FIX bug where expected_mutual_information may miscalculate

doc/whats_new.rst

@@ -200,6 +200,9 @@ Bug fixes
       :class:`linear_model.SGDClassifier` and :class:`linear_model.SGDRegressor`
       (`#6764 <https://github.com/scikit-learn/scikit-learn/pull/6764>`_). By `Wenhua Yang`_.
 
+    - Fix bug where expected and adjusted mutual information were incorrect if
+      cluster contingency cells exceeded ``2**16``. By `Joel Nothman`_.
+
 
 API changes summary
 -------------------
@@ -4179,5 +4182,8 @@ David Huard, Dave Morrill, Ed Schofield, Travis Oliphant, Pearu Peterson.
 .. _Ori Ziv: https://github.com/zivori
 
 .. _Sears Merritt: https://github.com/merritts
+<<<<<<< HEAD
 
 .. _Wenhua Yang: https://github.com/geekoala
+=======
+>>>>>>> FIX bug where expected_mutual_information may miscalculate

sklearn/metrics/cluster/expected_mutual_info_fast.pyx

@@ -39,7 +39,7 @@ def expected_mutual_information(contingency, int n_samples):
     term1 = nijs / N
     # term2 is log((N*nij) / (a * b)) == log(N * nij) - log(a * b)
     # term2 uses the outer product
-    log_ab_outer = np.log(np.outer(a, b))
+    log_ab_outer = np.log(a)[:, np.newaxis] + np.log(b)
     # term2 uses N * nij
     log_Nnij = np.log(N * nijs)
     # term3 is large, and involved many factorials. Calculate these in log

sklearn/metrics/cluster/tests/test_supervised.py

@@ -158,6 +158,12 @@ def test_adjusted_mutual_info_score():
     assert_almost_equal(ami, 0.37, 2)
 
 
+def test_expected_mutual_info_overflow():
+    # Test for regression where contingency cell exceeds 2**16
+    # leading to overflow in np.outer, resulting in EMI > 1
+    assert expected_mutual_information(np.array([[70000]]), 70000) <= 1
+
+
 def test_entropy():
     ent = entropy([0, 0, 42.])
     assert_almost_equal(ent, 0.6365141, 5)