with regards to the Logistic Regression cost function of:
And hypothesis:
Is there a way to tell the +/- of the error for how "confident" the hypothesis is?
E.g. if the +/- of the error was 0.1, I would know that if my hypothesis predicted 0.4 it could be 0.1 greater (0.5) or 0.1 less (0.3)
This is for binary classification
Logistic regression is just a generalized linear model, so there is a linear regression lurking in here whose errors are supposed to be normally distributed, and from which you can get confidence intervals in the usual way.
That is you have a linear predictor (the -theta' * x part), transformed by the inverse of a link function (the logistic function). You can transform prediction +/- confidence interval using this inverse link to get your +/- in probability terms. It won't be symmetric.
Nice writeup of how to do this in R: https://stackoverflow.com/a/14424417/64174
