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The conformalization (or "calibration") set
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**MAPIE** is based on two types of techniques for measuring uncertainty in regression and classification:

- the split-conformal predictions,
- the cross-conformal predictions.

In all cases, the training/conformalization process can be broken down as follows:

- Train a model using the training set (or full dataset if cross-conformal).
- Estimate conformity scores using the conformalization set (or full dataset if cross-conformal).
- Predict target on test data to obtain prediction intervals/sets based on these conformity scores.


1. Split conformal predictions
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- Compute conformity scores ("conformalization") on a conformalization set not seen by the model during training.
  (Use :func:`~mapie.utils.train_conformalize_test_split` to obtain the different sets.)

**MAPIE** then uses the conformity scores to estimate sets associated with the desired coverage on new data with strong theoretical guarantees.

Split conformal predictions with a pre-trained model
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.. image:: images/cp_prefit.png
    :width: 800
    :align: center


Split conformal predictions with an untrained model
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.. image:: images/cp_split.png
    :width: 800
    :align: center


2. Cross conformal predictions
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- Conformity scores on the whole dataset obtained by cross-validation,
- Perturbed models generated during the cross-validation.

**MAPIE** then combines all these elements in a way that provides prediction intervals on new data with strong theoretical guarantees.

.. image:: images/cp_cross.png
    :width: 600
    :align: center