diff --git a/lib/cpp/preprocessing/longitudinal_features_lagger.cpp b/lib/cpp/preprocessing/longitudinal_features_lagger.cpp
index f6e7f352f..5c3e61813 100644
--- a/lib/cpp/preprocessing/longitudinal_features_lagger.cpp
+++ b/lib/cpp/preprocessing/longitudinal_features_lagger.cpp
@@ -6,34 +6,38 @@
 
 #include "tick/preprocessing/longitudinal_features_lagger.h"
 
+
 LongitudinalFeaturesLagger::LongitudinalFeaturesLagger(
-    const SBaseArrayDouble2dPtrList1D &features,
-    const SArrayULongPtr n_lags)
-    : n_intervals(features[0]->n_rows()),
-      n_lags(n_lags),
-      n_samples(features.size()),
-      n_observations(n_samples * n_intervals),
-      n_features(features[0]->n_cols()),
-      n_lagged_features(n_lags->sum() + n_lags->size()) {
-  col_offset = ArrayULong(n_lags->size());
-  col_offset.init_to_zero();
-  if (n_features != n_lags->size()) {
-    TICK_ERROR("Features matrix column number should match n_lags length.");
-  }
-  if ((*n_lags)[0] >= n_intervals) {
-    TICK_ERROR("n_lags elements must be between 0 and (n_intervals - 1).");
-  }
+    ulong n_intervals,
+    SArrayULongPtr _n_lags)
+    : n_intervals(n_intervals),
+      n_lags(_n_lags),
+      n_features(_n_lags->size()),
+      n_lagged_features(_n_lags->size() + _n_lags->sum()) {
+  if (n_lags != nullptr) compute_col_offset(n_lags);
+}
+
+void LongitudinalFeaturesLagger::compute_col_offset(const SArrayULongPtr n_lags) {
+  ArrayULong col_offset_temp = ArrayULong(n_lags->size());
+  col_offset_temp.init_to_zero();
   for (ulong i(1); i < n_lags->size(); i++) {
     if ((*n_lags)[i] >= n_intervals) {
       TICK_ERROR("n_lags elements must be between 0 and (n_intervals - 1).");
     }
-    col_offset[i] = col_offset[i - 1] + (*n_lags)[i-1] + 1;
+    col_offset_temp[i] = col_offset_temp[i - 1] + (*n_lags)[i-1] + 1;
   }
+  col_offset = col_offset_temp.as_sarray_ptr();
 }
 
 void LongitudinalFeaturesLagger::dense_lag_preprocessor(ArrayDouble2d &features,
                                                         ArrayDouble2d &out,
                                                         ulong censoring) const {
+  if (n_intervals != features.n_rows()) {
+    TICK_ERROR("Features matrix rows count should match n_intervals.");
+  }
+  if (n_features != features.n_cols()) {
+    TICK_ERROR("Features matrix column count should match n_lags length.");
+  }
   if (out.n_cols() != n_lagged_features) {
     TICK_ERROR(
         "n_columns of &out should be equal to n_features + sum(n_lags).");
@@ -47,8 +51,9 @@ void LongitudinalFeaturesLagger::dense_lag_preprocessor(ArrayDouble2d &features,
     n_cols_feature = (*n_lags)[feature] + 1;
     for (ulong j = 0; j < n_intervals; j++) {
       row = j;
-      col = col_offset[feature];
-      value = features(row, feature);
+      col = (*col_offset)[feature];
+      // use view_row instead of (row, feature) to be const
+      value = view_row(features, row)[feature];
       max_col = col + n_cols_feature;
       if (value != 0) {
         while (row < censoring && col < max_col) {
@@ -68,6 +73,7 @@ void LongitudinalFeaturesLagger::sparse_lag_preprocessor(ArrayULong &row,
                                                          ArrayULong &out_col,
                                                          ArrayDouble &out_data,
                                                          ulong censoring) const {
+  // TODO: add checks here ? Or do them in Python ?
   ulong j(0), r, c, offset, new_col, max_col;
   double value;
 
@@ -75,7 +81,7 @@ void LongitudinalFeaturesLagger::sparse_lag_preprocessor(ArrayULong &row,
     value = data[i];
     r = row[i];
     c = col[i];
-    offset = col_offset[c];
+    offset = (*col_offset)[c];
     max_col = offset + (*n_lags)[c] + 1;
     new_col = offset;
 
diff --git a/lib/cpp/preprocessing/sparse_longitudinal_features_product.cpp b/lib/cpp/preprocessing/sparse_longitudinal_features_product.cpp
index 9f935634d..a522a7594 100644
--- a/lib/cpp/preprocessing/sparse_longitudinal_features_product.cpp
+++ b/lib/cpp/preprocessing/sparse_longitudinal_features_product.cpp
@@ -7,10 +7,6 @@
 #include "tick/preprocessing/sparse_longitudinal_features_product.h"
 #include <map>
 
