forecasting interval and probabilistic prediction interface refactor/re-design

Let’s think about a re-factoring of the forecasting interface for interval and probabilistic predictions.

I think we should have:

• predict_interval, this should take alpha as in predict and return quantiles; one should be able to pass lists of alpha too (if the forecaster supports it). If a list is passed, we need to think about the return object - perhaps a data frame, with nested column index if we are in the multivariate case? Or, we could annotate columns [variablename]__[statistic], e.g., temperature__P95 using the reserved double-underscore.
• predict_var, this should return predictive variance (not quantiles) - note that that’s what comes out Gaussian process type regressors primarily.
• predict_proba, this returns a skpro-like distribution object. May requires work on skpro, or could use tensorflow-probability distributions.

For the first two, we could alternatively think about return flags and return objects in predict, but that just seems very messy to me.

Any opinions? @aiwalter, @mloning, @RNKuhns

[fkiraly]

I’m not aware of any other refactoring that’s ongoing that would interfere with this.

Not refactoring, but a minor interface change, #1410, might interfere, since it also changes the base forecasters’ predict. It’s probably not going to touch the same lines though, in predict, but worth being aware.

We could add the new interface point while maintaining the old one for now, perhaps that’s a first step.

That’s precisely what my STEP suggests in the “downwards compatibility” section 😃

[mloning]

I’m not aware of any other refactoring that’s ongoing that would interfere with this. It’s hard to say whether to split it up further. We could add the new interface point while maintaining the old one for now, perhaps that’s a first step. Then if everything works, we could deprecate the old way of generating prediction intervals (i.e. via the return_pred_int argument in predict).