EnbPI Prediction Intervals not centered correctly

[jawharmohammed]

Hello MAPIE team,

Congratulations on your excellent work! I have identified an error in the computation of the prediction intervals generated by EnbPI in MAPIE.

Describe the bug

The prediction intervals generated by the EnbPI method in MAPIE do not align with the expected behavior described in the pseudo code provided in the original paper.

Expected behavior

The prediction intervals should be centered at:
[
f^{\Phi}_t(x_t) = \Phi \left(f^{\Phi}_i(x_t), i = 1, \ldots, T \right)
]

However, in the predict function of the EnsembleRegressor class, where the interval bounds are initialized, the bounds are set with the out-of-fold (oof) prediction of a single estimator rather than the aggregation of y_pred_multi as indicated in the pseudocode. This issue is highlighted in the following screenshot:

Suggested Solution

A simple solution would be to replace this part with something like the following:

Thank you for your attention to this matter!