-SparseLongitudinalFeaturesProduct::SparseLongitudinalFeaturesProduct(
-    const SBaseArrayDouble2dPtrList1D &features)
-    : n_features(features[0]->n_cols()) {}
-
 ulong SparseLongitudinalFeaturesProduct::get_feature_product_col(
     ulong col1, ulong col2, ulong n_cols) const {
   if (col1 > col2) {  // ensure we have the right order as the following formula
diff --git a/lib/include/tick/preprocessing/longitudinal_features_lagger.h b/lib/include/tick/preprocessing/longitudinal_features_lagger.h
index 8856ec8d4..b9b24cb54 100644
--- a/lib/include/tick/preprocessing/longitudinal_features_lagger.h
+++ b/lib/include/tick/preprocessing/longitudinal_features_lagger.h
@@ -15,17 +15,21 @@ class LongitudinalFeaturesLagger {
  protected:
   ulong n_intervals;
   SArrayULongPtr n_lags;
-  ArrayULong col_offset;
-  ulong n_samples;
-  ulong n_observations;
   ulong n_features;
   ulong n_lagged_features;
+  SArrayULongPtr col_offset;
 
  public:
-  LongitudinalFeaturesLagger(const SBaseArrayDouble2dPtrList1D &features,
-                             const SArrayULongPtr n_lags);
+  // This exists solely for cereal/swig
+  LongitudinalFeaturesLagger() = default;
 
-  void dense_lag_preprocessor(ArrayDouble2d &features, ArrayDouble2d &out,
+  LongitudinalFeaturesLagger(ulong n_intervals,
+                             SArrayULongPtr n_lags);
+
+  void compute_col_offset(SArrayULongPtr n_lags);
+
+  void dense_lag_preprocessor(ArrayDouble2d &features,
+                              ArrayDouble2d &out,
                               ulong censoring) const;
 
   void sparse_lag_preprocessor(ArrayULong &row, ArrayULong &col,
@@ -34,14 +38,26 @@ class LongitudinalFeaturesLagger {
                                ulong censoring) const;
 
   template <class Archive>
-  void serialize(Archive &ar) {
+  void load(Archive &ar) {
+    ar(CEREAL_NVP(n_intervals));
+    ar(CEREAL_NVP(n_features));
+    ar(CEREAL_NVP(n_lagged_features));
+
+    Array<ulong> temp_n_lags, temp_col_offset;
+    ar(cereal::make_nvp("n_lags", temp_n_lags));
+
+    n_lags = temp_n_lags.as_sarray_ptr();
+    col_offset = temp_col_offset.as_sarray_ptr();
+  }
+
+
+  template <class Archive>
+  void save(Archive &ar) const {
     ar(CEREAL_NVP(n_intervals));
-    ar(CEREAL_NVP(n_lags));
-    ar(CEREAL_NVP(col_offset));
-    ar(CEREAL_NVP(n_samples));
-    ar(CEREAL_NVP(n_observations));
     ar(CEREAL_NVP(n_features));
     ar(CEREAL_NVP(n_lagged_features));
+    ar(cereal::make_nvp("n_lags", *n_lags));
+    ar(cereal::make_nvp("col_offset", *col_offset));
   }
 };
 
diff --git a/lib/include/tick/preprocessing/sparse_longitudinal_features_product.h b/lib/include/tick/preprocessing/sparse_longitudinal_features_product.h
index a8e7be058..4653aaafa 100644
--- a/lib/include/tick/preprocessing/sparse_longitudinal_features_product.h
+++ b/lib/include/tick/preprocessing/sparse_longitudinal_features_product.h
@@ -16,8 +16,11 @@ class SparseLongitudinalFeaturesProduct {
   ulong n_features;
 
  public:
+  // This exists soley for cereal/swig
+  SparseLongitudinalFeaturesProduct() = default;
+
   explicit SparseLongitudinalFeaturesProduct(
-      const SBaseArrayDouble2dPtrList1D &features);
+      const ulong n_features): n_features(n_features) {}
 
   inline ulong get_feature_product_col(ulong col1, ulong col2,
                                        ulong n_cols) const;
@@ -28,7 +31,12 @@ class SparseLongitudinalFeaturesProduct {
                                ArrayDouble &out_data) const;
 
   template <class Archive>
-  void serialize(Archive &ar) {
+  void load(Archive &ar) {
+    ar(CEREAL_NVP(n_features));
+  }
+
+  template <class Archive>
+  void save(Archive &ar) const {
     ar(CEREAL_NVP(n_features));
   }
 };
diff --git a/lib/swig/preprocessing/longitudinal_features_lagger.i b/lib/swig/preprocessing/longitudinal_features_lagger.i
index 7cef9bf80..7f9f647c5 100644
--- a/lib/swig/preprocessing/longitudinal_features_lagger.i
+++ b/lib/swig/preprocessing/longitudinal_features_lagger.i
@@ -4,24 +4,25 @@
 #include "tick/preprocessing/longitudinal_features_lagger.h"
 %}
 
