python中的联合熵

Question

I have two arrays:

import numpy as np
a = np.array(['1','2','3'])
b = np.array(['3','4','1','5'])

I want to calculate joint entropy. I've found some materials to make it like:

import numpy as np
def entropy(*X):
    return = np.sum(-p * np.log2(p) if p > 0 else 0 
        for p in (np.mean(reduce(np.logical_and, (predictions == c for predictions, c in zip(X, classes))))
        for classes in itertools.product(*[set(x) for x in X])))

Seems to work fine with len(a) = len(b) but it ends with error if len(a) != len(b)

UPD: Arrays a and b were created from exampled main input:

b:3 p1:1 p2:6 p5:7
b:4 p1:2 p7:2
b:1 p3:4 p5:8
b:5 p1:3 p4:4 

Where array a was created from p1 values. So not every line consists of every pK but every has b property. I need to calculate mutual information I(b,pK) for each pK .

Answer 1

Assuming you are talking about the Joint Shannon Entropy , the formula straightforward:

The problem with this, when I look at what you've done so far, is that you lack P(x,y) , ie the joint probability of the two variables occurring together. It looks like a,b are the individual probabilities for events a and b respectively.

You have other problems with your posted code (mentioned in the comments):

1. Your variables are not a numeric data type a=["1","2"] is not the same as a=[1,2] . One is a string, the other is a number.
2. The length of your input data must be the same, ie for every x in A, there must be ay in B AND you need to you know the joint probability P(x,y) .

Answer 2

Here is an idea:

• convert data to numbers
• add padding example zeros

import numpy as np
from scipy import stats

a = np.array(['1','2','3','0'])
b = np.array(['3','4','1','5'])
aa = [int(x) for x in a]
bb = [int(x) for x in b]
je =  stats.entropy(aa,bb)
print("joint entropy : ",je)

output: 0.9083449242695364