maskani-moh
diff --git a/‎sklearn/linear_model/bayes.py
Lines changed: 8 additions & 2 deletions b/‎sklearn/linear_model/bayes.py
Lines changed: 8 additions & 2 deletions
diff --git a/‎sklearn/linear_model/tests/test_bayes.py
Lines changed: 35 additions & 0 deletions b/‎sklearn/linear_model/tests/test_bayes.py
Lines changed: 35 additions & 0 deletions
@@ -162,7 +162,10 @@ def fit(self, X, y):
         n_samples, n_features = X.shape
 
         # Initialization of the values of the parameters
-        alpha_ = 1. / np.var(y)
+        eps = np.finfo(np.float64).eps
+        # Add `eps` in the denominator to omit division by zero if `np.var(y)`
+        # is zero
+        alpha_ = 1. / (np.var(y) + eps)
         lambda_ = 1.
 
         verbose = self.verbose
@@ -445,7 +448,10 @@ def fit(self, X, y):
         verbose = self.verbose
 
         # Initialization of the values of the parameters
-        alpha_ = 1. / np.var(y)
+        eps = np.finfo(np.float64).eps
+        # Add `eps` in the denominator to omit division by zero if `np.var(y)`
+        # is zero
+        alpha_ = 1. / (np.var(y) + eps)
         lambda_ = np.ones(n_features)
 
         self.scores_ = list()
 
@@ -8,7 +8,9 @@
 from sklearn.utils.testing import assert_array_equal
 from sklearn.utils.testing import assert_array_almost_equal
 from sklearn.utils.testing import assert_almost_equal
+from sklearn.utils.testing import assert_array_less
 from sklearn.utils.testing import SkipTest
+from sklearn.utils import check_random_state
 from sklearn.linear_model.bayes import BayesianRidge, ARDRegression
 from sklearn.linear_model import Ridge
 from sklearn import datasets
@@ -60,6 +62,39 @@ def test_toy_bayesian_ridge_object():
     assert_array_almost_equal(clf.predict(test), [1, 3, 4], 2)
 
 
+def test_prediction_bayesian_ridge_ard_with_constant_input():
+    # Test BayesianRidge and ARDRegression predictions for edge case of
+    # constant target vectors
+    n_samples = 4
+    n_features = 5
+    random_state = check_random_state(42)
+    constant_value = random_state.rand()
+    X = random_state.random_sample((n_samples, n_features))
+    y = np.full(n_samples, constant_value)
+    expected = np.full(n_samples, constant_value)
+
+    for clf in [BayesianRidge(), ARDRegression()]:
+        y_pred = clf.fit(X, y).predict(X)
+        assert_array_almost_equal(y_pred, expected)
+
+
+def test_std_bayesian_ridge_ard_with_constant_input():
+    # Test BayesianRidge and ARDRegression standard dev. for edge case of
+    # constant target vector
+    # The standard dev. should be relatively small (< 0.01 is tested here)
+    n_samples = 4
+    n_features = 5
+    random_state = check_random_state(42)
+    constant_value = random_state.rand()
+    X = random_state.random_sample((n_samples, n_features))
+    y = np.full(n_samples, constant_value)
+    expected_upper_boundary = 0.01
+    for clf in [BayesianRidge(), ARDRegression()]:
+        _, y_std = clf.fit(X, y).predict(X, return_std=True)
+        assert_array_less(y_std, expected_upper_boundary)
+
+
 def test_toy_ard_object():
     # Test BayesianRegression ARD classifier
     X = np.array([[1], [2], [3]])