+%include serialization.i
+
 class LongitudinalFeaturesLagger {
 
  public:
-  LongitudinalFeaturesLagger(const SBaseArrayDouble2dPtrList1D &features,
-                             const SArrayULongPtr n_lags);
+  // This exists soley for cereal/swig
+  LongitudinalFeaturesLagger();
+
+  LongitudinalFeaturesLagger(ulong n_intervals,
+                             SArrayULongPtr n_lags);
 
   void dense_lag_preprocessor(ArrayDouble2d &features,
                               ArrayDouble2d &out,
                               ulong censoring) const;
 
-  void sparse_lag_preprocessor(ArrayULong &row,
-                               ArrayULong &col,
-                               ArrayDouble &data,
-                               ArrayULong &out_row,
-                               ArrayULong &out_col,
-                               ArrayDouble &out_data,
+  void sparse_lag_preprocessor(ArrayULong &row, ArrayULong &col,
+                               ArrayDouble &data, ArrayULong &out_row,
+                               ArrayULong &out_col, ArrayDouble &out_data,
                                ulong censoring) const;
-
 };
 
 TICK_MAKE_PICKLABLE(LongitudinalFeaturesLagger);
\ No newline at end of file
diff --git a/lib/swig/preprocessing/sparse_longitudinal_features_product.i b/lib/swig/preprocessing/sparse_longitudinal_features_product.i
index 4675c182f..a0a25c55d 100644
--- a/lib/swig/preprocessing/sparse_longitudinal_features_product.i
+++ b/lib/swig/preprocessing/sparse_longitudinal_features_product.i
@@ -4,10 +4,15 @@
 #include "tick/preprocessing/sparse_longitudinal_features_product.h"
 %}
 
+%include serialization.i
+
 class SparseLongitudinalFeaturesProduct {
 
   public:
-    SparseLongitudinalFeaturesProduct(const SBaseArrayDouble2dPtrList1D &features);
+    // This exists soley for cereal/swig
+    SparseLongitudinalFeaturesProduct();
+
+    SparseLongitudinalFeaturesProduct(const ulong n_features);
 
     void sparse_features_product(ArrayULong &row,
                                  ArrayULong &col,
diff --git a/tick/preprocessing/base/longitudinal_preprocessor.py b/tick/preprocessing/base/longitudinal_preprocessor.py
index 2f3f39ee0..173b75f23 100644
--- a/tick/preprocessing/base/longitudinal_preprocessor.py
+++ b/tick/preprocessing/base/longitudinal_preprocessor.py
@@ -2,6 +2,7 @@
 
 from abc import ABC, abstractmethod
 from tick.base import Base
+from multiprocessing import cpu_count
 
 
 class LongitudinalPreprocessor(ABC, Base):
@@ -14,9 +15,14 @@ class LongitudinalPreprocessor(ABC, Base):
         set to the number of cores.
     """
 
-    def __init__(self, n_jobs=-1):
+    _attrinfos = {'n_jobs': {'writable': True}}
+
+    def __init__(self, n_jobs=1):
         Base.__init__(self)
-        self.n_jobs = n_jobs
+        if n_jobs == -1:
+            self.n_jobs = cpu_count()
+        else:
+            self.n_jobs = n_jobs
 
     @abstractmethod
     def fit(self, features, labels, censoring) -> None:
diff --git a/tick/preprocessing/longitudinal_features_lagger.py b/tick/preprocessing/longitudinal_features_lagger.py
index 5451b9073..52b5b76ed 100644
--- a/tick/preprocessing/longitudinal_features_lagger.py
+++ b/tick/preprocessing/longitudinal_features_lagger.py
@@ -3,10 +3,13 @@
 import numpy as np
 import scipy.sparse as sps
 from tick.preprocessing.base import LongitudinalPreprocessor
-from .build.preprocessing import LongitudinalFeaturesLagger\
+from tick.preprocessing.build.preprocessing import LongitudinalFeaturesLagger\
     as _LongitudinalFeaturesLagger
-from .utils import check_longitudinal_features_consistency,\
+from tick.preprocessing.utils import check_longitudinal_features_consistency,\
     check_censoring_consistency
+from multiprocessing.pool import Pool
+from copy import deepcopy
+from functools import partial, partialmethod
 
