Predicting with confidence: the best machine learning idea you never heard of

One of the disadvantages of machine learning as a discipline is the lack of reasonable confidence intervals on a given prediction. There are all kinds of reasons you might want such a thing, but I think machine learning and data science practitioners are so drunk with newfound powers, they forget where such a thing might be useful. If you're really confident, for example, that someone will click on an ad, you probably want to serve one that pays a nice click through rate. If you have some kind of gambling engine, you want to bet more money on the predictions you are more confident of. Or if you're diagnosing an illness in a patient, it would be awfully nice to be able to tell the patient how certain you are of the diagnosis and what the confidence in the prognosis is. There are various ad hoc ways that people do this sort of thing.