglwb3BGcm9udE4oIHJyLCBudW0g KTsNCglyZXR1cm4gcmFuZG9tU2FtcGxlSW1wbCggcmVzdWx0LCByciApOw0KfQ0K DQp2b2lkIG1haW4oICkgew0KCXdyaXRlbG4oICJSYW5nZSBzYW1wbGU6IiApOw0K CWZvcmVhY2ggKCBlOyByYW5kb21TYW1wbGVSYW5nZSggIlNhbXBsZSB0ZXh0Iiwg MyApICkgew0KCQl3cml0ZWxuKCBlICk7DQoJfQ0KCXdyaXRlbG4oICJTaW5nbGUg c2FtcGxlOiIgKTsNCgl3cml0ZWxuKCByYW5kb21TYW1wbGUoICJTYW1wbGUgdGV4 dCIsIDMgKSApOw0KfQ== ------------xSiOOR6ZU4bV01lWI6ZjHX--
Feb 02 2011
prev sibling parent Magnus Lie Hetland <magnus hetland.org> writes:
On 2011-02-02 16:32:25 +0100, Andrei Alexandrescu said:

 randomSample is designed to subsample a large stream in constant space 
 and without needing to scan the entire stream in order to output the 
 first element.

Sure. I was just thinking that you could have a version for the cases where there was no end in sight :)
 I used in in my dissertation where e.g. I had to select 100K samples 
 from a stream of many millions.

Cool.
 Having a reservoir sample available would be nice. I'd be thrilled if 
 you coded up a reservoirSample(r, n) function for addition to 
 std.random.

Seems Simen beat me to it :) -- Magnus Lie Hetland http://hetland.org
Feb 02 2011