def testRemoveCommonCondRelVarOnlyFromRelVars(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
schema.addAttribute('A', 'X3')
model = Model(schema, ['[A].X1 -> [A].X2', '[A].X2 -> [A].X3'])
dsep = DSeparation(model)
self.assertTrue(
dsep.dSeparated(0, ['[A].X1', '[A].X2'], ['[A].X3'], ['[A].X2']))
self.assertTrue(
dsep.dSeparated(0, ['[A].X1', '[A].X2'], ['[A].X2', '[A].X3'],
['[A].X2']))
def testIntersectingInputRelVars(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
model = Model(schema, [])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X1'], []))
self.assertFalse(
dsep.dSeparated(0, ['[A].X2', '[A].X1'], ['[A].X1', '[A].X2'], []))
self.assertFalse(
dsep.dSeparated(0, ['[A].X2', '[A].X1'], ['[A].X1'], []))
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X')
schema.addEntity('B')
schema.addAttribute('B', 'Y')
schema.addRelationship('AB', ('A', Schema.MANY), ('B', Schema.MANY))
schema.addEntity('C')
schema.addAttribute('C', 'Z')
schema.addRelationship('BC', ('B', Schema.ONE), ('C', Schema.MANY))
model = Model(schema, [])
dsep = DSeparation(model)
self.assertFalse(
dsep.dSeparated(6, ['[A, AB, B, AB, A, AB, B].Y'],
['[A, AB, B, BC, C, BC, B].Y'], []))
def testBadRelVarInput(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
model = Model(schema, [])
dsep = DSeparation(model)
TestUtil.assertRaisesMessage(
self, Exception,
"relVars1 must be a non-empty sequence of parseable RelationalVariable strings",
dsep.dSeparated, 0, None, ['[A].X2'], [])
TestUtil.assertRaisesMessage(
self, Exception,
"relVars2 must be a non-empty sequence of parseable RelationalVariable strings",
dsep.dSeparated, 0, ['[A].X1'], None, [])
TestUtil.assertRaisesMessage(
self, Exception,
"condRelVars must be a sequence of parseable RelationalVariable strings",
dsep.dSeparated, 0, ['[A].X1'], ['[A].X2'], None)
TestUtil.assertRaisesMessage(
self, Exception,
"relVars1 must be a non-empty sequence of parseable RelationalVariable strings",
dsep.dSeparated, 0, [], ['[A].X2'], [])
TestUtil.assertRaisesMessage(
self, Exception,
"relVars2 must be a non-empty sequence of parseable RelationalVariable strings",
DSeparation.dSeparated, model, 0, ['[A].X1'], [], [])
class Oracle(CITest):
def __init__(self, model, hopThreshold=0):
self.model = model
self.hopThreshold = hopThreshold
self.dsep = DSeparation(model)
@functools.lru_cache(maxsize=10000)
def isConditionallyIndependent(self, relVar1Str, relVar2Str, condRelVarStrs):
return self.dsep.dSeparated(self.hopThreshold, [relVar1Str], [relVar2Str], condRelVarStrs)
def testTwoVariableModels(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
model = Model(schema, [])
dsep = DSeparation(model)
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
model = Model(schema, ['[A].X1 -> [A].X2'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
def testRelVarCheckerUsed(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X')
schema.addEntity('B')
schema.addAttribute('B', 'Y')
schema.addRelationship('AB', ('A', Schema.MANY), ('B', Schema.MANY))
schema.addEntity('C')
schema.addAttribute('C', 'Z')
schema.addRelationship('BC', ('B', Schema.ONE), ('C', Schema.MANY))
model = Model(schema,
['[B, AB, A].X -> [B].Y', '[C, BC, B].Y -> [C].Z'])
dsep = DSeparation(model)
