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For example:

The probabilistic approach of logistic regression involves the MLE (maximum likelihood estimation) maximizing the likelihood function, or in other words, finding the best parameters for the best fit line using partial derivatives. These parameters are then used in the logit and sigmoid functions for the final binary classification.

The geometric approach involves assigning +1 and -1 to the classes 1 and 0 respectively. A random line is fit to the data. The distance between the points and the line is calculated, and the correct and incorrect misclassifications are identified based on the y*d formula. This process continues till we find a line with the least number of misclassifications.

These classification approaches are completely different from each other. So, which one does logistic regression use? And why do we have two different approaches?

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Logistic regression uses the first approach.

Despite this common misconception, logistic regression does not do classification. Logistic regression returns probability values, and then we can do what we want with the probability values, which may or may not be classification.

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  • $\begingroup$ Thank you very much. This is the concise answer I was looking for. And why do we have a geometric approach when it isn't used? $\endgroup$
    – Apoorva
    Dec 16, 2021 at 12:31
  • $\begingroup$ The second approach is like an SVM, which has shown itself to have strong performance…but it isn’t logistic regression. @Apoorva $\endgroup$
    – Dave
    Dec 16, 2021 at 12:53

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