alt Hacker NewsFor a single prediction, sure. But the model doesn't make a single prediction and then stop existing. It makes an unbounded number of future predictions and under that assumption it is reasonable to expect the model to behave optimally under Bayes rule - which has a unique global minimizer at E[(Y-F(X))^2].
So counter to your claim that "It doesn't trivially imply that the model would learn sensible distributions under uncertainty" I think you need to consider what it means to optimally update a posterior under the global minimizer of the true conditional distribution.
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> It makes an unbounded number of future predictions
nit: it's trained on finitely many samples.
> So counter to your claim that "It doesn't trivially imply that the model would learn sensible distributions under uncertainty" I think you need to consider what it means to optimally update a posterior under the global minimizer of the true conditional distribution.
Huh? That's not counter to anything I said. All I said was it's not trivially implied.
The thing I had to wrap my head around is: For a "classic" classifier, the classes are fixed and the data distribution is p(x,y). The calibration is checked over this single distribution. Jev makes the tasks part of the input, so the data distribution is p(task,x,y) and calibration is averaged over that joint distribution. What follows is that while for classic classifiers, calibration brakes down if your x was out-of-distribution, it can now also break if your task is out of distribution. The big question now is: Can subtle differences in phrasing your task already lead to this? And the only way to verify calibration is having ground truth data to validate on. Also: Calibration over p(task, x, y) means calibrated on average across tasks. Even an in-distribution task can be over- or underconfident while the average looks fine.