I am facing a rather strange problem. Machine learning gives us a probability of a data point belonging to either class (classification) or the actual estimate of the dependent variable given independent variables (regression).
I am interested in building a model that has output such as $P(y \leq \hat{y} | x)$, that is, the 'probability of actual value to be less than or equal to predicted-value given x'.
I have gone through confidence intervals and predictions intervals for Logistic Regression. Are they best, I can do? Is there stream of research or machine learning, which I am missing.