 
 class LongitudinalFeaturesLagger(LongitudinalPreprocessor):
@@ -75,9 +78,6 @@ class LongitudinalFeaturesLagger(LongitudinalPreprocessor):
         "_n_intervals": {
             "writable": False
         },
-        "_cpp_preprocessor": {
-            "writable": False
-        },
         "_fitted": {
             "writable": False
         }
@@ -92,7 +92,6 @@ def __init__(self, n_lags, n_jobs=-1):
         self._n_init_features = None
         self._n_output_features = None
         self._n_intervals = None
-        self._cpp_preprocessor = None
         self._fitted = False
 
     def _reset(self):
@@ -100,7 +99,6 @@ def _reset(self):
         self._set("_n_init_features", None)
         self._set("_n_output_features", None)
         self._set("_n_intervals", None)
-        self._set("_cpp_preprocessor", None)
         self._set("_fitted", False)
 
     def fit(self, features, labels=None, censoring=None):
@@ -137,10 +135,7 @@ def fit(self, features, labels=None, censoring=None):
         self._set("_n_init_features", n_init_features)
         self._set("_n_intervals", n_intervals)
         self._set("_n_output_features", int((self.n_lags + 1).sum()))
-        self._set("_cpp_preprocessor",
-                  _LongitudinalFeaturesLagger(features, self.n_lags))
         self._set("_fitted", True)
-
         return self
 
     def transform(self, features, labels=None, censoring=None):
@@ -166,7 +161,6 @@ def transform(self, features, labels=None, censoring=None):
         output : `[numpy.ndarrays]`  or `[csr_matrices]`, shape=(n_intervals, n_features)
             The list of features matrices with added lagged features.
         """
-
         n_samples = len(features)
         if censoring is None:
             censoring = np.full((n_samples,), self._n_intervals,
@@ -175,36 +169,57 @@ def transform(self, features, labels=None, censoring=None):
         base_shape = (self._n_intervals, self._n_init_features)
         features = check_longitudinal_features_consistency(
             features, base_shape, "float64")
-        if sps.issparse(features[0]):
-            X_with_lags = [
-                self._sparse_lagger(x, int(censoring[i]))
-                for i, x in enumerate(features)
-            ]
-            # TODO: Don't get why int() is required here as censoring_i is uint64
-        else:
-            X_with_lags = [
-                self._dense_lagger(x, int(censoring[i]))
-                for i, x in enumerate(features)
-            ]
+
+        initializer = partial(self._inject_cpp_object,
+                              n_intervals=self._n_intervals,
+                              n_lags=self.n_lags)
+        callback = self._sparse_lagger if sps.issparse(features[0]) \
+            else self._dense_lagger
+        callback = partial(callback, n_intervals=self._n_intervals,
+                           n_output_features=self._n_output_features,
+                           n_lags=self.n_lags)
+
+        with Pool(self.n_jobs, initializer=initializer) as pool:
+            X_with_lags = pool.starmap(callback, zip(features, censoring))
 
         return X_with_lags, labels, censoring
 
-    def _dense_lagger(self, feature_matrix, censoring_i):
-        output = np.zeros((self._n_intervals, self._n_output_features),
-                          dtype="float64")
-        self._cpp_preprocessor.dense_lag_preprocessor(feature_matrix, output,
-                                                      censoring_i)
+    @staticmethod
+    def _inject_cpp_object(n_intervals, n_lags):
+        """Creates a global instance of the CPP preprocessor object.
+
+        WARNING: to be used only as a multiprocessing.Pool initializer.
+        In multiprocessing context, each process has its own namespace, so using
+        global is not as bad as it seems. Still, it requires to proceed with
+        caution.
+        """
+        global _cpp_preprocessor
+        _cpp_preprocessor = _LongitudinalFeaturesLagger(n_intervals, n_lags)
+
+    @staticmethod
+    def _dense_lagger(feature_matrix, censoring_i, n_intervals,
+                      n_output_features, n_lags):
+        """Creates a lagged version of a dense matrixrepresenting longitudinal
+        features."""
+        global _cpp_preprocessor
+        output = np.zeros((n_intervals, n_output_features), dtype="float64")
+        _cpp_preprocessor.dense_lag_preprocessor(feature_matrix, output,
+                                                 int(censoring_i))
         return output
 
