Causal Identification from Counterfactual Data: Completeness and Bounding Results

摘要

Previous work establishing completeness results for *counterfactual identification* has been limited to the setting where the input data belongs to observational and interventional distributions (Layers 1 and 2 of Pearl's Causal Hierarchy), since it was generally presumed impossible to obtain data from counterfactual distributions, belonging to Layer 3. However, recent work (Raghavan & Bareinboim, 2025) has formally characterized a family of counterfactual distributions which can be directly estimated via experimental methods - a notion they call *counterfactual realizabilty*. This leaves open the question of what *additional* Layer 3 quantities now become identifiable, given this new access to (some) Layer 3 data. We develop the **ctfIDu+** algorithm for identifying a counterfactual query from an arbitrary set of Layer 3 data, and prove that it is complete for this task. Using this, we establish the theoretical limit of which counterfactuals can be identified from physically realizable data, thus implying the *fundamental limit to exact causal inference in the non-parametric setting*. Finally, we derive novel analytic bounds for important non-identifiable quantities given realizable counterfactual data, that are provably tighter than the previously established benchmark. We corroborate using simulations that even if a quantity is non-identifiable, counterfactual data can be used to further tighten bounds for its range.