How To Use Softmax Output In Python For Neural-network And Machine-learning To Interpret Multinomial Logit Model?

It involves the use of softmax function output for machine-learning and neural-network to understand and interpret Multinomial Logit Model.

Solution 1:

Softmax function is one of the most important output function used in deep learning within the neural networks (see Understanding Softmax in minute by Uniqtech). The Softmax function is apply where there are three or more classes of outcomes. The softmax formula takes the e raised to the exponent score of each value score and devide it by the sum of e raised the exponent scores values. For example, if I know the Logit scores of these four classes to be: [3.00, 2.0, 1.00, 0.10], in order to obtain the probabilities outputs, the softmax function can be apply as follows:

1. import numpy as np

2. def softmax(x):

3. z = np.exp(x - np.max(x))
4. return z / z.sum()
5. scores = [3.00, 2.0, 1.00, 0.10]

6. print(softmax(scores))

7. Output: probabilities (p) = 0.642 0.236 0.087 0.035

The sum of all probabilities (p) = 0.642 + 0.236 + 0.087 + 0.035 = 1.00. You can try to substitute any value you know in the above scores, and you will get a different values. The sum of all the values or probabilities will be equal to one. That’s makes sense, because the sum of all probability is equal to one, thereby turning Logit scores to probability scores, so that we can predict better. Finally, the softmax output, can help us to understand and interpret Multinomial Logit Model. If you like the thoughts, please leave your comments below.