On the Granularity of Causal Effect Identifiability

2025-10-19

AI Summary

Conventional causal identification operates at the variable level, potentially overlooking estimable causal effects that exist only at a finer-grained, state-specific level—i.e., the effect of a particular value of a treatment variable on a specific value of an outcome variable. Method: We formalize “state-based causal effects” and analyze their identifiability under structural constraints, particularly context-specific independence (CSI) and conditional functional dependencies (CFD), while distinguishing these from mere domain restrictions on variable values. Contribution/Results: We show that state-level effects may remain identifiable even when variable-level effects are not—provided CSI or CFD assumptions are introduced. In contrast, domain constraints alone do not improve identifiability; however, when combined with CSI/CFD, they jointly enhance identifiability for both variable- and state-level effects. This work extends the identifiability boundary of standard causal graph models, uncovers latent estimable effects obscured by variable-level abstractions, and establishes a theoretical foundation for fine-grained causal inference.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The classical notion of causal effect identifiability is defined in terms of treatment and outcome variables. In this note, we consider the identifiability of state-based causal effects: how an intervention on a particular state of treatment variables affects a particular state of outcome variables. We demonstrate that state-based causal effects may be identifiable even when variable-based causal effects may not. Moreover, we show that this separation occurs only when additional knowledge -- such as context-specific independencies and conditional functional dependencies -- is available. We further examine knowledge that constrains the states of variables, and show that such knowledge does not improve identifiability on its own but can improve both variable-based and state-based identifiability when combined with other knowledge such as context-specific independencies. Our findings highlight situations where causal effects of interest may be estimable from observational data and this identifiability may be missed by existing variable-based frameworks.

Problem

• Identifies state-based causal effects beyond variable-level analysis
• Shows identifiability separation requires context-specific independence knowledge
• Demonstrates constraints improve identifiability when combined with other knowledge

Innovation

• Identifies state-based causal effects from interventions
• Uses context-specific independencies for identifiability
• Combines variable constraints with other causal knowledge