scikit learn - How does logistic regression build Sigmoid curve from categorical dependent variable?

Question

I'm exploring the Scikit-learn logistic regression algorithm. I understand that as part of the training, the algorithm builds a regression curve where the y-variable ranges from 0 to 1 (sigmoid S-curve). The y-variable is a continuous variable here (although in reality it is a discrete variable). .

How is the algorithm able to learn the S-curve, when the training dataset reflects reality and includes the y-variable as a discrete variable? There is no probability estimate in the training, so I'm wondering how is the algorithm able to learn the S-curve.

question from:https://stackoverflow.com/questions/65546466/how-does-logistic-regression-build-sigmoid-curve-from-categorical-dependent-vari

Answer 1

There is no probability estimate in the training

Sure, but we pretend there is for modeling purposes. We want to maximize the probability of, as you call it, “reality”—if the observed response (the discrete value you refer to) is a 0, we want to predict that with probability 1; similarly, if the response is a 1, we want to predict that with probability 1.

Fitting the model to one data point, getting the right answer with probability 1, would be easy. Of course, we have more than one data point. We have to balance concerns between these. We want the predicted value sigmoid(weights * features) to be close to the true response (0 or 1) for all of the data points, but there may not be a way to set the parameters of the model to achieve this. (That is, the data may not be linearly separable.)