样本量为 1 是否考虑水库采样？

Question

I just want to know that my code is reservoir sampling. I have a stream of pageviews that I just want to process. I'm processing one pageview at a time. However, since most of the pageviews are the same so I just want to randomly pick any pageview (one at a time to process). For example, I have a pageview of

[www.example.com, www.example.com, www.example1.com, www.example3.com, ...]

I'm processing one element at a time. Here's my code.

import random

def __init__(self):
  self.counter = 0

def processable():
  self.counter += 1
  return random.random() < 1.0 / self.counter

Answer 1

Following the algorithm for the reservoir sampling (can be found here: https://en.wikipedia.org/wiki/Reservoir_sampling ) where we store just one pageview (reservoir size=1), the following implementation shows that how the strategy of probabilistic selection from the streaming pageviews leads to a uniform selection probabilities:

import numpy as np
import matplotlib.pyplot as plt
max_num = 10 # maximum number of pageviews we want to consider
# replicate the experiment ntrials times and find the probability for selection of any pageview
pageview_indices = []
ntrials = 10000
for _ in range(ntrials):
    pageview_index = None # index of the single pageview to be kept
    i = 0
    while True: # streaming pageviews
        i += 1 # next pageview
        if i > max_num:
            break
        # keep first pageview and from next pageview onwards discard the old one kept with probability 1 - 1/i
        pageview_index = 1 if i == 1 else np.random.choice([pageview_index, i], 1, p=[1-1./i, 1./i])[0]
        #print 'pageview chosen:',  pageview_index
    print 'Final pageview chosen:',  pageview_index
    pageview_indices.append(pageview_index)
plt.hist(pageview_indices, max_num, normed=1, facecolor='green', alpha=0.75)
plt.xlabel('Pageview Index')
plt.ylabel('Probability Chosen')
plt.title('Reservoir Sampling')
plt.axis([0, max_num+1, 0, 0.15])
plt.xticks(range(1, max_num+1))
plt.grid(True)

As can be seen from above, the probability of the pageview indices chosen is almost uniform (1/10 for each of 10 pageviews), it can be mathematically proved to be uniform too.