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I have two questions regarding the use of Sigmoid in MLE:

  • Clearly, the Sigmoid Function is not a PDF. But in the MLE of Logistic Regression, we see Sigmoid being used as if it is a PDF. Is my understanding correct? If not, how to see it correctly? If yes, what is the reason behind it?

  • I have seen at multiple places that people take the Sigmoid to infer probability. However there is not any constraint put to ensure that the sum of all those probabilities must be 1. What is the correct explanation behind it? For example, in arxiv.org/pdf/1402.3722.pdf , please view page 3.

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