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This research establishes the theoretical completeness of identifying counterfactual queries using recently realizable Layer 3 data, defining fundamental limits for exact causal inference in non-parametric settings. By deriving analytic bounds for non-identifiable quantities, the CTFIDU+ algorithm demonstrates how accessible counterfactual distributions can tighten uncertainty estimates in practical applications. The work advances core machine learning theory by bridging the gap between observational data and physically realizable counterfactuals within Pearl's causal hierarchy.
Causal Identification from Counterfactual Data: Completeness and Bounding Results
arXiv:2602.23541v3 Announce Type: replace Abstract: Previous work establishing completeness results for counterfactual identification has been circumscribed to the setting where the input data belongs to observational or interventional distributions (Layers 1 and 2 of Pearl's Causal Hierarchy), since it was generally presumed impossible to obtain data from counterfactual distributions, which belong 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 realizability. This leaves open the question of what additional counterfactual quantities now become identifiable, given this new access to (some) Layer 3 data. To answer this question, we develop the CTFIDU+ algorithm for identifying counterfactual queries from an arbitrary set of Layer 3 distributions, and prove that it is complete for this task. Building on this, we establish the theoretical limit of which counterfactuals can be identified from physically realizable distributions, thus implying the fundamental limit to exact causal inference in the non-parametric setting. Finally, given the impossibility of identifying certain critical types of counterfactuals, we derive novel analytic bounds for such quantities using realizable counterfactual data, and corroborate using simulations that counterfactual data helps tighten the bounds for non-identifiable quantities in practice.
Abstract:Previous work establishing completeness results for counterfactual identification has been circumscribed to the setting where the input data belongs to observational or interventional distributions (Layers 1 and 2 of Pearl's Causal Hierarchy), since it was generally presumed impossible to obtain data from counterfactual distributions, which belong 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 realizability. This leaves open the question of what additional counterfactual quantities now become identifiable, given this new access to (some) Layer 3 data. To answer this question, we develop the CTFIDU+ algorithm for identifying counterfactual queries from an arbitrary set of Layer 3 distributions, and prove that it is complete for this task. Building on this, we establish the theoretical limit of which counterfactuals can be identified from physically realizable distributions, thus implying the fundamental limit to exact causal inference in the non-parametric setting. Finally, given the impossibility of identifying certain critical types of counterfactuals, we derive novel analytic bounds for such quantities using realizable counterfactual data, and corroborate using simulations that counterfactual data helps tighten the bounds for non-identifiable quantities in practice.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2602.23541 [cs.AI]
(or arXiv:2602.23541v3 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2602.23541 Focus to learn more arXiv-issued DOI via DataCite
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