Causal Identification from Counterfactual Data: Completeness and Bounding Results

2026-02-26

AI Summary

This work investigates the identifiability of counterfactual quantities under a novel setting where physically realizable counterfactual data—corresponding to Layer 3 of Pearl’s causal hierarchy—are available. The study characterizes the theoretical limits and estimation bounds for non-identifiable counterfactuals and introduces the CTFIDU+ algorithm, which achieves complete identification of arbitrary Layer-3 counterfactual queries for the first time. It establishes a completeness theory for causal identification grounded in physically realizable counterfactual data, rigorously delineating the fundamental limits of exact causal inference in nonparametric settings. Furthermore, the paper derives analytical methods to effectively tighten the bounds of non-identifiable quantities using such data. Simulations demonstrate the efficacy of the proposed approach.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Previous work establishing completeness results for $\textit{counterfactual identification}$ 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 $\textit{counterfactual realizabilty}$. This leaves open the question of what $\textit{additional}$ 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 $\textit{fundamental limit to exact causal inference in the non-parametric setting}$. 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.

Problem

• counterfactual identification
• causal inference
• counterfactual realizability
• non-parametric identification
• causal hierarchy

Innovation

• counterfactual identification
• causal hierarchy
• counterfactual realizability
• CTFIDU+ algorithm
• non-parametric bounds