MCAR for decision tree

Signed-off-by: Adam Li <adam2392@gmail.com>

sklearn/tree/tests/test_tree.py

@@ -2602,6 +2602,35 @@ def test_missing_value_is_predictive():
     assert tree.score(X_test, y_test) >= 0.85
 
 
+def test_missing_value_is_not_predictive_with_mcar():
+    """Check the tree doesnt learns when the missing value is forced to be unpredictive."""
+    rng = np.random.RandomState(0)
+    n_samples = 1000
+
+    X = rng.standard_normal(size=(n_samples, 10))
+    y = rng.randint(0, high=2, size=n_samples)
+
+    # Create a predictive feature using `y` and with some noise
+    X_random_mask = rng.choice([False, True], size=n_samples, p=[0.9, 0.1])
+    y_mask = y.copy().astype(bool)
+    y_mask[X_random_mask] = ~y_mask[X_random_mask]
+
+    X_predictive = rng.standard_normal(size=n_samples)
+    X_predictive[y_mask] = np.nan
+
+    X[:, 5] = X_predictive
+
+    X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=rng)
+    tree = DecisionTreeClassifier(random_state=rng, missing_car=True).fit(
+        X_train, y_train
+    )
+    non_mcar_tree = DecisionTreeClassifier(random_state=rng, missing_car=False).fit(
+        X_train, y_train
+    )
+
+    non_mcar_tree.score(X_test, y_test) > tree.score(X_test, y_test) + 0.2
+
+
 @pytest.mark.parametrize(
     "make_data, Tree",
     [