Transportability

Transportability decides whether a causal effect learned in one or more source domains transfers to a target domain that differs in some mechanisms, and produces the formula to compute it. Domains are related by a selection diagram — a causal graph whose selection-marked variables have a mechanism that differs from the target.

causalrl implements this over the ID algorithm: the target effect is decomposed into c-factors and each is taken from whichever domain can supply it. With a single observational source this is the complete single-domain sID; surrogate experiments (mz) and multiple source domains (meta) extend it. See Guarantees And Scope for the precise contract.

Faithful to E. Bareinboim & J. Pearl, Transportability of Causal Effects: Completeness Results (AAAI 2012), A General Algorithm for Deciding Transportability of Experimental Results (Journal of Causal Inference 2013), and Meta-Transportability of Causal Effects (AISTATS 2013).

Covariate shift (single source)

The running example: a treatment X, an outcome Y, and a covariate Z whose distribution differs between source and target (Z → X, Z → Y, X → Y). The effect transports by re-weighting the source's invariant Y mechanism with the target's P*(Z):

from causalrl import CausalGraph, identify_transport

graph = CausalGraph(directed_edges=[("Z", "X"), ("Z", "Y"), ("X", "Y")])
estimand = identify_transport(graph, ["X"], ["Y"], selection=["Z"])
print(estimand.render())  # mixes P_target(Z) with the invariant P_source(...)

The shifted Z is taken from the target; the invariant Y mechanism from the source.

Surrogate experiments (mz)

When a c-factor is a hedge that no observational distribution identifies, an experiment in a source domain can supply it. For a bow arc (X ↔ Y, X → Y) the effect is not transportable from observation alone, but a source do(X) experiment identifies it:

from causalrl import CausalGraph, Domain, is_transportable_general

graph = CausalGraph(directed_edges=[("X", "Y")], bidirected_edges=[("X", "Y")])
assert not is_transportable_general(graph, ["X"], ["Y"], [Domain("source")])

source = Domain("source", experiments=frozenset({frozenset({"X"})}))
assert is_transportable_general(graph, ["X"], ["Y"], [source])

Multiple domains (meta)

With several source domains marked differently, each invariant c-factor is contributed by a domain where it is invariant. With Z1 shifted in domain a and Z2 shifted in domain b, the target effect is assembled from both:

from causalrl import CausalGraph, Domain, identify_transport_general

graph = CausalGraph(
    directed_edges=[("Z1", "X"), ("Z2", "X"), ("Z1", "Y"), ("Z2", "Y"), ("X", "Y")]
)
domains = [Domain("a", frozenset({"Z1"})), Domain("b", frozenset({"Z2"}))]
print(identify_transport_general(graph, ["X"], ["Y"], domains).render())  # references P_a and P_b

Evaluate any of these on data with estimate_transport_general — one observational dataset per domain name (including "target"), plus a randomized dataset per (domain, intervention) pair for experiments. When no domain can supply a needed c-factor the call raises NotIdentifiableError with the witnessing transport-hedge.