mockRelVarSetChecker = MagicMock(
wraps=RelationalValidity.checkValidityOfRelationalVariableSet)
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'], [],
relationalVariableSetChecker=mockRelVarSetChecker)
self.assertEqual(1, mockRelVarSetChecker.call_count)
relVarsPassed = {
ParserUtil.parseRelVar('[A].X'),
ParserUtil.parseRelVar('[A, AB, B, BC, C].Z')
}
mockRelVarSetChecker.assert_called_with(model.schema, 8, relVarsPassed)
mockRelVarSetChecker = MagicMock(
wraps=RelationalValidity.checkValidityOfRelationalVariableSet)
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, BC, C, BC, B].Y'],
relationalVariableSetChecker=mockRelVarSetChecker)
self.assertEqual(1, mockRelVarSetChecker.call_count)
relVarsPassed = {
ParserUtil.parseRelVar('[A].X'),
ParserUtil.parseRelVar('[A, AB, B, BC, C].Z'),
ParserUtil.parseRelVar('[A, AB, B].Y'),
ParserUtil.parseRelVar('[A, AB, B, BC, C, BC, B].Y')
}
mockRelVarSetChecker.assert_called_with(model.schema, 8, relVarsPassed)
def __init__(self, model, hopThreshold=0):
self.model = model
self.hopThreshold = hopThreshold
self.dsep = DSeparation(model)
def testThreeEntityRDSJMLRExample(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X')
schema.addEntity('B')
schema.addAttribute('B', 'Y')
schema.addRelationship('AB', ('A', Schema.MANY), ('B', Schema.MANY))
schema.addEntity('C')
schema.addAttribute('C', 'Z')
schema.addRelationship('BC', ('B', Schema.ONE), ('C', Schema.MANY))
model = Model(schema,
['[B, AB, A].X -> [B].Y', '[C, BC, B].Y -> [C].Z'])
dsep = DSeparation(model)
self.assertFalse(
dsep.dSeparated(4, ['[A].X'], ['[A, AB, B, BC, C].Z'], []))
self.assertTrue(
dsep.dSeparated(4, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y']))
self.assertFalse(
dsep.dSeparated(6, ['[A].X'], ['[A, AB, B, BC, C].Z'], []))
self.assertFalse(
dsep.dSeparated(6, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y']))
self.assertTrue(
dsep.dSeparated(6, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, AB, A].X']))
self.assertTrue(
dsep.dSeparated(6, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, AB, A, AB, B].Y']))
self.assertTrue(
dsep.dSeparated(6, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, BC, C, BC, B].Y']))
self.assertFalse(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'], []))
self.assertFalse(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y']))
self.assertTrue(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, AB, A].X']))
self.assertFalse(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, AB, A, AB, B].Y']))
self.assertTrue(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'], [
'[A, AB, B].Y', '[A, AB, B, AB, A, AB, B].Y',
'[A, AB, B, BC, C, BC, B].Y'
]))
# forces intersection variables to be added to relVars2 in d-separation
self.assertFalse(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'],
['[A, AB, B].Y', '[A, AB, B, BC, C, BC, B].Y']))
self.assertFalse(
dsep.dSeparated(8, ['[A].X'], ['[A, AB, B, BC, C].Z'], [
'[A, AB, B].Y', '[A, AB, B, BC, C, BC, B].Y',
'[A, AB, B, BC, C, BC, B, AB, A].X'
]))
# forces intersection variables to be added to relVars1 in d-separation
self.assertFalse(
dsep.dSeparated(8, ['[A, AB, B, BC, C].Z'], ['[A].X'],
['[A, AB, B].Y', '[A, AB, B, BC, C, BC, B].Y']))
