scikit-learn · glemaitre · Oct 14, 2021 · Mar 15, 2021 · Mar 15, 2021 · Sep 27, 2021
diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
@@ -45,6 +45,13 @@ Changelog
   `pos_label` to specify the positive class label.
   :pr:`21032` by :user:`Guillaume Lemaitre <glemaitre>`.
 
+:mod:`sklearn.cross_decomposition`
+..................................
+
+- |Enhancement| :func:`cross_decomposition._PLS.inverse_transform` now allows
+  reconstruction of a `X` target when a `Y` parameter is given. :pr:`19680` by
+  :user:`Robin Thibaut <robinthibaut>`.
+
 :mod:`sklearn.ensemble`
 ...........................
 

diff --git a/sklearn/cross_decomposition/_pls.py b/sklearn/cross_decomposition/_pls.py
@@ -398,7 +398,7 @@ def transform(self, X, Y=None, copy=True):
 
         return x_scores
 
-    def inverse_transform(self, X):
+    def inverse_transform(self, X, Y=None):
         """Transform data back to its original space.
 
         Parameters
@@ -407,10 +407,17 @@ def inverse_transform(self, X):
             New data, where `n_samples` is the number of samples
             and `n_components` is the number of pls components.
 
+        Y : array-like of shape (n_samples, n_components)
+            New target, where `n_samples` is the number of samples
+            and `n_components` is the number of pls components.
+
         Returns
         -------
-        self : ndarray of shape (n_samples, n_features)
-            Return the reconstructed array.
+        X_reconstructed : ndarray of shape (n_samples, n_features)
+            Return the reconstructed `X` data.
+
+        Y_reconstructed : ndarray of shape (n_samples, n_targets)
+            Return the reconstructed `X` target. Only returned when `Y` is given.
 
         Notes
         -----
@@ -420,10 +427,19 @@ def inverse_transform(self, X):
         X = check_array(X, dtype=FLOAT_DTYPES)
         # From pls space to original space
         X_reconstructed = np.matmul(X, self.x_loadings_.T)
-
         # Denormalize
         X_reconstructed *= self._x_std
         X_reconstructed += self._x_mean
+
+        if Y is not None:
+            Y = check_array(Y, dtype=FLOAT_DTYPES)
+            # From pls space to original space
+            Y_reconstructed = np.matmul(Y, self.y_loadings_.T)
+            # Denormalize
+            Y_reconstructed *= self._y_std
+            Y_reconstructed += self._y_mean
+            return X_reconstructed, Y_reconstructed
+
         return X_reconstructed
 
     def predict(self, X, copy=True):

diff --git a/sklearn/cross_decomposition/tests/test_pls.py b/sklearn/cross_decomposition/tests/test_pls.py
@@ -59,6 +59,8 @@ def test_pls_canonical_basics():
     # Check that inverse_transform works
     X_back = pls.inverse_transform(Xt)
     assert_array_almost_equal(X_back, X)
+    _, Y_back = pls.inverse_transform(Xt, Yt)
+    assert_array_almost_equal(Y_back, Y)
 
 
 def test_sanity_check_pls_regression():