Design - comparison `MapieTimeSeriesRegressor` and `sktime` APIs

[fkiraly]

As previously discussed, a quick review of MapieTimeSeriesRegressor against sktime APIs.

• I think the regressor is simply a forecaster, with tags: capability:pred_int (can predict probabilistically), and ignores-exogeneous-X: False, as it uses exogenous data
• The interface matches as follows:
  • fit and predict map onto each other, with slightly different args.
  • mapie's partial_fit is sktime's update method.
  • The probabilisitc predict (if alpha is passed) is sktime's predict_interval.
• possibly inconsistent interface elements:
  • it looks like exogenous data X is absolutely required in mapie (is that true?), whereas theoretically the implemented estimator does not need it, and sktime also assumes that every forecaster can be run without X, with y only
  • sample weights are currently not supported in sktime
• in sktime, fit and predict cannot be given additional parameters, all non-data/task arguments should be in the constructor. So, ensemble or optimize_beta should move to the constructor, from predict.

From an interfacing perspective, using the maximal extension template with filling only predict_interval should work: https://github.com/sktime/sktime/blob/main/extension_templates/forecasting.py
(possibly also filling in predict_proba with an Empirical distribution)