-    def _sparse_lagger(self, feature_matrix, censoring_i):
+    @staticmethod
+    def _sparse_lagger(feature_matrix, censoring_i, n_intervals,
+                       n_output_features, n_lags):
+        """Creates a lagged version of a sparse matrix representing longitudinal
+        features."""
+        global _cpp_preprocessor
         coo = feature_matrix.tocoo()
-        estimated_nnz = coo.nnz * int((self.n_lags + 1).sum())
+        estimated_nnz = coo.nnz * int((n_lags + 1).sum())
         out_row = np.zeros((estimated_nnz,), dtype="uint64")
         out_col = np.zeros((estimated_nnz,), dtype="uint64")
         out_data = np.zeros((estimated_nnz,), dtype="float64")
-        self._cpp_preprocessor.sparse_lag_preprocessor(
+        _cpp_preprocessor.sparse_lag_preprocessor(
             coo.row.astype("uint64"), coo.col.astype("uint64"), coo.data,
-            out_row, out_col, out_data, censoring_i)
+            out_row, out_col, out_data, int(censoring_i))
         return sps.csr_matrix((out_data, (out_row, out_col)),
-                              shape=(self._n_intervals,
-                                     self._n_output_features))
+                              shape=(n_intervals, n_output_features))
diff --git a/tick/preprocessing/longitudinal_features_product.py b/tick/preprocessing/longitudinal_features_product.py
index 5dcdbd175..1d46ed3b4 100644
--- a/tick/preprocessing/longitudinal_features_product.py
+++ b/tick/preprocessing/longitudinal_features_product.py
@@ -5,10 +5,12 @@
 from itertools import combinations
 from copy import deepcopy
 from scipy.misc import comb
-from sklearn.externals.joblib import Parallel, delayed
 from tick.preprocessing.base import LongitudinalPreprocessor
-from .build.preprocessing import SparseLongitudinalFeaturesProduct
-from .utils import check_longitudinal_features_consistency
+from tick.preprocessing.build.preprocessing \
+    import SparseLongitudinalFeaturesProduct
+from tick.preprocessing.utils import check_longitudinal_features_consistency
+from functools import partial
+from multiprocessing import Pool
 
 
 class LongitudinalFeaturesProduct(LongitudinalPreprocessor):
@@ -41,7 +43,7 @@ class LongitudinalFeaturesProduct(LongitudinalPreprocessor):
 
     Attributes
     ----------
-    mapper : `dict`
+    mapping : `dict`
         Map product features to column indexes of the resulting matrices.
 
     Examples
@@ -71,10 +73,10 @@ class LongitudinalFeaturesProduct(LongitudinalPreprocessor):
     """
 
     _attrinfos = {
-        "exposure_type": {
+        "_exposure_type": {
             "writable": False
         },
-        "_mapper": {
+        "_mapping": {
             "writable": False
         },
         "_n_init_features": {
@@ -86,9 +88,6 @@ class LongitudinalFeaturesProduct(LongitudinalPreprocessor):
         "_n_intervals": {
             "writable": False
         },
-        "_preprocessor": {
-            "writable": False
-        },
         "_fitted": {
             "writable": False
         }
@@ -99,31 +98,13 @@ def __init__(self, exposure_type="infinite", n_jobs=-1):
         if exposure_type not in ["infinite", "finite"]:
             raise ValueError("exposure_type should be either 'infinite' or\
              'finite', not %s" % exposure_type)
+        self._exposure_type = None
         self.exposure_type = exposure_type
-        self._reset()
-
-    def _reset(self):
-        """Resets the object its initial construction state."""
-        self._set("_n_init_features", None)
-        self._set("_n_output_features", None)
-        self._set("_n_intervals", None)
-        self._set("_mapper", {})
-        self._set("_preprocessor", None)
-        self._set("_fitted", False)
-
-    @property
-    def mapper(self):
-        """Get the mapping between the feature products and column indexes.
-
-        Returns
-        -------
-        output : `dict`
-            The column index - feature mapping.
-        """
-        if not self._fitted:
-            raise ValueError(
-                "cannot get mapper if object has not been fitted.")
-        return deepcopy(self._mapper)
+        self._mapping = None
+        self._n_init_features = None
+        self._n_output_features = None
+        self._n_intervals = None
+        self._fitted = False
 
     def fit(self, features, labels=None, censoring=None):
         """Fit the feature product using the features matrices list.
@@ -151,17 +132,11 @@ def fit(self, features, labels=None, censoring=None):
         self._set("_n_init_features", n_init_features)
         self._set("_n_intervals", n_intervals)
         comb_it = combinations(range(n_init_features), 2)
-        mapper = {i + n_init_features: c for i, c in enumerate(comb_it)}
-        self._set("_mapper", mapper)
+        mapping = {i + n_init_features: c for i, c in enumerate(comb_it)}
+        self._set("_mapping", mapping)
         self._set("_n_output_features",
                   int(n_init_features + comb(n_init_features, 2)))
-
-        if sps.issparse(features[0]) and self.exposure_type == "infinite":
-            self._set("_preprocessor",
-                      SparseLongitudinalFeaturesProduct(features))
-
         self._set("_fitted", True)
-
         return self
 
     def transform(self, features, labels=None, censoring=None):
@@ -182,76 +157,116 @@ def transform(self, features, labels=None, censoring=None):
             The list of features matrices with added product features.
             n_new_features = n_features + comb(n_features, 2)
         """
-
         base_shape = (self._n_intervals, self._n_init_features)
         features = check_longitudinal_features_consistency(
             features, base_shape, "float64")
-        if self.exposure_type == "finite":
-            X_with_products = self._finite_exposure_products(features)
-        elif self.exposure_type == "infinite":
-            X_with_products = self._infinite_exposure_products(features)
-        else:
-            raise ValueError("exposure_type should be either 'infinite' or\
-                         'finite', not %s" % self.exposure_type)
 
