我正在Pytorch和Tensorflow2中实现Skipgram模型。我对常用字的二次采样的实施方式有疑问。根据本文的逐字记录，二次采样单词wi的概率计算为

其中t是自定义阈值（通常是一个很小的值，例如 0.0001 ），而f是文档中单词的出现频率。尽管作者以不同但几乎等效的方式实现了它，但让我们坚持这个定义。

在计算P(wi)时，我们最终会得到负值。例如，假设我们有100个单词，并且其中一个单词的出现频率比其他单词高得多（因为我的数据集就是这种情况）。

import numpy as np
import seaborn as sns

np.random.seed(12345)

# generate counts in [1,20]
counts = np.random.randint(low=1,high=20,size=99)

# add an extremely bigger count
counts = np.insert(counts,100000)

# compute frequencies
f = counts/counts.sum()

# define threshold as in paper
t = 0.0001

# compute probabilities as in paper
probs = 1 - np.sqrt(t/f)
sns.distplot(probs);

问：使用这种“概率”实现子采样的正确方法是什么？

作为附加信息，我已经看到在keras函数keras.preprocessing.sequence.make_sampling_table中采用了不同的方法：

def make_sampling_table(size,sampling_factor=1e-5):
    """Generates a word rank-based probabilistic sampling table.
    Used for generating the `sampling_table` argument for `skipgrams`.
    `sampling_table[i]` is the probability of sampling
    the i-th most common word in a dataset
    (more common words should be sampled less frequently,for balance).
    The sampling probabilities are generated according
    to the sampling distribution used in word2vec:
    ```
    p(word) = (min(1,sqrt(word_frequency / sampling_factor) /
        (word_frequency / sampling_factor)))
    ```
    We assume that the word frequencies follow Zipf's law (s=1) to derive
    a numerical approximation of frequency(rank):
    `frequency(rank) ~ 1/(rank * (log(rank) + gamma) + 1/2 - 1/(12*rank))`
    where `gamma` is the Euler-Mascheroni constant.
    # Arguments
        size: Int,number of possible words to sample.
        sampling_factor: The sampling factor in the word2vec formula.
    # Returns
        A 1D Numpy array of length `size` where the ith entry
        is the probability that a word of rank i should be sampled.
    """
    gamma = 0.577
    rank = np.arange(size)
    rank[0] = 1
    inv_fq = rank * (np.log(rank) + gamma) + 0.5 - 1. / (12. * rank)
    f = sampling_factor * inv_fq

    return np.minimum(1.,f / np.sqrt(f))