How do I sample randomly based on some probability(wightage)?

Sumitava Mukherjee smukh at cognobytes.com
Sun May 31 09:08:44 CEST 2009

```On May 27, 8:08 pm, Scott David Daniels <Scott.Dani... at Acm.Org> wrote:
> Sumitava Mukherjee wrote:
> > I need to randomly sample from a list where all choices have weights
> > attached to them. The probability of them being choosen is dependent
> > on the weights.
>
> I am not sure why everybody is normalizing by dividing the weights.
> This isa possibility (I had fun writing it).
>
> def sample_without_replacement(choices, weights):
>      '''Yield elements sampled w/o replacement by weighting'''
>      if len(weights) != len(choices):
>          raise ValueError('%d choices, but %d weights?' % (
>              len(choices), len(weights)))
>      if min(weights) < 0:
>          raise ValueError('Negative weights?: %s' % (
>                      [(i, w) for i, w in enumerate(weights) if w < 0]))
>
>      # look at only non-zero probabilities
>      combined = [(w, v) for w, v in zip(weights, choices) if w > 0]
>
>      # Go from highest probability down to reduce expected traversal
>      combined.sort(key=operator.itemgetter(0), reverse=True)
>
>      total = sum(w for w, v in combined) # sum(weights) also works
>      while combined:
>          spot = sample = random.random() * total
>          for n, (weight, choice) in enumerate(combined):
>              spot -= weight
>              if spot <= 0:
>                  break
>          else:
>              # n, (weight, choice) = 0, combined[0] # Highest probability
>              raise ValueError('%f left after choosing %f/%f?: %s' % (
>                                  spot, sample, total, combined))
>          yield choice
>          total -= weight
>          if weight > total * 256: # arbitrary choice for recalculation
>              # precision affected, rebuild
>              total = sum(w for w, v in combined)
>          del combined[n]
>      raise ValueError('Samplng more than %d without replacement?' % (
>                        sum(1 for w in weights if w > 0)))
>
> for n in range(10):
>      gen = sample_without_replacement('abcdef', [32,16,8,4,2,1])
>      print gen.next(), gen.next(), gen.next()
>
> --Scott David Daniels
> Scott.Dani... at Acm.Org

Among all the help (all of which I really appreciate), I found your
solution closest to what I was expecting. Thanks a lot Scott.

```