-        return X_with_products, labels, censoring
-
-    def _infinite_exposure_products(self, features):
-        """Add product features to features in the infinite exposure case."""
-        if sps.issparse(features[0]):
-            X_with_products = [
-                self._sparse_infinite_product(arr) for arr in features
-            ]
-            # TODO later: fix multiprocessing
-            # X_with_products = Parallel(n_jobs=self.n_jobs)(
-            #     delayed(self._sparse_infinite_product)(arr) for arr in features)
-            # Should be done in C++
+        is_sparse = sps.issparse(features[0])
+
+        callback = None
+        initializer = None
+
+        if is_sparse and self.exposure_type == 'infinite':
+            initializer = partial(self._inject_cpp_object,
+                                  n_features=self._n_init_features)
+        if is_sparse:
+            if self.exposure_type == 'infinite':
+                callback = partial(self._sparse_infinite_product,
+                                   n_intervals=self._n_intervals,
+                                   n_output_features=self._n_output_features)
+            else:
+                callback = partial(self._sparse_finite_product,
+                                   mapping=self._mapping)
         else:
-            raise ValueError("Infinite exposures should be stored in \
-                    sparse matrices as this hypothesis induces sparsity in the \
-                    feature matrix.")
-
-        return X_with_products
+            if self.exposure_type == 'infinite':
+                raise ValueError("Infinite exposures should be stored in \
+                                  sparse matrices as this hypothesis induces \
+                                  sparsity in the feature matrix.")
+            else:
+                callback = partial(self._dense_finite_product,
+                                   mapping=self._mapping)
 
-    def _finite_exposure_products(self, features):
-        """Add product features to features in the finite exposure case."""
-        if sps.issparse(features[0]):
-            X_with_products = Parallel(n_jobs=self.n_jobs)(
-                delayed(self._sparse_finite_product)(arr) for arr in features)
-        else:
-            X_with_products = Parallel(n_jobs=self.n_jobs)(
-                delayed(self._dense_finite_product)(arr) for arr in features)
+        with Pool(self.n_jobs, initializer=initializer) as pool:
+            X_with_products = pool.map(callback, features)
 
-        return X_with_products
+        return X_with_products, labels, censoring
 
-    def _dense_finite_product(self, feat_mat):
+    @staticmethod
+    def _dense_finite_product(feat_mat, mapping):
         """Performs feature product on a numpy.ndarray containing
         finite exposures."""
         feat = [feat_mat]
         feat.extend([(feat_mat[:, i] * feat_mat[:, j]).reshape((-1, 1))
-                     for i, j in self._mapper.values()])
+                     for i, j in mapping.values()])
         return np.hstack(feat)
 
-    def _sparse_finite_product(self, feat_mat):
+    @staticmethod
+    def _sparse_finite_product(feat_mat, mapping):
         """Performs feature product on a scipy.sparse.csr_matrix containing
         finite exposures."""
         feat = [feat_mat.tocsc()]
         feat.extend([(feat_mat[:, i].multiply(feat_mat[:, j]))
-                     for i, j in self.mapper.values()])
+                     for i, j in mapping.values()])
         return sps.hstack(feat).tocsr()
 
