[MRG+1] BUG Avoid unexpected error in PCA when n_components='mle' (scikit-learn#9886)

* n_components mle

* update doc

* improve

* update what's new

* update what's new

Author: qinhanmin2014

doc/whats_new/v0.20.rst

@@ -107,6 +107,10 @@ Decomposition, manifold learning and clustering
 - Fixed a bug in :func:`datasets.fetch_kddcup99`, where data were not properly
   shuffled. :issue:`9731` by `Nicolas Goix`_.
 
+- Fixed a bug in :class:`decomposition.PCA` where users will get unexpected error
+  with large datasets when ``n_components='mle'`` on Python 3 versions.
+  :issue:`9886` by :user:`Hanmin Qin <qinhanmin2014>`.
+
 Metrics
 
 - Fixed a bug due to floating point error in :func:`metrics.roc_auc_score` with

sklearn/decomposition/pca.py

@@ -130,14 +130,18 @@ class PCA(_BasePCA):
 
             n_components == min(n_samples, n_features)
 
-        if n_components == 'mle' and svd_solver == 'full', Minka\'s MLE is used
-        to guess the dimension
-        if ``0 < n_components < 1`` and svd_solver == 'full', select the number
-        of components such that the amount of variance that needs to be
+        If ``n_components == 'mle'`` and ``svd_solver == 'full'``, Minka\'s
+        MLE is used to guess the dimension. Use of ``n_components == 'mle'``
+        will interpret ``svd_solver == 'auto'`` as ``svd_solver == 'full'``.
+
+        If ``0 < n_components < 1`` and ``svd_solver == 'full'``, select the
+        number of components such that the amount of variance that needs to be
         explained is greater than the percentage specified by n_components.
-        If svd_solver == 'arpack', the number of components must be strictly
-        less than the minimum of n_features and n_samples.
-        Hence, the None case results in:
+
+        If ``svd_solver == 'arpack'``, the number of components must be
+        strictly less than the minimum of n_features and n_samples.
+
+        Hence, the None case results in::
 
             n_components == min(n_samples, n_features) - 1
 
@@ -386,8 +390,8 @@ def _fit(self, X):
         # Handle svd_solver
         svd_solver = self.svd_solver
         if svd_solver == 'auto':
-            # Small problem, just call full PCA
-            if max(X.shape) <= 500:
+            # Small problem or n_components == 'mle', just call full PCA
+            if max(X.shape) <= 500 or n_components == 'mle':
                 svd_solver = 'full'
             elif n_components >= 1 and n_components < .8 * min(X.shape):
                 svd_solver = 'randomized'

sklearn/decomposition/tests/test_pca.py

@@ -7,6 +7,7 @@
 from sklearn.utils.testing import assert_true
 from sklearn.utils.testing import assert_equal
 from sklearn.utils.testing import assert_greater
+from sklearn.utils.testing import assert_raise_message
 from sklearn.utils.testing import assert_raises
 from sklearn.utils.testing import assert_raises_regex
 from sklearn.utils.testing import assert_no_warnings
@@ -453,6 +454,26 @@ def test_randomized_pca_inverse():
     assert_less(relative_max_delta, 1e-5)
 
 
+def test_n_components_mle():
+    # Ensure that n_components == 'mle' doesn't raise error for auto/full
+    # svd_solver and raises error for arpack/randomized svd_solver
+    rng = np.random.RandomState(0)
+    n_samples = 600
+    n_features = 10
+    X = rng.randn(n_samples, n_features)
+    n_components_dict = {}
+    for solver in solver_list:
+        pca = PCA(n_components='mle', svd_solver=solver)
+        if solver in ['auto', 'full']:
+            pca.fit(X)
+            n_components_dict[solver] = pca.n_components_
+        else:  # arpack/randomized solver
+            error_message = ("n_components='mle' cannot be a string with "
+                             "svd_solver='{}'".format(solver))
+            assert_raise_message(ValueError, error_message, pca.fit, X)
+    assert_equal(n_components_dict['auto'], n_components_dict['full'])
+
+
 def test_pca_dim():
     # Check automated dimensionality setting
     rng = np.random.RandomState(0)