在python加权随机样本 [英] Weighted random sample in python
问题描述
我正在寻找一个函数 weighted_sample
的合理界定,不给定重量的名单(这会是这样恢复只是一个随机指标P>
I'm looking for a reasonable definition of a function weighted_sample
that does not return just one random index for a list of given weights (which would be something like
def weighted_choice(weights, random=random):
""" Given a list of weights [w_0, w_1, ..., w_n-1],
return an index i in range(n) with probability proportional to w_i. """
rnd = random.random() * sum(weights)
for i, w in enumerate(weights):
if w<0:
raise ValueError("Negative weight encountered.")
rnd -= w
if rnd < 0:
return i
raise ValueError("Sum of weights is not positive")
要给出一个明确的分布常数权重),但 K
那些随机抽样,无需更换,就像 random.sample
的行为方式相比, random.choice
。
to give a categorical distribution with constant weights) but a random sample of k
of those, without replacement, just as random.sample
behaves compared to random.choice
.
正如 weighted_choice
可以写成
lambda weights: random.choice([val for val, cnt in enumerate(weights)
for i in range(cnt)])
weighted_sample
可以写成
lambda weights, k: random.sample([val for val, cnt in enumerate(weights)
for i in range(cnt)], k)
但我想不需要我去解开这个权重成(可能是巨大的)列表中选择一个解决方案。
but I would like a solution that does not require me to unravel the weights into a (possibly huge) list.
编辑:如果有任何好的算法,给我回的频率的柱状图/列表(在相同的格式参数权重
),而不是指数序列,这也将是非常有用的。
If there are any nice algorithms that give me back a histogram/list of frequencies (in the same format as the argument weights
) instead of a sequence of indices, that would also be very useful.
推荐答案
从code:..
weight_sample_indexes = lambda weights, k: random.sample([val
for val, cnt in enumerate(weights) for i in range(cnt)], k)
。我认为权重是正整数,以无需更换你不用更换为拆开的序列意思。
.. I assume that weights are positive integers and by "without replacement" you mean without replacement for the unraveled sequence.
下面是一个基于random.sample和O(log n)的一个解决方案 __ __的GetItem
:
Here's a solution based on random.sample and O(log n) __getitem__
:
import bisect
import random
from collections import Counter, Sequence
def weighted_sample(population, weights, k):
return random.sample(WeightedPopulation(population, weights), k)
class WeightedPopulation(Sequence):
def __init__(self, population, weights):
assert len(population) == len(weights) > 0
self.population = population
self.cumweights = []
cumsum = 0 # compute cumulative weight
for w in weights:
cumsum += w
self.cumweights.append(cumsum)
def __len__(self):
return self.cumweights[-1]
def __getitem__(self, i):
if not 0 <= i < len(self):
raise IndexError(i)
return self.population[bisect.bisect(self.cumweights, i)]
示例
total = Counter()
for _ in range(1000):
sample = weighted_sample("abc", [1,10,2], 5)
total.update(sample)
print(sample)
print("Frequences %s" % (dict(Counter(sample)),))
# Check that values are sane
print("Total " + ', '.join("%s: %.0f" % (val, count * 1.0 / min(total.values()))
for val, count in total.most_common()))
输出
['b', 'b', 'b', 'c', 'c']
Frequences {'c': 2, 'b': 3}
Total b: 10, c: 2, a: 1
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