What is causal about causal models and representations? (2501.19335v2)

Abstract: Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which interventions in the model. For example, to interpret an action as an intervention on a treatment variable, the action will presumably have to a) change the distribution of treatment in a way that corresponds to the intervention, and b) not change other aspects, such as how the outcome depends on the treatment; while the marginal distributions of some variables may change as an effect. We introduce a formal framework to make such requirements for different interpretations of actions as interventions precise. We prove that the seemingly natural interpretation of actions as interventions is circular: Under this interpretation, every causal Bayesian network that correctly models the observational distribution is trivially also interventionally valid, and no action yields empirical data that could possibly falsify such a model. We prove an impossibility result: No interpretation exists that is non-circular and simultaneously satisfies a set of natural desiderata. Instead, we examine non-circular interpretations that may violate some desiderata and show how this may in turn enable the falsification of causal models. By rigorously examining how a causal Bayesian network could be a 'causal' model of the world instead of merely a mathematical object, our formal framework contributes to the conceptual foundations of causal representation learning, causal discovery, and causal abstraction, while also highlighting some limitations of existing approaches.

• The paper introduces a formal framework for redefining actions as interventions, aligning statistical models with observable outcomes.
• The paper critiques circular interpretations in causal modeling, showing that models fitting observational data often fail under interventional tests.
• The paper establishes an impossibility theorem that no non-circular interpretation can meet all desired causal criteria, paving the way for refined methodologies.

Analyzing Interpretations in Causal Models: A Systematic Framework

The paper "What is causal about causal models and representations?" critically explores the linkage between causal Bayesian networks (CBNs) and their real-world applications, focusing on how actions are interpreted as interventions within these models. This paper embarks on an ambitious attempt to clarify the often implicit connections and assumptions that underlie causal models and their applicability to real-world scenarios. The authors propose a rigorous mathematical framework addressing how actions can be interpreted non-circularly as interventions, providing an explicit foundation to the philosophy and practice of causal model interpretation.

Core Contributions and Findings

1. Framework for Action Interpretation: The authors introduce a formal framework articulating when and how actions in the world align with model interventions. They mandate that such a delineation is crucial for ensuring that CBNs are not only mathematically sound but also empirically valid representations. The work explores criteria like the correspondence of interventional predictions to observable outcomes and provides formal definitions that bridge theoretical predictions with practical implications.
2. Critique of Circularity: A critical contribution is the identification of circular reasoning often present in the interpretation of causal models. The paper highlights that under a seemingly natural interpretation of actions as interventions, every model that fits observational data also fits interventional data, rendering such models non-falsifiable. This presents a methodological dead-end where interventional predictions do not aid in the empirical falsification of a model.
3. Impossibility Theorem: The paper establishes a pivotal impossibility result: a non-circular interpretation that can simultaneously meet all desirable properties elucidated in the work (correct conditionals on intervened nodes, consistency, etc.) does not exist. This inherently questions the robustness of current practices and calls for reconsideration in causal analysis paradigms.
4. Alternative Interpretations: In considering foundational desiderata, the paper develops several non-circular interpretations where actions as interventions satisfy subsets of the desired properties, albeit not completely. These interpretations allow for potential falsifiability of CBNs, partially bridging the gap between theoretical models and empirical data.
5. Application to Causal Discovery and Representation Learning: The inquiry extends into implications for fields such as causal representation learning and causal discovery, underlining that identifiability of a model does not equate to its interventional validity. The authors suggest that assumptions about actions, rather than equivalence classes of transformations, could better determine causal validity within these approaches.

Theoretical and Practical Implications

The insights from this work offer significant ramifications both theoretically and practically:

• Rigorous Interpretations: The results urge the necessity for more rigorous interpretations in causal modeling. Instead of vague or universal assumptions about interventions, they propose precise mechanisms through which causal inferences can be made reliable and valid.
• Framework for Validation: By exploring and establishing robust criteria for the interconnection between interventions and actions, the paper contributes to a structured pathway for validating causal models in real-world applications, compelling a move away from traditional indirect methods.
• Guidance for Future Research: The exploration offers fertile ground for future research to develop models and interpretations that encapsulate both mathematical soundness and empirical relevance. It also suggests that further refinement and understanding of the complexity of actions could underpin future methodologies in causal inference.

Speculation on Future AI Developments

The investigation into interpretation and validity of causal models will likely influence future AI developments in areas requiring strong causal inference, especially in contexts demanding accountability and empirical substantiation, such as healthcare AI or autonomous systems. As AI systems become increasingly complex, a profound understanding of causal structures and their real-world applicability will be essential in ensuring that their predictions and actions are both reliable and justifiable.

In conclusion, this paper presents a solid theoretical scaffolding for the interpretation of actions as interventions in causal Bayesian networks, punctuated by the inability of current models to entirely escape circular justification without losing practical applicability. It challenges the causal inference community to reevaluate and refine how causal mechanisms are understood and interpreted, setting the stage for substantial theoretical and methodological advancements.