diff --git a/quapy/data/base.py b/quapy/data/base.py
index 8ba0aec..72561e4 100644
--- a/quapy/data/base.py
+++ b/quapy/data/base.py
@@ -9,6 +9,7 @@ from sklearn.model_selection import train_test_split, RepeatedStratifiedKFold
 from numpy.random import RandomState
 from quapy.functional import strprev
 from quapy.util import temp_seed
+import functional as F
 
 
 class LabelledCollection:
@@ -34,8 +35,7 @@ class LabelledCollection:
         self.labels = np.asarray(labels)
         n_docs = len(self)
         if classes is None:
-            self.classes_ = np.unique(self.labels)
-            self.classes_.sort()
+            self.classes_ = F.classes_from_labels(self.labels)
         else:
             self.classes_ = np.unique(np.asarray(classes))
             self.classes_.sort()
diff --git a/quapy/functional.py b/quapy/functional.py
index fd7a88f..b508d76 100644
--- a/quapy/functional.py
+++ b/quapy/functional.py
@@ -7,6 +7,20 @@ import scipy
 import numpy as np
 
 
+# ------------------------------------------------------------------------------------------
+# General utils
+# ------------------------------------------------------------------------------------------
+
+def classes_from_labels(labels):
+    """
+    Obtains a np.ndarray with the (sorted) classes
+    :param labels:
+    :return:
+    """
+    classes = np.unique(labels)
+    classes.sort()
+    return classes
+
 # ------------------------------------------------------------------------------------------
 # Counter utils
 # ------------------------------------------------------------------------------------------
diff --git a/quapy/method/_neural.py b/quapy/method/_neural.py
index c2b4de6..404090f 100644
--- a/quapy/method/_neural.py
+++ b/quapy/method/_neural.py
@@ -149,13 +149,13 @@ class QuaNetTrainer(BaseQuantifier):
         train_data_embed = LabelledCollection(self.classifier.transform(train_data.instances), train_data.labels, self._classes_)
 
         self.quantifiers = {
-            'cc': CC(self.classifier).fit(None, fit_classifier=False),
-            'acc': ACC(self.classifier).fit(None, fit_classifier=False, val_split=valid_data),
-            'pcc': PCC(self.classifier).fit(None, fit_classifier=False),
-            'pacc': PACC(self.classifier).fit(None, fit_classifier=False, val_split=valid_data),
+            'cc': CC(self.classifier, fit_classifier=False).fit(*valid_data.Xy),
+            'acc': ACC(self.classifier, fit_classifier=False).fit(*valid_data.Xy),
+            'pcc': PCC(self.classifier, fit_classifier=False).fit(*valid_data.Xy),
+            'pacc': PACC(self.classifier, fit_classifier=False).fit(*valid_data.Xy),
         }
         if classifier_data is not None:
-            self.quantifiers['emq'] = EMQ(self.classifier).fit(classifier_data, fit_classifier=False)
+            self.quantifiers['emq'] = EMQ(self.classifier, fit_classifier=False).fit(*valid_data.Xy)
 
         self.status = {
             'tr-loss': -1,
diff --git a/quapy/method/aggregative.py b/quapy/method/aggregative.py
index 0be9fb1..e890be9 100644
--- a/quapy/method/aggregative.py
+++ b/quapy/method/aggregative.py
@@ -100,7 +100,7 @@ class AggregativeQuantifier(BaseQuantifier, ABC):
         # consistency checks: fit_classifier?
         if self.fit_classifier:
             if fitted:
-                raise RuntimeWarning(f'the classifier is already fitted, by {fit_classifier=} was requested')
+                raise RuntimeWarning(f'the classifier is already fitted, but {fit_classifier=} was requested')
         else:
             assert fitted, (f'{fit_classifier=} requires the classifier to be already trained, '
                             f'but this does not seem to be')
@@ -158,7 +158,7 @@ class AggregativeQuantifier(BaseQuantifier, ABC):
 
