Is the distinction between "aleatoric" and "epistemic" uncertainty practically meaningful (or even well defined) in any real sense? Aleotoric uncertainty refers to irreducible unpredictability (e.g. unrealized randomness in nature) whereas epistemic refers to model uncertainty.
But note that there is no way to distinguish the two empirically: Suppose the world is such that the probability of rain every day is 1/2. Alternately, suppose the probability of rain is 1 or 0 every day, but selected at random. And suppose I predict p = 1/2 every day.
In the first case my model is correct and the uncertainty is all aleatoric. In the second case there is in fact no aleatoric uncertainty and my uncertainty is epistemic. But of course the two scenarios are observationally equivalent --- there is no way to distinguish the two.
It is hard for me as a computer scientist to put lots of importance on a distinction that has no observational consequences. At a more fundamental level, whether uncertainty is epistemic or aleotoric seems to have everything to do with our model and nothing to do with the world.
We think of coin flips as being random (pure aleotoric uncertainty) but that is only because we don't measure the initial conditions accurately enough and perform the necessary computations. If we did the aleotoric uncertainty vanishes. So maybe the uncertainty is epistemic.
Anyhow lots of people seem to think it is important so I'm willing to believe my thinking is naive. What is the case for this distinction being of first order importance?
Deciding when to devote resources to reduce uncertainty is important but this is true even if all uncertainty is epistemic --- the marginal cost of reducing uncertainty can vary widely (e.g. the coinflip example) and it might not always be your best return on invesment.
@Aaroth Just ask multiple times a day in your example whether it rains and the difference becomes clear. Epistemic uncertainty as reducible uncertainty makes a lot of sense for a given model, where you can either use the expected information gain for the parameters or future
@Aaroth @fbickfordsmith has some excellent work addressing this issue that might be of interest:
@Aaroth I agree, but I'm a nobody, so please take my views with a grain of salt. Aleatoric and epistemic are well defined in statistics, but their interpretation in deep learning is very vague. Model complexity which strongly affects aleatoric and epistemic is not factored in usually.
@Aaroth Agree. *The only* way I can think of isolating aleatoric uncertainty is to have a perfectly specified model, and then asymptotically as n → ∞ epistemic uncertainty shrinks to zero and whatever uncertainty remains is aleatoric. Any other situation, they seem inseparable.
@Aaroth Yeah aleatoric uncertainty rarely exists. Better to model it as partially observable if you really care.
@Aaroth you say aleatoric, and I say aleotoric. why can’t we just get along?
@Aaroth I think they are useful concepts practically b/c often you can't reduce a model's prediction error to zero even if it is an optimal model. So keeping the concept of reducible and irreducible uncertainty in mind when modeling is helpful to figure out what "optimal" even means.
@Aaroth A practical implication is for ML models that can refrain from predicting. Aleatoric uncertainty translates into ML models that reject cases close to their decision boundary. Epistemic translates into models that reject instances that are far away from the training distribution.
@Aaroth If you're deciding which data is going to be useful for training your model, you want data that has high epistemic uncertainty samples and not high aleotoric uncertainty (only).
@Aaroth Well technically epistemic is lack of knowledge. Still you're right that they're not black and white. Most problems have a mix of both. But without trying to account for them you have no idea whether it's worth trying to reduce epistemic uncertainty
@Aaroth No there isn't. Just a bunch of Google papers that mostly mislead the community on the topic for like ~5 years.
@Aaroth I think the first example actually points to the fact that under some kind of non-stationarity that it's difficult to distinguish; however, if you are talking about model performance for some fixed underlying distribution, maybe there's a meaningful difference?