-    def _sparse_infinite_product(self, feat_mat):
+    @staticmethod
+    def _sparse_infinite_product(feat_mat, n_intervals, n_output_features):
         """Performs feature product on a scipy.sparse.csr_matrix containing
         infinite exposures."""
+        global _cpp_preprocessor
         coo = feat_mat.tocoo()
         nnz = coo.nnz
-        new_nnz = self._n_output_features * nnz
+        new_nnz = n_output_features * nnz
         new_row = np.zeros((new_nnz,), dtype="uint64")
         new_col = np.zeros((new_nnz,), dtype="uint64")
         new_data = np.zeros((new_nnz,), dtype="float64")
-        self._preprocessor.sparse_features_product(
+        _cpp_preprocessor.sparse_features_product(
             coo.row.astype("uint64"), coo.col.astype("uint64"), coo.data,
             new_row, new_col, new_data)
         return sps.csr_matrix((new_data, (new_row, new_col)),
-                              shape=(self._n_intervals,
-                                     self._n_output_features))
+                              shape=(n_intervals, n_output_features))
+
+    @staticmethod
+    def _inject_cpp_object(n_features):
+        """Creates a global instance of the CPP preprocessor object.
+
+        WARNING: to be used only as a multiprocessing.Pool initializer.
+        In multiprocessing context, each process has its own namespace, so using
+        global is not as bad as it seems. Still, it requires to proceed with
+        caution.
+        """
+        global _cpp_preprocessor
+        _cpp_preprocessor = SparseLongitudinalFeaturesProduct(n_features)
+
+    def _reset(self):
+        """Resets the object its initial construction state."""
+        self._set("_n_init_features", None)
+        self._set("_n_output_features", None)
+        self._set("_n_intervals", None)
+        self._set("_mapping", {})
+        self._set("_fitted", False)
+
+    @property
+    def mapping(self):
+        """Get the mapping between the feature products and column indexes.
+
+        Returns
+        -------
+        output : `dict`
+            The column index - feature mapping.
+        """
+        if not self._fitted:
+            raise ValueError(
+                "cannot get mapping if object has not been fitted.")
+        return deepcopy(self._mapping)
+
+    @property
+    def exposure_type(self):
+        return self._exposure_type
+
+    @exposure_type.setter
+    def exposure_type(self, value):
+        if value not in ['infinite', 'finite']:
+            raise ValueError("exposure_type should be either 'finite' or "
+                             "'infinite'")
+        self._set('_exposure_type', value)
diff --git a/tick/preprocessing/tests/longitudinal_features_lagger_test.py b/tick/preprocessing/tests/longitudinal_features_lagger_test.py
index 5aec583b7..215590dba 100644
--- a/tick/preprocessing/tests/longitudinal_features_lagger_test.py
+++ b/tick/preprocessing/tests/longitudinal_features_lagger_test.py
@@ -4,6 +4,9 @@
 from scipy.sparse import csr_matrix
 import unittest
 from tick.preprocessing import LongitudinalFeaturesLagger
+from tick.preprocessing.build.preprocessing import LongitudinalFeaturesLagger\
+    as _LongitudinalFeaturesLagger
+import pickle
 
 
 class Test(unittest.TestCase):
@@ -13,6 +16,7 @@ def setUp(self):
             np.array([[1, 1, 1], [0, 0, 1], [1, 1, 0]], dtype="float64")
         ]
         self.sparse_features = [csr_matrix(f) for f in self.features]
+        self.n_intervals, self.n_features = self.features[0].shape
 
         self.censoring = np.array([2, 3], dtype="uint64")
 
@@ -26,15 +30,45 @@ def setUp(self):
         self.n_lags = np.array([1, 2, 1], dtype="uint64")
 
     def test_dense_pre_convolution(self):
-        feat_prod, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags)\
+        lagged_feat, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags,
+                                                       n_jobs=1)\
             .fit_transform(self.features, censoring=self.censoring)
-        np.testing.assert_equal(feat_prod, self.expected_output)
+        np.testing.assert_equal(lagged_feat, self.expected_output)
 
     def test_sparse_pre_convolution(self):
-        feat_prod, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags)\
+        lagged_feat, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags,
+                                                       n_jobs=1)\
             .fit_transform(self.sparse_features, censoring=self.censoring)
-        feat_prod = [f.todense() for f in feat_prod]
-        np.testing.assert_equal(feat_prod, self.expected_output)
+        lagged_feat = [f.todense() for f in lagged_feat]
+        np.testing.assert_equal(lagged_feat, self.expected_output)
+
+    def test_parallelization_sparse(self):
+        lagged_feat, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags,
+                                                       n_jobs=1) \
+            .fit_transform(self.sparse_features, censoring=self.censoring)
+        p_lagged_feat, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags,
+                                                         n_jobs=-1)\
+            .fit_transform(self.sparse_features, censoring=self.censoring)
+        lagged_feat = [f.toarray() for f in lagged_feat]
+        p_lagged_feat = [f.toarray() for f in p_lagged_feat]
+        np.testing.assert_equal(lagged_feat, p_lagged_feat)
+
+    def test_parallelization_dense(self):
+        lagged_feat, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags,
+                                                       n_jobs=1) \
+            .fit_transform(self.features, censoring=self.censoring)
+        p_lagged_feat, _, _ = LongitudinalFeaturesLagger(n_lags=self.n_lags,
+                                                         n_jobs=-1)\
+            .fit_transform(self.features, censoring=self.censoring)
+        np.testing.assert_equal(lagged_feat, p_lagged_feat)
+
+    def test_serialization(self):
+        python = LongitudinalFeaturesLagger(n_lags=self.n_lags, n_jobs=1)
+        cpp = _LongitudinalFeaturesLagger(self.n_intervals, self.n_lags)
+        pickle.loads(pickle.dumps(python))
+        pickle.loads(pickle.dumps(cpp))
+        # Cannot check equality as CPP underlying objects will not be created in
+        # the same memory slot
 
