Canonical Representations of Markovian Structural Causal Models: A Framework for Counterfactual Reasoning

TL;DR

This paper introduces canonical representations of structural causal models in the Markovian setting, enabling flexible counterfactual reasoning without additional estimation, and clarifies the role of counterfactuals in causality.

Contribution

It proposes a new framework for representing counterfactuals compatible with causal graphs, allowing flexible assumptions while preserving interventional constraints.

Findings

Enables choice of counterfactual assumptions via probability distributions.

Disentangles counterfactual assumptions from interventional knowledge.

Provides theoretical and numerical illustrations of the approach.

Abstract

Counterfactual reasoning aims at answering contrary-to-fact questions like ``Would have Alice recovered had she taken aspirin?'' and corresponds to the most fine-grained layer of causation. Critically, while many counterfactual statements cannot be falsified-even by randomized experiments-they underpin fundamental concepts like individual-wise fairness. Therefore, providing models to formalize and implement counterfactual beliefs remains a fundamental scientific problem. In the Markovian setting of Pearl's causal framework, we propose an alternative approach to structural causal models to represent counterfactuals compatible with a given causal graphical model. More precisely, we introduce counterfactual models, also called canonical representations of structural causal models. They enable analysts to choose a counterfactual assumption via random-process probability distributions with preassigned marginals and characterize the counterfactual equivalence class of structural causal models. Using these representations, we present a normalization procedure to disentangle the (arbitrary and unfalsifiable) counterfactual choice from the (typically testable) interventional constraints. In contrast to structural causal models, this allows to implement many counterfactual assumptions while preserving interventional knowledge, and does not require any estimation step at the individual-counterfactual layer: only to make a choice. Finally, we illustrate the specific role of counterfactuals in causality and the benefits of our approach on theoretical and numerical examples.