def testOneToManyRDS(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X')
schema.addEntity('B')
schema.addAttribute('B', 'Y')
schema.addRelationship('AB', ('A', Schema.MANY), ('B', Schema.ONE))
model = Model(schema, ['[B, AB, A].X -> [B].Y'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(4, ['[B].Y'], ['[B, AB, A].X'], []))
self.assertFalse(dsep.dSeparated(4, ['[B, AB, A].X'], ['[B].Y'], []))
self.assertFalse(dsep.dSeparated(2, ['[A, AB, B].Y'], ['[A].X'], []))
self.assertFalse(dsep.dSeparated(2, ['[A].X'], ['[A, AB, B].Y'], []))
self.assertFalse(dsep.dSeparated(3, ['[AB, B].Y'], ['[AB, A].X'], []))
self.assertFalse(dsep.dSeparated(3, ['[AB, A].X'], ['[AB, B].Y'], []))
self.assertFalse(
dsep.dSeparated(3, ['[AB, A].X'], ['[AB, A, AB, B].Y'], []))
schema.addAttribute('A', 'Z')
model = Model(schema,
['[B, AB, A].X -> [B].Y', '[A, AB, B].Y -> [A].Z'])
dsep = DSeparation(model)
self.assertFalse(
dsep.dSeparated(4, ['[B, AB, A].X'], ['[B, AB, A].Z'], []))
self.assertFalse(dsep.dSeparated(2, ['[A].Z'], ['[A].X'], []))
self.assertFalse(dsep.dSeparated(3, ['[AB, A].X'], ['[AB, A].Z'], []))
self.assertTrue(
dsep.dSeparated(2, ['[A].X'], ['[A].Z'], ['[A, AB, B].Y']))
self.assertFalse(
dsep.dSeparated(4, ['[B, AB, A].X'], ['[B, AB, A].Z'], ['[B].Y']))
self.assertFalse(
dsep.dSeparated(4, ['[B, AB, A].X'], ['[B, AB, A].Z'],
['[B, AB, A, AB, B].Y']))
self.assertTrue(
dsep.dSeparated(4, ['[B, AB, A].X'], ['[B, AB, A].Z'],
['[B].Y', '[B, AB, A, AB, B].Y']))
self.assertFalse(
dsep.dSeparated(3, ['[AB, A].X'], ['[AB, A].Z'], ['[AB, B].Y']))
self.assertFalse(
dsep.dSeparated(3, ['[AB, A].X'], ['[AB, A].Z'],
['[AB, A, AB, B].Y']))
# true with both, forces intersection between '[AB, B].Y', '[AB, A, AB, B].Y' to be included automatically
self.assertTrue(
dsep.dSeparated(3, ['[AB, A].X'], ['[AB, A].Z'],
['[AB, B].Y', '[AB, A, AB, B].Y']))
def testOneToOneRDS(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X')
schema.addEntity('B')
schema.addAttribute('B', 'Y')
schema.addRelationship('AB', ('A', Schema.ONE), ('B', Schema.ONE))
model = Model(schema, [])
dsep = DSeparation(model)
self.assertTrue(dsep.dSeparated(2, ['[A, AB, B].Y'], ['[A].X'], []))
self.assertTrue(dsep.dSeparated(2, ['[A].X'], ['[A, AB, B].Y'], []))
self.assertTrue(dsep.dSeparated(2, ['[B].Y'], ['[B, AB, A].X'], []))
self.assertTrue(dsep.dSeparated(2, ['[B, AB, A].X'], ['[B].Y'], []))
self.assertTrue(dsep.dSeparated(1, ['[AB, B].Y'], ['[AB, A].X'], []))
self.assertTrue(dsep.dSeparated(1, ['[AB, A].X'], ['[AB, B].Y'], []))
model = Model(schema, ['[B, AB, A].X -> [B].Y'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(2, ['[B].Y'], ['[B, AB, A].X'], []))
self.assertFalse(dsep.dSeparated(2, ['[B, AB, A].X'], ['[B].Y'], []))
self.assertFalse(dsep.dSeparated(2, ['[A, AB, B].Y'], ['[A].X'], []))
self.assertFalse(dsep.dSeparated(2, ['[A].X'], ['[A, AB, B].Y'], []))
self.assertFalse(dsep.dSeparated(1, ['[AB, B].Y'], ['[AB, A].X'], []))
self.assertFalse(dsep.dSeparated(1, ['[AB, A].X'], ['[AB, B].Y'], []))
schema.addAttribute('A', 'Z')
model = Model(schema,
['[B, AB, A].X -> [B].Y', '[A, AB, B].Y -> [A].Z'])
dsep = DSeparation(model)
self.assertFalse(
dsep.dSeparated(2, ['[B, AB, A].X'], ['[B, AB, A].Z'], []))
self.assertFalse(dsep.dSeparated(2, ['[A].Z'], ['[A].X'], []))