         predictions, labels = None, None
         if isinstance(self.val_split, int):
-            assert self.fit_classifier, f'unexpected value for {self.fit_classifier=}'
+            assert self.fit_classifier, f'{self.__class__}: unexpected value for {self.fit_classifier=}'
             num_folds = self.val_split
             n_jobs = self.n_jobs if hasattr(self, 'n_jobs') else qp._get_njobs(None)
             predictions = cross_val_predict(self.classifier, X, y, cv=num_folds, n_jobs=n_jobs, method=self._classifier_method())
diff --git a/quapy/method/base.py b/quapy/method/base.py
index a2dcfe0..1d7ad34 100644
--- a/quapy/method/base.py
+++ b/quapy/method/base.py
@@ -46,7 +46,7 @@ class BaseQuantifier(BaseEstimator):
         :param X: array-like
         :return: `np.ndarray` of shape `(n_classes,)` with class prevalence estimates.
         """
-        ...
+        return self.predict(X)
 
 
 class BinaryQuantifier(BaseQuantifier):
diff --git a/quapy/method/confidence.py b/quapy/method/confidence.py
index f68f956..f54768c 100644
--- a/quapy/method/confidence.py
+++ b/quapy/method/confidence.py
@@ -450,17 +450,13 @@ class BayesianCC(AggregativeCrispQuantifier, WithConfidenceABC):
 
     :param classifier: a scikit-learn's BaseEstimator, or None, in which case the classifier is taken to be
         the one indicated in `qp.environ['DEFAULT_CLS']`
-    :param fit_classifier: whether to train the learner (default is True). Set to False if the
-        learner has been trained outside the quantifier.
-    :param val_split: specifies the data used for generating classifier predictions. This specification
+    :param val_split:  specifies the data used for generating classifier predictions. This specification
         can be made as float in (0, 1) indicating the proportion of stratified held-out validation set to
         be extracted from the training set; or as an integer (default 5), indicating that the predictions
         are to be generated in a `k`-fold cross-validation manner (with this integer indicating the value
-        for `k`); or as a tuple (X,y) defining the specific set of data to use for validation.
-        This hyperparameter is only meant to be used when the heuristics are to be applied, i.e., if a
-        calibration is required. The default value is None (meaning the calibration is not required). In
-        case this hyperparameter is set to a value other than None, but the calibration is not required
-        (calib=None), a warning message will be raised.
+        for `k`); or as a tuple `(X,y)` defining the specific set of data to use for validation. Set to
+        None when the method does not require any validation data, in order to avoid that some portion of
+        the training data be wasted.
     :param num_warmup: number of warmup iterations for the MCMC sampler (default 500)
     :param num_samples: number of samples to draw from the posterior (default 1000)
     :param mcmc_seed: random seed for the MCMC sampler (default 0)
@@ -484,11 +480,9 @@ class BayesianCC(AggregativeCrispQuantifier, WithConfidenceABC):
         if num_samples <= 0:
             raise ValueError(f'parameter {num_samples=} must be a positive integer')
 
-        # if (not isinstance(val_split, float)) or val_split <= 0 or val_split >= 1:
-        #     raise ValueError(f'val_split must be a float in (0, 1), got {val_split}')
-
         if _bayesian.DEPENDENCIES_INSTALLED is False:
-            raise ImportError("Auxiliary dependencies are required. Run `$ pip install quapy[bayes]` to install them.")
+            raise ImportError("Auxiliary dependencies are required. "
+                              "Run `$ pip install quapy[bayes]` to install them.")
 
