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The best method to calculate mutual information for pairs using numpy is to use the mutual_info_score() function from the sklearn.metrics module.

Here is an example code:

import numpy as np
from sklearn.metrics import mutual_info_score

# generate sample data
x = np.random.randint(0, 5, 100)
y = np.random.randint(0, 5, 100)

# calculate mutual information between x and y
mi = mutual_info_score(x, y)
print(mi)

In this example, we generate two random arrays x and y with 100 elements each. We then pass them to the mutual_info_score() function, which returns the mutual information score between the two arrays.