DOC: Update The conformity (or "calibration") set page, with an emphasis on MAPIE methods rather than the internal works (#625)

Author: Valentin-Laurent

doc/images/cp_cross.png

@@ -1,45 +1,46 @@
 ################################################################
-The calibration (or "conformity") set
+The conformity (or "calibration") set
 ################################################################
 
-**MAPIE** is based on two types of techniques:
+**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/calibration process can be broken down as follows:
+In all cases, the training/conformalization process can be broken down as follows:
 
-- Identify a basic model (or pre-trained model).
-- Wrap it with the MAPIE class.
-- Fit new model to calibration data (or full data if cross-validation) to estimate conformity scores.
-- Predict target on test data to obtain prediction intervals/sets based on conformity scores.
+- Train a model using the training set (or full dataset if cross-conformal).
+- Estimate conformity scores using the conformity 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
 ==============================
 
-- Construction of a conformity score.
-- Calibration of the conformity score on a calibration set not seen by the model during training.
+- Compute conformity scores ("conformalization") on a conformity set not seen by the model during training.
 
-**MAPIE** then uses the calibrated conformity scores to estimate sets associated with the desired coverage on new data with strong theoretical guarantees.
+**MAPIE** then uses the conformity scores to estimate sets associated with the desired coverage on new data with strong theoretical guarantees.
 
-.. image:: images/cp_split.png
+Split conformal predictions with a pre-trained model
+------------------------------------------------------------------------------------
+
+.. image:: images/cp_prefit.png
     :width: 600
     :align: center
 
 
-Prefit mode of split conformal predictions
-------------------------------------------
+Split conformal predictions with an untrained model
+------------------------------------------------------------------------------------
 
-.. image:: images/cp_prefit.png
+.. image:: images/cp_split.png
     :width: 600
     :align: center
 
 
 2. Cross conformal predictions
 ==============================
 
-- Conformity scores on the whole training set obtained by cross-validation,
+- 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.