         super().__init__(classifier, fit_classifier, val_split)
         self.num_warmup = num_warmup
@@ -514,8 +508,11 @@ class BayesianCC(AggregativeCrispQuantifier, WithConfidenceABC):
         """
         pred_labels = classif_predictions
         true_labels = labels
-        self._n_and_c_labeled = confusion_matrix(y_true=true_labels, y_pred=pred_labels,
-                                                 labels=self.classifier.classes_)
+        self._n_and_c_labeled = confusion_matrix(
+            y_true=true_labels,
+            y_pred=pred_labels,
+            labels=self.classifier.classes_
+        ).astype(float)
 
     def sample_from_posterior(self, classif_predictions):
         if self._n_and_c_labeled is None:
diff --git a/quapy/method/meta.py b/quapy/method/meta.py
index 3e9ce4c..17c9903 100644
--- a/quapy/method/meta.py
+++ b/quapy/method/meta.py
@@ -414,15 +414,15 @@ def _delayed_new_instance(args):
     sample = data.sampling_from_index(sample_index)
 
     if val_split is not None:
-        model.fit(sample, val_split=val_split)
+        model.fit(*sample.Xy, val_split=val_split)
     else:
-        model.fit(sample)
+        model.fit(*sample.Xy)
 
     tr_prevalence = sample.prevalence()
     tr_distribution = get_probability_distribution(posteriors[sample_index]) if (posteriors is not None) else None
 
     if verbose:
-        print(f'\t\--fit-ended for prev {F.strprev(prev)}')
+        print(f'\t--fit-ended for prev {F.strprev(prev)}')
 
     return (model, tr_prevalence, tr_distribution, sample if keep_samples else None)
 
diff --git a/quapy/method/non_aggregative.py b/quapy/method/non_aggregative.py
index 00bdbed..eff2283 100644
--- a/quapy/method/non_aggregative.py
+++ b/quapy/method/non_aggregative.py
@@ -20,14 +20,16 @@ class MaximumLikelihoodPrevalenceEstimation(BaseQuantifier):
     def __init__(self):
         self._classes_ = None
 
-    def fit(self, data: LabelledCollection):
+    def fit(self, X, y):
         """
         Computes the training prevalence and stores it.
 
-        :param data: the training sample
+        :param X: array-like of shape `(n_samples, n_features)`, the training instances
+        :param y: array-like of shape `(n_samples,)`, the labels
         :return: self
         """
-        self.estimated_prevalence = data.prevalence()
+        self._classes_ = F.classes_from_labels(labels=y)
+        self.estimated_prevalence = F.prevalence_from_labels(y, classes=self._classes_)
         return self
 
     def predict(self, X):
@@ -114,9 +116,10 @@ class DMx(BaseQuantifier):
         """
         self.nfeats = X.shape[1]
         self.feat_ranges = _get_features_range(X)
+        n_classes = len(np.unique(y))
 
         self.validation_distribution = np.asarray(
-            [self.__get_distributions(X[y==cat]) for cat in range(data.n_classes)]
+            [self.__get_distributions(X[y==cat]) for cat in range(n_classes)]
         )
 
         return self
diff --git a/quapy/tests/test_methods.py b/quapy/tests/test_methods.py
index c2931b9..f2d9cdd 100644
--- a/quapy/tests/test_methods.py
+++ b/quapy/tests/test_methods.py
@@ -80,7 +80,7 @@ class TestMethods(unittest.TestCase):
 
             print(f'testing {base_quantifier} on dataset {dataset.name} with {policy=}')
             ensemble = Ensemble(quantifier=base_quantifier, size=3, policy=policy, n_jobs=-1)
-            ensemble.fit(dataset.training)
+            ensemble.fit(*dataset.training.Xy)
             estim_prevalences = ensemble.predict(dataset.test.instances)
             self.assertTrue(check_prevalence_vector(estim_prevalences))
 
@@ -116,6 +116,7 @@ class TestMethods(unittest.TestCase):
                 print('testing', q)
                 q.fit(*dataset.training.Xy)
                 estim_prevalences = q.predict(dataset.test.X)
+                print(estim_prevalences)
                 self.assertTrue(check_prevalence_vector(estim_prevalences))