Testing for Random Value - Thoughts on this Approach?

Answer 1

Random is Random. Even if the same picture shows up 4 times in a row, it could still be considered random.

Answer 2

It's impossible to test if a value is truly random or not. The best you can do is perform the test some large number of times and test that you got an appropriate distribution, but if the results are truly random, even this has a (very small) chance of failing.

If you're doing white box testing, and you know your random seed, then you can actually compute the expected result, but you may need a separate test to test the randomness of your RNG.

Answer 3

My opinion is that anything random cannot be properly tested.

Sure you can attempt to test it, but there are so many combinations to try that you are better off just relying on the RNG and spot checking a large handful of cases.

Answer 4

Well, the problem is that random numbers by definition can get repeated (because they are... wait for it: random). Maybe what you want to do is save the latest random number and compare the calculated one to that, and if equal just calculate another... but now your numbers are less random (I know there's not such a thing as "more or less" randomness, but let me use the term just this time), because they are guaranteed not to repeat.

Anyway, you should never give random numbers so much thought. :)

Answer 5

As others have pointed out, it is impossible to really test for randomness. You can (and should) have the randomness contained to one particular method, and then write unit tests for every other method. That way, you can test all of the other functionality, assuming that you can get a random number out of that one last part.

Answer 6

If you have a fixed set of items, and you don't want them to repeat too often, shuffle the collection randomly. Then you will be sure that you never see the same image twice in a row, feel like you're listening to Top 20 radio, etc. You'll make a full pass through the collection before repeating.

Item[] foo = …
for (int idx = foo.size(); idx > 1; --idx) {
  /* Pick random number from half-open interval [0, idx) */
  int rnd = random(idx); 
  Item tmp = foo[idx - 1];
  foo[idx - 1] = foo[rnd];
  foo[rnd] = tmp;
}

If you have too many items to collect and shuffle all at once (10s of thousands of images in a repository), you can add some divide-and-conquer to the same approach. Shuffle groups of images, then shuffle each group.

A slightly different approach that sounds like it might apply to your revised problem statement is to have your "image selector" implementation keep its recent selection history in a queue of at most Y length. Before returning an image, it tests to see if its in the queue X times already, and if so, it randomly selects another, until it find one that passes.

If you are really asking about testing the quality of the random number generator, I'll have to open the statistics book.

Answer 7

store the random values and before you use the next generated random number, check against the stored value.

Answer 8

The generation of random numbers is too important to be left to chance. -- Robert R. Coveyou

To solve the psychological problem:

A decent way to prevent apparent repetitions is to select a few items at random from the full set, discarding duplicates. Play those, then select another few. How many is "a few" depends on how fast you're playing them and how big the full set is, but for example avoiding a repeat inside the larger of "20", and "5 minutes" might be OK. Do user testing - as the programmer you'll be so sick of slideshows you're not a good test subject.

To test randomising code, I would say:

Step 1: specify how the code MUST map the raw random numbers to choices in your domain, and make sure that your code correctly uses the output of the random number generator. Test this by Mocking the generator (or seeding it with a known test value if it's a PRNG).

Step 2: make sure the generator is sufficiently random for your purposes. If you used a library function, you do this by reading the documentation. If you wrote your own, why?

Step 3 (advanced statisticians only): run some statistical tests for randomness on the output of the generator. Make sure you know what the probability is of a false failure on the test.

Answer 9

Any good pseudo-random number generator will let you seed the generator. If you seed the generator with same number, then the stream of random numbers generated will be the same. So why not seed your random number generator and then create your unit tests based on that particular stream of numbers?

Answer 10

Test from the requirement : "so you don't see the same images too often"

Ask for 100 images. Did you see an image too often?

Answer 11

There is a handy list of statistical randomness tests and related research on Wikipedia. Note that you won't know for certain that a source is truly random with most of these, you'll just have ruled out some ways in which it may be easily predictable.

Answer 12

To get a series of non-repeating random numbers:

1. Create a list of random numbers.
2. Add a sequence number to each random number
3. Sort the sequenced list by the original random number
4. Use your sequence number as a new random number.

Answer 13

Don't test the randomness, test to see if the results your getting are desirable (or, rather, try to get undesirable results a few times before accepting that your results are probably going to be desirable). It will be impossible to ensure that you'll never get an undesirable result if you're testing a random output, but you can at least increase the chances that you'll notice it happening.

I would either take N pools of Y size, checking for any results that appear more than X number of times, or take one pool of N*Y size, checking every group of Y size for any result that appears more than X times (1 to Y, 2 to Y + 1, 3 to Y + 2, etc). What N is would depend on how reliable you want the test to be.

Answer 14

What the Random and similar functions give you is but pseudo-random numbers, a series of numbers produced through a function. Usually, you give that function it's first input parameter (a.k.a. the "seed") which is used to produce the first "random" number. After that, each last value is used as the input parameter for the next iteration of the cycle. You can check the Wikipedia article on "Pseudorandom number generator", the explanation there is very good.

All of these algorithms have something in common: the series repeats itself after a number of iterations. Remember, these aren't truly random numbers, only series of numbers that seem random. To select one generator over another, you need to ask yourself: What do you want it for?

