Add implementation of is_outcome_ancestor

Author: vartikatewari

.idea/.gitignore

@@ -2,6 +2,7 @@
 
 """Predicates for good, bad, and neutral controls."""
 
+from .algorithm.conditional_independencies import are_d_separated
 from .dsl import Probability, Variable
 from .graph import NxMixedGraph
 
@@ -44,3 +45,27 @@ def is_bad_control(graph: NxMixedGraph, query: Probability, variable: Variable)
     """
     _control_precondition(graph, query, variable)
     raise NotImplementedError
+
+
+def is_outcome_ancestor(
+    graph: NxMixedGraph, cause: Variable, effect: Variable, variable: Variable
+) -> bool:
+    """Check if the variable is an outcome ancestor given a causal query and graph.
+
+    > In Model 8, Z is not a confounder nor does it block any back-door paths. Likewise,
+    controlling for Z does not open any back-door paths from X to Y . Thus, in terms of
+    asymptotic bias, Z is a “neutral control.” Analysis shows, however, that controlling for
+    Z reduces the variation of the outcome variable Y , and helps to improve the precision
+    of the ACE estimate in finite samples (Hahn, 2004; White and Lu, 2011; Henckel et al.,
+    2019; Rotnitzky and Smucler, 2019).
+
+    :param graph: An ADMG
+    :param cause: The intervention in the causal query
+    :param effect: The outcome of the causal query
+    :param variable: The variable to check
+    :return: If the variable is a bad control
+    """
+    if variable == cause:
+        return False
+    judgement = are_d_separated(graph, cause, variable)
+    return judgement.separated and variable in graph.ancestors_inclusive(effect)

.idea/inspectionProfiles/profiles_settings.xml

@@ -4,7 +4,7 @@
 
 import unittest
 
-from y0.controls import is_bad_control, is_good_control
+from y0.controls import is_bad_control, is_good_control, is_outcome_ancestor
 from y0.dsl import U1, U2, A, M, P, U, W, X, Y, Z
 from y0.graph import NxMixedGraph
 
@@ -95,3 +95,7 @@ def test_bad_controls(self):
         for model in bad_test_models:
             with self.subTest():
                 self.assertTrue(is_bad_control(model, P(Y @ X), Z))
+
+    def test_neutral_controls(self):
+        """Test neutral controls."""
+        self.assertTrue(is_outcome_ancestor(model_8, X, Y, Z))