def test_introduced_bias_reversed_sign(self) -> None:
cbn = CausalBayesianNetwork([("A", "D"), ("A", "Y")])
cbn.add_cpds(A=discrete_uniform([0, 1]), D=lambda a: 0, Y=lambda a: a)
assert introduced_total_effect(cbn, "A", "D", "Y") == pytest.approx(-1)
cbn.add_cpds(Y=lambda a: -a)
assert introduced_total_effect(
cbn, "A", "D", "Y", adapt_marginalized=True) == pytest.approx(-1)
def test_introduced_bias(imputed_cid_introduced_bias: CID) -> None:
assert introduced_total_effect(imputed_cid_introduced_bias, "A", "D",
"Y", 0, 1) == pytest.approx(-0.5)
imputed_cid_introduced_bias.impute_conditional_expectation_decision(
"D", "Y")
assert introduced_total_effect(imputed_cid_introduced_bias, "A", "D",
"Y", 0, 1) == pytest.approx(1 / 3)
def test_introduced_bias_reversed_sign(self) -> None:
cbn = CausalBayesianNetwork([("A", "D"), ("A", "Y")])
cbn.add_cpds(
UniformRandomCPD("A", [0, 1]),
FunctionCPD("D", lambda a: 0),
FunctionCPD("Y", lambda a: a),
)
assert introduced_total_effect(cbn, "A", "D", "Y") == pytest.approx(-1)
cbn.add_cpds(FunctionCPD("Y", lambda a: -a))
assert introduced_total_effect(
cbn, "A", "D", "Y", adapt_marginalized=True) == pytest.approx(-1)
def test_introduced_bias_y_nodep_x(
imputed_cid_introduced_bias: CID) -> None:
# Modified model where Y doesn't depend on X
cid = imputed_cid_introduced_bias
cid.add_cpds(FunctionCPD("Y", lambda x, z: z)) # type: ignore
cid.impute_conditional_expectation_decision("D", "Y")
assert introduced_total_effect(cid, "A", "D", "Y", 0,
1) == pytest.approx(1 / 3)
def test_introduced_bias_x_nodep_z(
imputed_cid_introduced_bias: CID) -> None:
# Modified model where X doesn't depend on Z
cid = imputed_cid_introduced_bias
cid.add_cpds(X=lambda a, z: a) # type: ignore
cid.impute_conditional_expectation_decision("D", "Y")
assert introduced_total_effect(cid, "A", "D", "Y", 0,
1) == pytest.approx(0)