How do you test randomness? Indeed you can. There are plenty of tests for that. The first and most simple is, of course, run your pseudo-random number generator an enormous number of times, and compile the number of times each result appears. In the end, each result should've appeared a number of times very close to (number of iterations)/(number of possible results). The greater the standard deviation of this, the worse your generator is.

The second is: how much random numbers are you using at the time? 2, 3? Take them in pairs (or tripplets) and repeat the previous experiment: after a very long number of iterations, each expected result should have appeared at least once, and again the number of times each result has appeared shouldn't be too far away from the expected. There are some generators which work just fine for taking one or 2 at a time, but fail spectacularly when you're taking 3 or more (RANDU anyone?).

There are other, more complex tests: some involve plotting the results in a logarithmic scale, or onto a plane with a circle in the middle and then counting how much of the plots fell within, others... I believe those 2 above should suffice most of the times (unless you're a finicky mathematician).

Answer 15

Random numbers are generated from a distribution. In this case, every value should have the same propability of appearing. If you calculate an infinite amount of randoms, you get the exact distribution.

In practice, call the function many times and check the results. If you expect to have N images, calculate 100*N randoms, then count how many of each expected number were found. Most should appear 70-130 times. Re-run the test with different random-seed to see if the results are different.

If you find the generator you use now is not good enough, you can easily find something. Google for "Mersenne Twister" - that is much more random than you ever need.

To avoid images re-appearing, you need something less random. A simple approach would be to check for the unallowed values, if its one of those, re-calculate.

Answer 16

Although you cannot test for randomness, you can test that for correlation, or distribution, of a sequence of numbers.

Hard to test goal: Each time we need an image, select 1 of 4 images at random.

Easy to test goal: For every 100 images we select, each of the 4 images must appear at least 20 times.

Answer 17

I agree with Adam Rosenfield. For the situation you're talking about, the only thing you can usefully test for is distribution across the range.

The situation I usually encounter is that I'm generating pseudorandom numbers with my favourite language's PRNG, and then manipulating them into the desired range. To check whether my manipulations have affected the distribution, I generate a bunch of numbers, manipulate them, and then check the distribution of the results.

To get a good test, you should generate at least a couple orders of magnitude more numbers than your range holds. The more values you use, the better the test. Obviously if you have a really large range, this won't work since you'll have to generate far too many numbers. But in your situation it should work fine.

Here's an example in Perl that illustrates what I mean:

for (my $i=0; $i<=100000; $i++) {
   my $r = rand;        # Get the random number
   $r = int($r * 1000); # Move it into the desired range
   $dist{$r} ++;        # Count the occurrences of each number
}

print "Min occurrences: ", (sort { $a <=> $b } values %dist)[1], "\n";
print "Max occurrences: ", (sort { $b <=> $a } values %dist)[1], "\n";

If the spread between the min and max occurrences is small, then your distribution is good. If it's wide, then your distribution may be bad. You can also use this approach to check whether your range was covered and whether any values were missed.

Again, the more numbers you generate, the more valid the results. I tend to start small and work up to whatever my machine will handle in a reasonable amount of time, e.g. five minutes.

Answer 18

Supposing you are testing a range for randomness within integers, one way to verify this is to create a gajillion (well, maybe 10,000 or so) 'random' numbers and plot their occurrence on a histogram.

          ******    ******           ****
***********************************************
*************************************************
*************************************************
*************************************************
*************************************************
*************************************************
*************************************************
*************************************************
*************************************************
         1         2         3         4         5
12345678901234567890123456789012345678901234567890

The above shows a 'relatively' normal distribution.

if it looked more skewed, such as this:

          ******    ******           ****
    ************  ************  ************
    ************  ************  ***************
    ************  ************  ****************
    ************  ************  *****************
    ************  ************  *****************
   ***************************  ******************
   **************************** ******************
******************************* ******************
**************************************************
         1         2         3         4         5
12345678901234567890123456789012345678901234567890

Then you can see there is less randomness. As others have mentioned, there is the issue of repetition to contend with as well.

If you were to write a binary file of say 10,000 random numbers from your generator using, say a random number from 1 to 1024 and try to compress that file using some compression (zip, gzip, etc.) then you could compare the two file sizes. If there is 'lots' of compression, then it's not particularly random. If there isn't much of a change in size, then it's 'pretty random'.

Why this works

The compression algorithms look for patterns (repetition and otherwise) and reduces that in some way. One way to look a these compression algorithms is a measure of the amount of information in a file. A highly compressed file has little information (e.g. randomness) and a little-compressed file has much information (randomness)

Answer 19

There are whole books one can write about randomness and evaluating if something appears to be random, but I'll save you the pages of mathematics. In short, you can use a chi-square test as a way of determining how well an apparently "random" distribution fits what you expect.

If you're using Perl, you can use the Statistics::ChiSquare module to do the hard work for you.

However if you want to make sure that your images are evenly distributed, then you probably won't want them to be truly random. Instead, I'd suggest you take your entire list of images, shuffle that list, and then remove an item from it whenever you need a "random" image. When the list is empty, you re-build it, re-shuffle, and repeat.

This technique means that given a set of images, each individual image can't appear more than once every iteration through your list. Your images can't help but be evenly distributed.

All the best,

Paul