In machine learning, linear regression is often used for prediction and logistic regression for classification. Both may be implemented through gradient descent. Additionaly, linear regression has also a closed form set of equations that allow for finding the solution in one step, but there is no known closed form equivalent for logistic regression.
However, if we focus on the points closest to the linear decision boundary, it seems that a reasonable solution may come from a linear regression of those particular points only. In other words, one may attempt to solve the logistic regression as a weighted linear regression, where the weight of each data point is associated to some local measure of uncertainty.
The question is how such an uncertainty can be defined as a function of available data.