self.assertFalse(dsep.dSeparated(1, ['[AB, A].X'], ['[AB, A].Z'], []))
self.assertTrue(
dsep.dSeparated(2, ['[A].X'], ['[A].Z'], ['[A, AB, B].Y']))
self.assertTrue(
dsep.dSeparated(1, ['[AB, A].X'], ['[AB, A].Z'], ['[AB, B].Y']))
self.assertTrue(
dsep.dSeparated(2, ['[B, AB, A].X'], ['[B, AB, A].Z'], ['[B].Y']))
def testCondRelVarsSameAsOneRelVar(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
schema.addAttribute('A', 'X3')
model = Model(schema, ['[A].X1 -> [A].X2', '[A].X1 -> [A].X3'])
dsep = DSeparation(model)
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], ['[A].X2']))
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], ['[A].X1']))
self.assertTrue(
dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], ['[A].X1', '[A].X2']))
self.assertTrue(
dsep.dSeparated(0, ['[A].X1'], ['[A].X2', '[A].X3'],
['[A].X1', '[A].X2']))
self.assertTrue(
dsep.dSeparated(0, ['[A].X1'], ['[A].X2', '[A].X3'],
['[A].X2', '[A].X3']))
self.assertTrue(
dsep.dSeparated(0, ['[A].X2', '[A].X3'], ['[A].X1'],
['[A].X2', '[A].X3']))
# test for sequences of length > 1
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'A')
schema.addAttribute('A', 'B')
schema.addAttribute('A', 'C')
schema.addAttribute('A', 'D')
schema.addAttribute('A', 'E')
schema.addAttribute('A', 'F')
schema.addAttribute('A', 'G')
schema.addAttribute('A', 'H')
dependencies = [
'[A].A -> [A].B', '[A].A -> [A].C', '[A].B -> [A].D',
'[A].C -> [A].D', '[A].E -> [A].F', '[A].E -> [A].G',
'[A].F -> [A].H', '[A].G -> [A].H'
]
model = Model(schema, dependencies)
dsep = DSeparation(model)
self.assertTrue(
dsep.dSeparated(0, ['[A].A', '[A].E'], ['[A].D', '[A].H'],
['[A].B', '[A].C', '[A].E', '[A].H']))
self.assertFalse(
dsep.dSeparated(0, ['[A].A', '[A].E', '[A].F'],
['[A].D', '[A].H', '[A].G'],
['[A].B', '[A].C', '[A].E', '[A].H']))
def testThreeVariableModels(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
schema.addAttribute('A', 'X3')
model = Model(schema, [])
dsep = DSeparation(model)
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], ['[A].X3']))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], ['[A].X1']))
self.assertTrue(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], ['[A].X2']))
# one dependency model: only one in isomorphic class
model = Model(schema, ['[A].X2 -> [A].X3'])
dsep = DSeparation(model)
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], ['[A].X3']))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'],
['[A].X1']))
self.assertTrue(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], ['[A].X2']))
# two dependency models: four in isomorphic class
model = Model(schema, ['[A].X1 -> [A].X2', '[A].X1 -> [A].X3'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], ['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'],
['[A].X2']))
model = Model(schema, ['[A].X1 -> [A].X2', '[A].X3 -> [A].X1'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], ['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'],
['[A].X2']))
model = Model(schema, ['[A].X2 -> [A].X1', '[A].X1 -> [A].X3'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], ['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'],
['[A].X2']))
