The Sigmoid Function in Logistic Regression

In learning about logistic regression, I was at first confused as to why a sigmoid function was used to map from the inputs to the predicted output. I mean, sure, it's a nice function that cleanly maps from any real number to a range of -1 to 1, but where did it come from? This notebook hopes to explain. With classification, we have a sample with some attributes (a.k.a features), and based on those attributes, we want to know whether it belongs to a binary class or not. The regression algorithm could fit these weights to the data it sees, however, it would seem hard to map an arbitrary linear combination of inputs, each would may range from -\infty to \infty to a probability value in the range of 0 to 1 .