 
 if __name__ == "__main__":
diff --git a/tick/preprocessing/tests/longitudinal_features_product_test.py b/tick/preprocessing/tests/longitudinal_features_product_test.py
index 9cde68d88..216462e17 100644
--- a/tick/preprocessing/tests/longitudinal_features_product_test.py
+++ b/tick/preprocessing/tests/longitudinal_features_product_test.py
@@ -4,6 +4,9 @@
 from scipy.sparse import csr_matrix
 import unittest
 from tick.preprocessing import LongitudinalFeaturesProduct
+from tick.preprocessing.build.preprocessing \
+    import SparseLongitudinalFeaturesProduct
+import pickle
 
 
 class Test(unittest.TestCase):
@@ -24,6 +27,8 @@ def setUp(self):
             csr_matrix(f) for f in self.infinite_exposures
         ]
 
+        self.n_intervals, self.n_features = self.finite_exposures[0].shape
+
     def test_finite_features_product(self):
         expected_output = \
             [np.array([[0, 1, 0, 0, 0, 0],
@@ -35,7 +40,7 @@ def test_finite_features_product(self):
                        [1, 1, 0, 1, 0, 0],
                        ], dtype="float64")
              ]
-        pp = LongitudinalFeaturesProduct("finite")
+        pp = LongitudinalFeaturesProduct("finite", n_jobs=1)
 
         feat_prod, _, _ = pp.fit_transform(self.finite_exposures)
         np.testing.assert_equal(feat_prod, expected_output)
@@ -55,12 +60,37 @@ def test_sparse_infinite_features_product(self):
                        [0, 0, 0, 0, 0, 0],
                        ], dtype="float64")
              ]
-        sparse_feat = [csr_matrix(f) for f in self.infinite_exposures]
-        feat_prod, _, _ = LongitudinalFeaturesProduct("infinite")\
-            .fit_transform(sparse_feat)
+        feat_prod, _, _ = LongitudinalFeaturesProduct("infinite", n_jobs=1)\
+            .fit_transform(self.sparse_infinite_exposures)
         feat_prod = [f.toarray() for f in feat_prod]
         np.testing.assert_equal(feat_prod, expected_output)
 
+    def test_parallelization(self):
+        for exp_type in ['finite', 'infinite']:
+            feat_prod, _, _ = LongitudinalFeaturesProduct(exp_type, n_jobs=1)\
+                .fit_transform(self.sparse_infinite_exposures)
+            p_feat_prod, _, _ = LongitudinalFeaturesProduct(exp_type,
+                                                            n_jobs=-1)\
+                .fit_transform(self.sparse_infinite_exposures)
+            feat_prod = [f.toarray() for f in feat_prod]
+            p_feat_prod = [f.toarray() for f in p_feat_prod]
+            np.testing.assert_equal(feat_prod, p_feat_prod)
+
+        exp_type = 'finite'
+        feat_prod, _, _ = LongitudinalFeaturesProduct(exp_type, n_jobs=1) \
+            .fit_transform(self.finite_exposures)
+        p_feat_prod, _, _ = LongitudinalFeaturesProduct(exp_type, n_jobs=-1) \
+            .fit_transform(self.finite_exposures)
+        np.testing.assert_equal(feat_prod, p_feat_prod)
+
+    def test_serialization(self):
+        python = LongitudinalFeaturesProduct()
+        cpp = SparseLongitudinalFeaturesProduct(self.n_features)
+        pickle.loads(pickle.dumps(python))
+        pickle.loads(pickle.dumps(cpp))
+        # Cannot check equality as CPP underlying objects will not be created in
+        # the same memory slot
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/tick/survival/convolutional_sccs.py b/tick/survival/convolutional_sccs.py
index cf223a9cf..f680b658c 100644
--- a/tick/survival/convolutional_sccs.py
+++ b/tick/survival/convolutional_sccs.py
@@ -355,7 +355,8 @@ def fit_kfold_cv(self, features, labels, censoring, C_tv_range: tuple = (),
             features, labels, censoring)
         # split the data with stratified KFold
         kf = StratifiedKFold(n_folds, shuffle, self.random_state)
-        labels_interval = np.nonzero(p_labels)[1]
+        # labels_interval = np.nonzero(p_labels)[1]
+        labels_interval = [np.nonzero(arr)[0][0] for arr in p_labels]
 
         # Training loop
         model_global_parameters = {