model = Model(schema, ['[A].X2 -> [A].X1', '[A].X3 -> [A].X1'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'],
['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'],
['[A].X2']))
# three dependency models: two in isomorphic class
model = Model(
schema,
['[A].X1 -> [A].X2', '[A].X1 -> [A].X3', '[A].X2 -> [A].X3'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'],
['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'],
['[A].X2']))
model = Model(
schema,
['[A].X1 -> [A].X2', '[A].X1 -> [A].X3', '[A].X3 -> [A].X2'])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'],
['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X3'], ['[A].X1'],
['[A].X2']))
def testEightVariableModel(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'A')
schema.addAttribute('A', 'B')
schema.addAttribute('A', 'C')
schema.addAttribute('A', 'D')
schema.addAttribute('A', 'E')
schema.addAttribute('A', 'F')
schema.addAttribute('A', 'G')
schema.addAttribute('A', 'H')
dependencies = [
'[A].A -> [A].C', '[A].A -> [A].D', '[A].B -> [A].D',
'[A].B -> [A].F', '[A].C -> [A].E', '[A].D -> [A].E',
'[A].E -> [A].G', '[A].E -> [A].H', '[A].F -> [A].H'
]
model = Model(schema, dependencies)
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].A'], ['[A].E'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].A'], ['[A].E'], ['[A].C']))
self.assertTrue(
dsep.dSeparated(0, ['[A].A'], ['[A].E'], ['[A].C', '[A].D']))
self.assertFalse(dsep.dSeparated(0, ['[A].B'], ['[A].E'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].B'], ['[A].E'], ['[A].D']))
self.assertTrue(
dsep.dSeparated(0, ['[A].B'], ['[A].E'], ['[A].C', '[A].D']))
self.assertFalse(
dsep.dSeparated(0, ['[A].B'], ['[A].E'],
['[A].C', '[A].D', '[A].H']))
# testing d-separation with sets of relVars
self.assertFalse(
dsep.dSeparated(0, ['[A].A', '[A].C'], {'[A].F', '[A].H'}, []))
self.assertFalse(
dsep.dSeparated(0, ('[A].A', '[A].C'), {'[A].F', '[A].H'},
['[A].E']))
self.assertTrue(
dsep.dSeparated(0, ('[A].A', '[A].C'), {'[A].F', '[A].H'},
{'[A].B', '[A].E'}))
def testFourVariableModels(self):
schema = Schema()
schema.addEntity('A')
schema.addAttribute('A', 'X1')
schema.addAttribute('A', 'X2')
schema.addAttribute('A', 'X3')
schema.addAttribute('A', 'X4')
model = Model(
schema,
['[A].X1 -> [A].X3', '[A].X2 -> [A].X3', '[A].X3 -> [A].X4'])
dsep = DSeparation(model)
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X2'],
['[A].X3']))
self.assertFalse(dsep.dSeparated(
0, ['[A].X1'], ['[A].X2'],
['[A].X4'])) # tests conditioning on descendant of a collider
self.assertFalse(
dsep.dSeparated(0, ['[A].X1'], ['[A].X2'], ['[A].X3', '[A].X4']))
# model has multiple paths
model = Model(schema, [
'[A].X1 -> [A].X3', '[A].X1 -> [A].X2', '[A].X2 -> [A].X4',
'[A].X4 -> [A].X3'
])
dsep = DSeparation(model)
self.assertFalse(dsep.dSeparated(0, ['[A].X1'], ['[A].X4'], []))
self.assertTrue(dsep.dSeparated(0, ['[A].X1'], ['[A].X4'], ['[A].X2']))
self.assertFalse(
dsep.dSeparated(0, ['[A].X1'], ['[A].X4'], ['[A].X2', '[A].X3']))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], []))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'],
['[A].X1']))
self.assertFalse(dsep.dSeparated(0, ['[A].X2'], ['[A].X3'],
['[A].X4']))
self.assertTrue(
dsep.dSeparated(0, ['[A].X2'], ['[A].X3'], ['[A].X1', '[A].X4']))